SUMMARY: Cryo-electron microscopy (cryo-EM) visualization transforms high-resolution 3D density volumes into intuitive representations, playing a vital role in structural biology. However, the increasing scale of cryo-EM data poses challenges for interactive visualization, including storage, transmission, and exploration. To address this, we propose a hybrid quantized implicit neural representation (INR) method that compresses cryo-EM volumes while supporting efficient on-demand access. To evaluate its effectiveness, we benchmark our approach against traditional compression techniques and one classic INR compressor, assessing both compression efficiency and visual quality. Beyond standard metrics, we examine performance on key cryo-EM tasks, including overall structure identification, secondary structure recognition, and fine-chain inspection. Our results demonstrate that the quantized INR achieves superior storage efficiency and task-relevant fidelity, and we provide an interactive tool and guidelines to assist users in selecting optimal compression strategies. AVAILABILITY: To facilitate future research, we provide our quantized neural representation approach and interactive tool available at Zenodo (https://doi.org/10.5281/zenodo.19688284) and GitHub (https://github.com/ChiefMoo/Lossy-Cryo-EM-Compression).

Given a collection of points in $\mathbb {R}^{3}$R3, KD-Tree and R-Tree are well-known nearest neighbor search (NNS) algorithms that rely on spatial partitioning and indexing techniques. However, when the query point is far from the data points or the data points inherently represent a 2-manifold surface, their query performance may degrade. To address this, we propose a novel dynamic programming technique that precomputes a Directed Acyclic Graph (DAG) to encode the proximity structure between data points. More specifically, the DAG captures how the proximity structure evolves during the incremental construction of the Voronoi diagram of the data points. Experimental results demonstrate that our method achieves a speed increase of 1-10x. Furthermore, our algorithm demonstrates significant practical value in diverse applications. We validated its effectiveness through extensive testing in four key applications: Point-to-Mesh Distance Queries, Iterative Closest Point (ICP) Registration, Density Peak Clustering, and Point-to-Segments Distance Queries. A particularly notable feature of our approach is its unique ability to efficiently identify the nearest neighbor among the first $k$k points in the point cloud, a capability that enables substantial acceleration in low-dimensional applications like Density Peak Clustering. As a natural extension of our incremental construction process, our method can also be readily adapted for farthest-point sampling tasks. These experimental results across multiple domains underscore the broad applicability and practical importance of our approach.

Accurately estimating human internal states, such as personality traits or behavioral patterns, is critical for enhancing the effectiveness of human–robot interaction, particularly in multi-agent settings. These insights are key in applications ranging from social navigation to autism diagnosis. However, prior methods are limited by scalability and passive observation, making real-time estimation in complex, multi-human settings difficult. In this work, we propose a practical method for active human personality estimation in crowds, with a focus on applications related to Autism Spectrum Disorder (ASD). Our method combines a personality-conditioned behavior model, based on the Eysenck 3-Factor theory, with an active robot information-gathering policy that triggers human behaviors through a receding-horizon planner. The robot’s belief about human personality is then updated via Bayesian inference. We demonstrate the effectiveness of our approach through proof-of-concept studies in simulation, user studies with typical adults, and preliminary experiments involving participants with ASD. Our results show that our method can scale to tens of humans and reduce personality estimation error by 29.2% and uncertainty by 79.9% in simulation compared to the passive baseline. User studies with typical adults confirm the method’s ability to generalize across complex personality distributions. Additionally, we explore its application in autism-related scenarios, demonstrating that the method can identify the difference between neurotypical and autistic behavior. The results suggest that our framework could serve as a foundation for future ASD-specific applications.

The Medial Axis Transform (MAT) is a complete shape descriptor capable of reconstructing the geometry of the original domain. A high-quality MAT should not only facilitate high-fidelity reconstruction but also capture structural features—for instance, by aligning the MAT boundary with the locus of rolling ball centers within fillet regions. However, computing such an ideal MAT remains a significant challenge, particularly when the input is a discrete triangle mesh. In this paper, we follow the established technical pipeline of initializing the MAT via a 3D Voronoi diagram of surface samples and subsequently simplifying the Voronoi structure through a QEM-like scheme. Our key insight is to explicitly track the correspondence between MAT vertices and surface regions throughout the progressive simplification process, ensuring that the resulting MAT triangles accurately reflect the intrinsic symmetries between surface patches. We translate these geometric requirements into a suite of priority control strategies that govern the sequencing of edge collapses. Through extensive evaluation against state-of-the-art MAT algorithms, we validate the strong performance of our approach regarding runtime efficiency, structural alignment, boundary regularity, triangle quality, and robustness to noise. Our resulting MATs remain highly expressive for both articulated shapes and CAD models, even under extreme simplification—effectively capturing the global structure of complex geometries with only a few hundred vertices. Finally, we showcase the utility of our approach through two potential applications: capturing the locus of rolling ball centers within fillet regions, a structural capability not previously demonstrated in the existing literature, and surface extraction from unsigned distance fields, where the medial axis of the є -isosurface naturally yields a clean single-layer result. Source code is available at https://github.com/sssomeone/structural-mat.

k -nearest neighbor ( k -NN) search is a fundamental primitive in geometry processing and computer graphics. While spatial partitioning structures such as kd -trees are standard, they are often manifold-blind, failing to exploit the intrinsic low-dimensional structure of points sampled from 2-manifolds. Recent advances in dynamic programming-based nearest neighbor search (DP-NNS) leverage incrementally constructed Voronoi diagrams to accelerate queries, where each site p maintains a list of successors that progressively refine its Voronoi cell. However, DP-NNS is restricted to single nearest neighbor ( k = 1) searches, precluding their adoption in applications that require local neighborhood statistics. In this paper, we generalize the DP-NNS framework to support arbitrary k -NN queries for manifold-aligned data. Our approach is founded on the geometric observation that if p i is the nearest neighbor of a query q in P , then the second nearest neighbor of q must reside either within the prefix set P 1: i -1 = [ p 1 , ..., p i-1 } or within p i 's successor list. By recursively extending this principle, we introduce Manifold k -NN, a recursive algorithmic scheme that significantly outperforms conventional kd -trees for manifold-aligned data. Our method achieves a 1×-10× speedup in volume-to-surface query scenarios and inherently supports dynamic prefix queries—enabling k -NN searches within any subset P 1: m ( m ≤ n ) with zero overhead. Furthermore, we extend the framework to support point deletion via local Delaunay updates, providing a complete suite of dynamic operations for point set modification. Comprehensive experiments on diverse geometric datasets demonstrate the efficiency and broad applicability of our approach for modern graphics pipelines. Source code is available at https://github.com/sssomeone/manifold-knn.

Cages are fundamental structures in computer graphics, serving as versatile proxies for a wide range of applications. A high-quality cage must balance two competing objectives: minimizing the face count to ensure simplicity, and maximizing tightness to maintain high geometric fidelity to the input mesh. In this paper, we propose PR-Cage, a nested optimization framework for automated cage generation. For the outer control layer, we introduce a thickness parameter τ that defines a feasibility region; the evolving cage is guided by the τ -offset surface. We observe that an optimal balance between simplicity and tightness is achievable by progressively relaxing the parameter τ via a staircase schedule. For the inner iterations, we extend the traditional Quadric Error Metric (QEM) framework by incorporating rigorous linear inequality constraints to suppress triangle degeneration and prevent normal flips. Our algorithm relies exclusively on the atomic operations of edge collapses and edge flips, resulting in high computational efficiency and robustness. Comparative experiments on public datasets demonstrate that PR-Cage consistently outperforms existing methods, achieving extreme simplification while maintaining high adherence to the underlying geometry; see the teaser figure. Due to these favorable properties, we demonstrate the utility of our method in several downstream applications, such as contact simulation and deformation, where PR-Cage exhibits significant advantages in both quality and performance.

In this paper, we study an under-explored but important factor of diffusion generative models, i.e., the combinatorial complexity. Data samples are generally high-dimensional, and for various structured generation tasks, additional attributes are combined to associate with data samples. We show that the space spanned by the combination of dimensions and attributes can be insufficiently covered by existing training schemes of diffusion generative models, potentially limiting test time performance. We present a simple fix to this problem by constructing stochastic processes that fully exploit the combinatorial structures, hence the name ComboStoc. Using this simple strategy, we show that network training is significantly accelerated across diverse data modalities, including images and 3D structured shapes. Moreover, ComboStoc enables a new way of test time generation which uses asynchronous time steps for different dimensions and attributes, thus allowing for varying degrees of control over them. Our code is available at: https://github.com/Xrvitd/ComboStoc.

Recovering a continuous colormap from a single 2D scalar field visualization can be quite challenging, especially in the absence of a corresponding color legend. In this paper, we propose a novel colormap recovery approach that extracts the colormap from a color-encoded 2D scalar field visualization by simultaneously predicting the colormap and underlying data using a decoupling-and-reconstruction strategy. Our approach first separates the input visualization into colormap and data using a decoupling module, then reconstructs the visualization with a differentiable color-mapping module. To guide this process, we design a reconstruction loss between the input and reconstructed visualizations, which serves both as a constraint to ensure strong correlation between colormap and data during training, and as a self-supervised optimizer for fine-tuning the predicted colormap of unseen visualizations during inferencing. To ensure smoothness and correct color ordering in the extracted colormap, we introduce a compact colormap representation using cubic B-spline curves and an associated color order loss. We evaluate our method quantitatively and qualitatively on a synthetic dataset and a collection of real-world visualizations from the VIS30K dataset [9]. Additionally, we demonstrate its utility in two prototype applications-colormap adjustment and colormap transfer-and explore its generalization to visualizations with color legends and ones encoded using discrete color palettes.

In recent years, encoding explicit mesh surfaces into compact neural representations has emerged as a prominent research direction. Compression ratio and representation accuracy present a fundamental trade-off for evaluating such algorithms. Traditional approaches typically decompose the input mesh into two components: a simplified base mesh and a neural displacement field. However, this paradigm faces inherent limitations. First, employing triangles or quadrilaterals as geometric primitives necessitates the explicit storage of vertex connectivity, incurring substantial memory overhead. Second, existing approaches typically treat base mesh generation as a decoupled preprocessing step, failing to fully leverage automatic differentiation frameworks to optimize the distribution of the base mesh. To address these issues, we propose RTF2Mesh, a method that achieves compact representation using only unstructured point clouds with feature vectors and network parameters. At its core, our approach leverages a meshless vertex-normal representation derived from the Restricted Tangent Face (RTF). Furthermore, we employ the Kolmogorov-Arnold Network (KAN) to encode both the displacement information and the normals of the vertex-normal representation. The KAN is chosen for its superior parameter efficiency compared to traditional Multi-Layer Perceptrons (MLPs). These two improvements enable RTF2Mesh to achieve a more compact neural representation while eliminating the need for explicit storage of vertex connectivity. During decoding, surface normals are reconstructed from the input point cloud using the KAN's learned weights to generate a base surface. The KAN-based network then predicts the displacements of the subdivided base surface, producing a high-resolution triangle mesh. Compared to current state-of-the-art (SOTA) methods, RTF2Mesh achieves highly competitive performance at equivalent compression rates.

Extracting high-fidelity mesh surfaces from Signed Distance Fields (SDFs) has become a fundamental operation in geometry processing. Despite significant progress over the past decades, key challenges remain-namely, how to automatically capture the intricate geometric and topological structures encoded in the zero level set of SDFs. In this paper, we present a novel isosurface extraction algorithm that introduces two key innovations: 1) An incrementally constructed power diagram through the addition of sample points, which enables repeated updates to the extracted surface via its dual-regular Delaunay tetrahedralization; and 2) An adaptive point insertion strategy that identifies regions exhibiting the greatest discrepancy between the current mesh and the underlying continuous surface. As Fig. 1 shows, our framework progressively refines the extracted mesh with minimal computational cost until it sufficiently approximates the underlying surface. Experimental results demonstrate that our approach outperforms state-of-the-art methods, particularly for models with intricate geometric variations and complex topologies.

Offset surfaces, defined as the Minkowski sum of a base surface and a rolling ball, play a crucial role in geometry processing, with applications ranging from coverage motion planning to brush modeling. While considerable progress has been made in computing constant-radius offset surfaces, computing variable-radius offset surfaces remains a challenging problem. In this paper, we present OffsetCrust, a novel framework that efficiently addresses the variable-radius offsetting problem by computing a power diagram. Let ${\mathcal {R}}$R denote the radius function defined on the base surface $\mathcal {S}$S. The power diagram is constructed from contributing sites, consisting of carefully sampled base points on $\mathcal {S}$S and their corresponding off-surface points, displaced along ${\mathcal {R}}$R-dependent directions. In the constant-radius case only, these displacement directions align exactly with the surface normals of $\mathcal {S}$S. Moreover, our method mitigates the misalignment issues commonly seen in crust-based approaches through a lightweight fine-tuning procedure. We validate the accuracy and efficiency of OffsetCrust through extensive experiments, and demonstrate its practical utility in applications such as reconstructing original boundary surfaces from medial axis transform (MAT) representations.

The development of intelligent robots seeks to seamlessly integrate them into the human world, providing assistance and companionship in daily life and work, with the ultimate goal of achieving human-robot symbiosis. This requires robots with intelligent interaction abilities to work naturally and effectively with humans. However, current robotic simulators fail to support real human participation, limiting their ability to provide authentic interaction experiences and gather valuable human feedback essential for enhancing robotic capabilities. In this paper, we introduce SymBridge, the first human-in-the-loop cyber-physical interactive system designed to enable the safe and efficient development, evaluation, and optimization of human-robot interaction methods. Specifically, we employ augmented reality technology to enable real humans to interact with virtual robots in physical environments, creating an authentic interactive experience. Building on this, we propose a novel robotic interaction model that generates responsive, precise robot actions in real time through continuous human behavior observation. The model incorporates multi-resolution human motion features and environmental affordances, ensuring contextually adaptive robotic responses. Additionally, SymBridge enables continuous robot learning by collecting human feedback and dynamically adapting the robotic interaction model. By leveraging a designed system architecture and modules, SymBridge builds a bridge between humans and robots, as well as between cyber and physical spaces, providing a natural and realistic interaction experience while facilitating the continuous evolution of robotic intelligence. Extensive experiments, user studies, and robot testing demonstrate the system’s promising performance and highlight its potential to significantly advance research on human-robot symbiosis.

Abstract Point cloud denoising task aims to recover the clean point cloud from the scanned data coupled with different levels or patterns of noise. The recent state‐of‐the‐art methods often train deep neural networks to update the point locations towards the clean point cloud, and empirically repeat the denoising process several times in order to obtain the denoised results. It is not clear how to efficiently arrange the iterative denoising processes to deal with different levels or patterns of noise. In this paper, we propose an adaptive and iterative point cloud denoising method based on the score‐based diffusion model. For a given noisy point cloud, we first estimate the noise variation and determine an adaptive denoising schedule with appropriate step sizes, then invoke the trained network iteratively to update point clouds following the adaptive schedule. To facilitate this adaptive and iterative denoising process, we design the network architecture and a two‐stage sampling strategy for the network training to enable feature fusion and gradient fusion for iterative denoising. Compared to the state‐of‐the‐art point cloud denoising methods, our approach obtains clean and smooth denoised point clouds, while preserving the shape boundary and details better. Our results not only outperform the other methods both qualitatively and quantitatively, but also are preferable on the synthetic dataset with different patterns of noises, as well as the real‐scanned dataset.

Abstract Swept volume computation—the determination of regions occupied by moving objects—is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex interactions, or employ implicit representations that trade off geometric fidelity and face optimization difficulties. We propose a novel inversion of motion perspective: rather than tracking object motion, we fix the object and trace spatial points backward in time, reducing complex trajectories to efficiently linearizable point motions. Based on this, we introduce a multi‐field tetrahedral framework that maintains multiple distance fileds per element, preserving fine geometric details at trajectory intersections where single‐field methods fail. Our method robustly computes swept volumes for diverse motions, including translations and screw motions, and enables practical applications in path planning and collision detection.

Abstract Simultaneous four‐axis machining involves a cutter that moves in all degrees of freedom during carving. This strategy provides higher‐quality surface finishing compared to positional machining. However, it has not been well‐studied in research. In this study, we propose the first end‐to‐end computational framework to optimize the toolpath for fabricating complex models using simultaneous four‐axis subtractive manufacturing. In our technique, we first slice the input 3D model into uniformly distributed 2D layers. For each slicing layer, we perform an accessibility analysis for each intersected contour within this layer. Then, we proceed with over‐segmentation and a bottom‐up connecting process to generate a minimal number of fabricable segments. Finally, we propose post‐processing techniques to further optimize the tool directionand the transfer path between segments. Physical experiments of nine models demonstrate our significant improvements in both fabrication quality and efficiency, compared to the positional strategy and two simultaneous tool paths generated by industry‐standard CAM systems.

Revolved 3D objects are widely used in industrial, manufacturing, and artistic fields, with subtractive manufacturing being a common production method. A key preprocessing step is to maximize raw material utilization by generating as many rough-machined inputs as possible from a single stock piece, which poses a packing problem constrained by tool accessibility. The main challenge is integrating tool accessibility into packing. This paper introduces the carvable packing problem for revolved objects, a critical but under-researched area in subtractive manufacturing. We propose a new carvable coarsening hull and a packing strategy that uses beam search and a bottom-up placement method to position these hulls in the stock material. Our method was tested on diverse sets of revolved objects with different geometries, and physical tests were conducted on a 5-axis machining platform, proving its ability to enhance material use and manufacturability.

The rapid evolution of digital orthodontics has highlighted a critical need for automated treatment planning systems that balance computational efficiency with clinical reliability. However, existing methods still suffer from several limitations, including excessive clinician involvement (accounting for over 35% of treatment planning time), reliance on empirically defined key frames, and limited biomechanical plausibility, particularly in cases of severe dental crowding. This paper proposes a novel collision-free optimization framework to address these issues simultaneously. Our method defines a total movement energy function evaluated over each tooth’s pose at intermediate time frames. This energy is minimized iteratively using a steepest descent strategy. A rollback mechanism is employed: if inter-tooth penetration is detected during an update, the step size is halved repeatedly until collisions are eliminated. The framework allows flexible control over the number of intermediate frames to enforce a strict constraint on per-tooth displacement, limiting it to 0.2 mm translation or 2 ° rotation every 10 to 14 days. Clinical evaluations show that the proposed algorithm can generate desirable and clinically valid tooth movement plans, even in complex cases, while significantly reducing the need for manual intervention.

Performing semantic segmentation on point clouds is the primary method by which machines perceive 3D scenes in a fine-grained manner. Deep learning algorithms usually require many pointwise annotations obtained with specialized tools, which is a laborious and inefficient process. To this end, we develop two frameworks for training point cloud semantic segmentation networks, one that utilizes fewer projected image annotations and another that employs sparse scribble image annotations, making the process more flexible and user friendly. However, back-projecting 2D-pixel labels to 3D points during loss calculations always introduces errors. To increase the back-projection accuracy of our approach, we first identify and record potential pixel-point correspondence errors and then develop strategies for constructing an accurate back-projection mapping matrix. Specifically, we filter out occluded and noisy points to avoid incorrect label allocations and permit multiclass assignments to adjust the ambiguity of boundary points. By incorporating an accurate back-projection mechanism into the loss functions of the proposed training frameworks, our networks can perform well with only four projected image annotations or even sparse scribble image annotations for each scene. This results in state-of-the-art performance compared with that of other weakly supervised point cloud semantic segmentation approaches, and the outcomes are even comparable to those produced by fully supervised methods on the S3DIS and ScanNet-v2 datasets.

Quadrilateral mesh generation plays a crucial role in numerical simulations within Computer-Aided Design and Engineering (CAD/E). Producing high-quality quadrangulation typically requires satisfying four key criteria. First, the quadrilateral mesh should closely align with principal curvature directions. Second, singular points should be strategically placed and effectively minimized. Third, the mesh should accurately conform to sharp feature edges. Lastly, quadrangulation results should exhibit robustness against noise and minor geometric variations. Existing methods generally involve first computing a regular cross field to represent quad element orientations across the surface, followed by extracting a quadrilateral mesh aligned closely with this cross field. A primary challenge with this approach is balancing the smoothness of the cross field with its alignment to pre-computed principal curvature directions, which are sensitive to small surface perturbations and often ill-defined in spherical or planar regions. To tackle this challenge, we propose NeurCross , a novel framework that simultaneously optimizes a cross field and a neural signed distance function (SDF), whose zero-level set serves as a proxy of the input shape. Our joint optimization is guided by three factors: faithful approximation of the optimized SDF surface to the input surface, alignment between the cross field and the principal curvature field derived from the SDF surface, and smoothness of the cross field. Acting as an intermediary, the neural SDF contributes in two essential ways. First, it provides an alternative, optimizable base surface exhibiting more regular principal curvature directions for guiding the cross field. Second, we leverage the Hessian matrix of the neural SDF to implicitly enforce cross field alignment with principal curvature directions, thus eliminating the need for explicit curvature extraction. Extensive experiments demonstrate that NeurCross outperforms the state-of-the-art methods in terms of singular point placement, robustness against surface noise and surface undulations, and alignment with principal curvature directions and sharp feature curves.

Cross fields play a critical role in various geometry processing tasks, especially for quad mesh generation. Existing methods for cross field generation often struggle to balance computational efficiency with generation quality, using slow per-shape optimization. We introduce CrossGen , a novel framework that supports both feed-forward prediction and latent generative modeling of cross fields for quad meshing by unifying geometry and cross field representations within a joint latent space. Our method enables extremely fast computation of high-quality cross fields of general input shapes, typically within one second without per-shape optimization. Our method assumes a point-sampled surface, also called a point-cloud surface , as input, so we can accommodate various surface representations by a straightforward point sampling process. Using an auto-encoder network architecture, we encode input point-cloud surfaces into a sparse voxel grid with fine-grained latent spaces, which are decoded into both SDF-based surface geometry and cross fields (see the teaser figure). We also contribute a dataset of models with both high-quality signed distance fields (SDFs) representations and their corresponding cross fields, and use it to train our network. Once trained, the network is capable of computing a cross field of an input surface in a feed-forward manner, ensuring high geometric fidelity, noise resilience, and rapid inference. Furthermore, leveraging the same unified latent representation, we incorporate a diffusion model for computing cross fields of new shapes generated from partial input, such as sketches. To demonstrate its practical applications, we validate CrossGen on the quad mesh generation task for a large variety of surface shapes. Experimental results demonstrate that CrossGen generalizes well across diverse shapes and consistently yields high-fidelity cross fields, thus facilitating the generation of high-quality quad meshes.

Hand-drawn vector sketches often contain implied lines, imprecise intersections, and unintended gaps, making it challenging to identify closed regions for colorization. These challenges become more pronounced as the number of strokes increases. In this paper, we present KISSColor, a novel method for inferring users' intended closed regions. Specifically, we propose intuitive stroke stretching by extending open strokes along tangent isolines of winding-number fields, which provably form geometrically aligned closed regions. Extending all open strokes can lead to overly fragmented regions due to redundant intersections. While a Mixed Integer Programming (MIP) formulation helps reduce redundancy, it is computationally expensive. To improve efficiency, we introduce kinetic stroke stretching, which grows all strokes simultaneously and prioritizes early intersections using a kinetic data structure. This approach preserves stylistic ambiguity for lines requiring long extensions. Based on the growth results, redundant regions are suppressed to minimize fragmentation. We conduct extensive experiments demonstrating the effectiveness of KISSColor, which generates more intuitive partitions, especially for imprecise sketches (see teaser figure). Our code and data will be released upon publication.

Filleting is a fundamental operation in CAD systems, akin to a ball rolling between two adjacent surface patches, resulting in a seamless connection. The reverse process, which we refer to as DeFillet in this paper, is crucial for CAE analysis and secondary design phases. However, it presents significant challenges, particularly when the input data originates from surface reconstruction or discretization processes. Our DeFillet algorithm is inspired by the observation that the rolling-ball center defines an osculating sphere, while the Voronoi diagram of surface samples provides sufficiently many rolling-ball center candidates. By leveraging this insight, we compute a transformation between the Voronoi vertices and the surface samples, enabling the efficient identification of fillet regions. Subsequently, we formulate the reconstruction of sharp features as a quadratic optimization problem. Our method's effectiveness has been validated through extensive testing using self-constructed models and 100 filleted models selected from the Fusion 360 Gallery dataset. The code for this paper is publicly available at https://github.com/xiaowuga/DeFillet.

Neural implicit shape representation has drawn significant attention in recent years due to its smoothness, differentiability, and topological flexibility. However, directly modeling the shape of a neural implicit surface, especially as the zero-level set of a neural signed distance function (SDF), with sparse geometric control is still a challenging task. Sparse input shape control typically includes 3D curve networks or, more generally, 3D curve sketches, which are unstructured and cannot be connected to form a curve network, and therefore more difficult to deal with. While 3D curve networks or curve sketches provide intuitive shape control, their sparsity and varied topology pose challenges in generating high-quality surfaces to meet such curve constraints. In this paper, we propose NeuVAS, a variational approach to shape modeling using neural implicit surfaces constrained under sparse input shape control, including unstructured 3D curve sketches as well as connected 3D curve networks. Specifically, we introduce a smoothness term based on a functional of surface curvatures to minimize shape variation of the zero-level set surface of a neural SDF. We also develop a new technique to faithfully model G 0 sharp feature curves as specified in the input curve sketches. Comprehensive comparisons with the state-of-the-art methods demonstrate the significant advantages of our method.

Invisible orthodontics, commonly known as clear alignment treatment, offers a more comfortable and aesthetically pleasing alternative in orthodontic care, attracting considerable attention in the dental community in recent years. It replaces conventional metal braces with a series of removable, and transparent aligners. Each aligner is crafted to facilitate a gradual adjustment of the teeth, ensuring progressive stages of dental correction. This necessitates the design for teeth motion. Here we present an automatic method and a system for generating collision-free teeth motion planning while avoiding gaps between adjacent teeth, which is unacceptable in clinical practice. To tackle this task, we formulate it as a constrained optimization problem and utilize the interior point method for its solution. We also developed an interactive system that enables dentists to easily visualize and edit the paths. Our method significantly speeds up the clear aligner planning process, creating the desired motion paths for a full set of teeth in under five minutes-a task that typically requires several hours of manual work. Our experiments and user studies confirm the effectiveness of this method in planning teeth movement, showcasing its potential to streamline orthodontic procedures.

While tooth alignment is crucial for digital dentistry, especially in orthodontic treatment, existing computer-aided methods mainly focus on the 3D dental crown but overlook the entire teeth, which is essential for applications in orthodontics. Besides, clinical orthodontic rules are not fully considered in these methods, i.e., there should be no collisions and gaps between teeth, the upper jaw and lower jaw should have correct occlusion relationships, the teeth should comply with a reasonable dental arch curve, etc. To generate optimal tooth alignment results, we propose a rule-based optimization method for solving the tooth alignment problem that takes into consideration the clinical rules functionally and aesthetically. We optimize rule-driven objective functions by adjusting the 6-DoF transformations of each tooth. Besides, our optimization formulation supports customization for different clinical scenarios by specifying the various energy terms. Extensive experiments, ablation studies, and user studies have been conducted to validate the effectiveness of our method. Quantitative and qualitative comparisons demonstrate that our method generates better tooth alignments than previous methods.

Extraction of a high-fidelity 3D medial axis is a crucial operation in CAD. When dealing with a polygonal model as input, ensuring accuracy and tidiness becomes challenging due to discretization errors inherent in the mesh surface. Commonly, existing approaches yield medial-axis surfaces with various artifacts, including zigzag boundaries, bumpy surfaces, unwanted spikes, and non-smooth stitching curves. Considering that the surface of a CAD model can be easily decomposed into a collection of surface patches, its 3D medial axis can be extracted by computing the Voronoi diagram of these surface patches, where each surface patch serves as a generator. However, no solver currently exists for accurately computing such an extended Voronoi diagram. Under the assumption that each generator defines a linear distance field over a sufficiently small range, our approach operates by tetrahedralizing the region of interest and computing the medial axis within each tetrahedral element. Just as SurfaceVoronoi computes surface-based Voronoi diagrams by cutting a 3D prism with 3D planes (each plane encodes a linear field in a triangle), the key operation in this paper is to conduct the hyperplane cutting process in 4D, where each hyperplane encodes a linear field in a tetrahedron. In comparison with the state-of-the-art, our algorithm produces better outcomes. Furthermore, it can also be used to compute the offset surface.

Category-level pose estimation is crucial for estimating the pose and size of unseen objects. Previous methods, mainly trained and tested on data with the same distribution, are limited in their ability to generalize to unseen domain data. For instance, when applied to new scenes or categories, frequent data collection and network training can be cumbersome. To address this issue, we propose a domain generalization method in category-level pose estimation based on structural superpoints, which is trained solely on simulated data and can generalize to unseen domain distributions in real datasets. Specifically, by extracting superpoints for structural correspondence in a self-supervised manner, our method achieves cross-domain data and cross-instance shape generalization. Accordingly, we designed a network and loss function, CoupleLoss, for regressing pose and size. Furthermore, we validated the effectiveness of our method on the wild6D and real275 datasets, achieving state-of-the-art results.

the input target wire with consecutive line segments and circular segments to ensure the bending manufacturing constraints for each segment, then generate tuned wire through a bilevel optimization.This involves selecting the bending points at the upper level with a beam search strategy and determining the specifically tuned angles at the lower level.We perform a thorough physical evaluation using a DIY wire-bending machine.The results show the effectiveness of our proposed approach in realizing a wide range of intricate and complex wire sculptures.

Given the rapid advancements in geometric deep-learning techniques, there has been a dedicated effort to create mesh-based convolutional operators that act as a link between irregular mesh structures and widely adopted backbone networks . Despite the numerous advantages of Convolutional Neural Networks (CNNs) over Multi-Layer Perceptrons (MLPs), mesh-oriented CNNs often require intricate network architectures to tackle irregularities of a triangular mesh. These architectures not only demand that the mesh be manifold and watertight but also impose constraints on the abundance of training samples . In this paper, we note that for specific tasks such as mesh classification and semantic part segmentation, large-scale shape features play a pivotal role . This is in contrast to the realm of shape correspondence, where a comprehensive understanding of 3D shapes necessitates considering both local and global characteristics. Inspired by this key observation, we introduce a task-driven neural network architecture that seamlessly operates in an end-to-end fashion. Our method takes as input mesh vertices equipped with the heat kernel signature (HKS) and dihedral angles between adjacent faces . Notably, we replace the conventional convolutional module, commonly found in ResNet architectures, with MLPs and incorporate Layer Normalization (LN) to facilitate layer-wise normalization. Our approach, with a seemingly straightforward network architecture, demonstrates an accuracy advantage. It exhibits a marginal 0.1% improvement in the mesh classification task and a substantial 1.8% enhancement in the mesh part segmentation task compared to state-of-the-art methodologies. Moreover, as the number of training samples decreases to 1/50 or even 1/100, the accuracy advantage of our approach becomes more pronounced. In summary, our convolution-free network is tailored for specific tasks relying on large-scale shape features and excels in the situation with a limited number of training samples, setting itself apart from state-of-the-art methodologies.

The auxetic structure demonstrates an unconventional deployable mechanism, expanding in transverse directions while being stretched longitudinally (exhibiting a negative Poisson’s ratio). This characteristic offers advantages in diverse fields such as structural engineering, flexible electronics, and medicine. The rotating (semi-)rigid structure, as a typical auxetic structure, has been introduced into the field of computer-aided design because of its well-defined motion patterns. These structures find application as deployable structures in various endeavors aiming to approximate and rapidly fabricate doubly-curved surfaces, thereby mitigating the challenges associated with their production and transportation. Nevertheless, prior designs relying on basic geometric elements primarily concentrate on exploring the inherent nature of the structure and often lack aesthetic appeal. To address this limitation, we propose a novel design and generation method inspired by dihedral Escher tessellations. By introducing a new metric function, we achieve efficient evaluation of shape deployability as well as filtering of tessellations, followed by a two-step deformation and edge-deployability optimization process to ensure compliance with deployability constraints while preserving semantic meanings. Furthermore, we optimize the shape through physical simulation to guarantee deployability in actual manufacturing and control Poisson’s ratio to a certain extent. Our method yields structures that are both semantically meaningful and aesthetically pleasing, showcasing promising potential for auxetic applications.

A thin shell model refers to a surface or structure, where the object’s thickness is considered negligible. In the context of 3D printing, thin shell models are characterized by having lightweight, hollow structures, and reduced material usage. Their versatility and visual appeal make them popular in various fields, such as cloth simulation, character skinning, and for thin-walled structures like leaves, paper, or metal sheets. Nevertheless, optimization of thin shell models without external support remains a challenge due to their minimal interior operational space. For the same reasons, hollowing methods are also unsuitable for this task. In fact, thin shell modulation methods are required to preserve the visual appearance of a two-sided surface which further constrain the problem space. In this paper, we introduce a new visual disparity metric tailored for shell models, integrating local details and global shape attributes in terms of visual perception. Our method modulates thin shell models using global deformations and local thickening while accounting for visual saliency, stability, and structural integrity. Thereby, thin shell models such as bas-reliefs, hollow shapes, and cloth can be stabilized to stand in arbitrary orientations, making them ideal for 3D printing.

Deep learning-based solutions have achieved impressive performance in semantic segmentation but often require large amounts of training data with fine-grained annotations. To alleviate such requisition, a variety of weakly supervised annotation strategies have been proposed, among which scribble supervision is emerging as a popular one due to its user-friendly annotation way. However, the sparsity and diversity of scribble annotations make it nontrivial to train a network to produce deterministic and consistent predictions directly. To address these issues, in this paper we propose holistic solutions involving the design of network structure, loss and training procedure, named CC4S to improve Certainty and Consistency for Scribble-Supervised Semantic Segmentation. Specifically, to reduce uncertainty, CC4S embeds a random walk module into the network structure to make neural representations uniformly distributed within similar semantic regions, which works together with a soft entropy loss function to force the network to produce deterministic predictions. To encourage consistency, CC4S adopts self-supervision training and imposes the consistency loss on the eigenspace of the probability transition matrix in the random walk module (we named neural eigenspace). Such self-supervision inherits the category-level discriminability from the neural eigenspace and meanwhile helps the network focus on producing consistent predictions for the salient parts and neglect semantically heterogeneous backgrounds. Finally, to further improve the performance, CC4S uses the network predictions as pseudo-labels and retrains the network with an extra color constraint regularizer. From comprehensive experiments, CC4S achieves comparable performance to those from fully supervised methods and shows promising robustness under extreme supervision cases.

With the fast development of the 5G wireless communications, the Internet of Things (IoT) becomes a hot research topic. Unmanned aerial vehicles (UAVs), due to the high mobility and low labor cost, have a big potential to be applied in the future IoT communication networks, e.g., data collection in remote areas. In this paper, we take a UAV as a monitor and an IoT device as an agent, and study how to utilize UAVs to establish network coverage and enhance the overall performance. Given ground agents and aerial monitors, each agent needs to be supervised by one monitor that can at most take charge of certain amount, while such assignment should guarantee the required service quality. This is much different from the conventional assumption that each monitor owns exactly a fixed number of agents without considering sensing quality under limited transmit power. Suppose that a monitor supervises an agent with a cost as the negative value of transmission rate in Rician fading, we then maximize the sum of transmission induced by every monitor-agent connection constrained with workload capacity for each monitor. To achieve the above goals, we first present a fast algorithm to report the least-cost assignment plan. Then, we seek for the minimum number of monitors to maintain the required service quality. Last, we discuss the assignment problem in the scenario of dynamic agents and dynamic monitors. We also give a set of strategies on how to initialize assignment, optimize monitor locations and manage power consumption. Extensive experimental results on both simulated datasets and real-life traffic data demonstrate our effectiveness and high performance.

Despite recent advances in reconstructing an organic model with the neural signed distance function (SDF), the high-fidelity reconstruction of a CAD model directly from low-quality unoriented point clouds remains a significant challenge. In this paper, we address this challenge based on the prior observation that the surface of a CAD model is generally composed of piecewise surface patches, each approximately developable even around the feature line. Our approach, named NeurCADRecon , is self-supervised, and its loss includes a developability term to encourage the Gaussian curvature toward 0 while ensuring fidelity to the input points (see the teaser figure). Noticing that the Gaussian curvature is non-zero at tip points, we introduce a double-trough curve to tolerate the existence of these tip points. Furthermore, we develop a dynamic sampling strategy to deal with situations where the given points are incomplete or too sparse. Since our resulting neural SDFs can clearly manifest sharp feature points/lines, one can easily extract the feature-aligned triangle mesh from the SDF and then decompose it into smooth surface patches, greatly reducing the difficulty of recovering the parametric CAD design. A comprehensive comparison with existing state-of-the-art methods shows the significant advantage of our approach in reconstructing faithful CAD shapes.

Surface offsetting is a crucial operation in digital geometry processing and computer-aided design, where an offset is defined as an iso-value surface of the distance field. A challenge emerges as even smooth surfaces can exhibit sharp features in their offsets due to the non-differentiable characteristics of the underlying distance field. Prevailing approaches to the offsetting problem involve approximating the distance field and then extracting the iso-surface. However, even with dual contouring (DC), there is a risk of degrading sharp feature points/lines due to the inaccurate discretization of the distance field. This issue is exacerbated when the input is a piecewise-linear triangle mesh. This study is inspired by the observation that a triangle-based distance field, unlike the complex distance field rooted at the entire surface, remains smooth across the entire 3D space except at the triangle itself. With a polygonal surface comprising n triangles, the final distance field for accommodating the offset surface is determined by minimizing these n triangle-based distance fields. In implementation, our approach starts by tetrahedralizing the space around the offset surface, enabling a tetrahedron-wise linear approximation for each triangle-based distance field. The final offset surface within a tetrahedral range can be traced by slicing the tetrahedron with planes. As illustrated in the teaser figure, a key advantage of our algorithm is its ability to precisely preserve sharp features. Furthermore, this paper addresses the problem of simplifying the offset surface's complexity while preserving sharp features, formulating it as a maximal-clique problem.

In mesh simplification, common requirements like accuracy, triangle quality, and feature alignment are often considered as a trade-off. Existing algorithms concentrate on just one or a few specific aspects of these requirements. For example, the well-known Quadric Error Metrics (QEM) approach [Garland and Heckbert 1997] prioritizes accuracy and can preserve strong feature lines/points as well, but falls short in ensuring high triangle quality and may degrade weak features that are not as distinctive as strong ones. In this paper, we propose a smooth functional that simultaneously considers all of these requirements. The functional comprises a normal anisotropy term and a Centroidal Voronoi Tessellation (CVT) [Du et al. 1999] energy term, with the variables being a set of movable points lying on the surface. The former inherits the spirit of QEM but operates in a continuous setting, while the latter encourages even point distribution, allowing various surface metrics. We further introduce a decaying weight to automatically balance the two terms. We selected 100 CAD models from the ABC dataset [Koch et al. 2019], along with 21 organic models, to compare the existing mesh simplification algorithms with ours. Experimental results reveal an important observation: the introduction of a decaying weight effectively reduces the conflict between the two terms and enables the alignment of weak features. This distinctive feature sets our approach apart from most existing mesh simplification methods and demonstrates significant potential in shape understanding. Please refer to the teaser figure for illustration.

The latest advancements in Virtual Reality (VR) enable the creation of 3D models within a holographic immersive simulation environment. In this article, we create QuickCSGModeling , a user-friendly mid-air interactive modeling system. We first prepare a dataset consisting of diverse components and precompute the discrete signed distance function (SDF) for each component. During the modeling phase, users can freely design complicated shapes with a pair of VR controllers. Based on the discrete SDF representation, any CSG-like operation (union, intersection, and subtraction) can be performed voxel-wisely. Also, we maintain a single dynamic SDF for the whole scene, whose zero-level set surface exactly encodes the most recent constructed shape. Both SDF fusion and surface extraction are implemented via GPU for a smooth user experience. A total of 34 volunteers were asked to create their favorite models using QuickCSGModeling. With a simple training, most of them can create a fascinating shape or even a descriptive scene quickly. We also discuss how to extend our system to create articulated models with hinges, where an adaptive cube subdivision has to be enforced to improve the reconstruction accuracy around the hinge part, followed by a Dual Contouring-based surface extraction. 1

Geometric deep learning has sparked a rising interest in computer graphics to perform shape understanding tasks, such as shape classification and semantic segmentation. When the input is a polygonal surface, one has to suffer from the irregular mesh structure. Motivated by the geometric spectral theory, we introduce Laplacian2Mesh, a novel and flexible convolutional neural network (CNN) framework for coping with irregular triangle meshes (vertices may have any valence). By mapping the input mesh surface to the multi-dimensional Laplacian-Beltrami space, Laplacian2Mesh enables one to perform shape analysis tasks directly using the mature CNNs, without the need to deal with the irregular connectivity of the mesh structure. We further define a mesh pooling operation such that the receptive field of the network can be expanded while retaining the original vertex set as well as the connections between them. Besides, we introduce a channel-wise self-attention block to learn the individual importance of feature ingredients. Laplacian2Mesh not only decouples the geometry from the irregular connectivity of the mesh structure but also better captures the global features that are central to shape classification and segmentation. Extensive tests on various datasets demonstrate the effectiveness and efficiency of Laplacian2Mesh, particularly in terms of the capability of being vulnerable to noise to fulfill various learning tasks.

Surface reconstruction is a challenging task when input point clouds, especially real scans, are noisy and lack normals. Observing that the Multilayer Perceptron (MLP) and the implicit moving least-square function (IMLS) provide a dual representation of the underlying surface, we introduce Neural-IMLS, a novel approach that directly learns a noise-resistant signed distance function (SDF) from unoriented raw point clouds in a self-supervised manner. In particular, IMLS regularizes MLP by providing estimated SDFs near the surface and helps enhance its ability to represent geometric details and sharp features, while MLP regularizes IMLS by providing estimated normals. We prove that at convergence, our neural network produces a faithful SDF whose zero-level set approximates the underlying surface due to the mutual learning mechanism between the MLP and the IMLS. Extensive experiments on various benchmarks, including synthetic and real scans, show that Neural-IMLS can reconstruct faithful shapes even with noise and missing parts. The source code can be found at https://github.com/bearprin/Neural-IMLS.

The Signed Distance Function (SDF), as an implicit surface representation, provides a crucial method for reconstructing a watertight surface from unorganized point clouds. The SDF has a fundamental relationship with the principles of surface vector calculus. Given a smooth surface, there exists a thin-shell space in which the SDF is differentiable everywhere such that the gradient of the SDF is an eigenvector of its Hessian matrix, with a corresponding eigenvalue of zero. In this paper, we introduce a method to directly learn the SDF from point clouds in the absence of normals. Our motivation is grounded in a fundamental observation: aligning the gradient and the Hessian of the SDF provides a more efficient mechanism to govern gradient directions. This, in turn, ensures that gradient changes more accurately reflect the true underlying variations in shape. Extensive experimental results demonstrate its ability to accurately recover the underlying shape while effectively suppressing the presence of ghost geometry.

Shape manipulation is a central research topic in computer graphics. Topology editing, such as breaking apart connections, joining disconnected ends, and filling/opening a topological hole, is generally more challenging than geometry editing. In this paper, we observe that the saddle points of the signed distance function (SDF) provide useful hints for altering surface topology deliberately. Based on this key observation, we parameterize the SDF into a cubic trivariate tensor-product B-spline function F whose saddle points {si} can be quickly exhausted based on a subdivision-based root-finding technique coupled with Newton’s method. Users can select one of the candidate points, say si, to edit the topology in real time. In implementation, we add a compactly supported B-spline function rooted at si, which we call a deformer in this paper, to F, with its local coordinate system aligning with the three eigenvectors of the Hessian. Combined with ray marching technique, our interactive system operates at 30 FPS. Additionally, our system empowers users to create desired bulges or concavities on the surface. An extensive user study indicates that our system is user-friendly and intuitive to operate. We demonstrate the effectiveness and usefulness of our system in a range of applications, including fixing surface reconstruction errors, artistic work design, 3D medical imaging and simulation, and antiquity restoration. Please refer to the attached video for a demonstration.

Voronoi diagrams on triangulated surfaces based on the geodesic metric play a key role in many applications of computer graphics. Previous methods of constructing such Voronoi diagrams generally depended on having an exact geodesic metric. However, exact geodesic computation is time-consuming and has high memory usage, limiting wider application of geodesic Voronoi diagrams (GVDs). In order to overcome this issue, instead of using exact methods, we reformulate a graph method based on Steiner point insertion, as an effective way to obtain geodesic distances. Further, since a bisector comprises hyperbolic and line segments, we utilize Apollonius diagrams to encode complicated structures, enabling Voronoi diagrams to encode a medial-axis surface for a dense set of boundary samples. Based on these strategies, we present an approximation algorithm for efficient Voronoi diagram construction on triangulated surfaces. We also suggest a measure for evaluating similarity of our results to the exact GVD. Although our GVD results are constructed using approximate geodesic distances, we can get GVD results similar to exact results by inserting Steiner points on triangle edges. Experimental results on many 3D models indicate the improved speed and memory requirements compared to previous leading methods.

Professional dance is characterized by high impulsiveness, elegance, and aesthetic beauty. In order to reach the desired professionalism, it requires years of long and exhausting practice, good physical condition, musicality, but also, a good understanding of choreography. Capturing dance motions and transferring them to digital avatars is commonly used in the film and entertainment industries. However, so far, access to high-quality dance data is very limited, mainly due to the many practical difficulties in capturing the movements of dancers, making it prohibitive for large-scale data acquisition. In this paper, we present a model that enhances the professionalism of amateur dance movements, allowing movement quality to be improved in both spatial and temporal domains. Our model consists of a dance-to-music alignment stage responsible for learning the optimal temporal alignment path between dance and music, and a dance-enhancement stage that injects features of professionalism in both spatial and temporal domains. To learn a homogeneous distribution and credible mapping between the heterogeneous professional and amateur datasets, we generate amateur data from professional dances taken from the AIST++ dataset. We demonstrate the effectiveness of our method by comparing it with two baseline motion transfer methods via thorough qualitative visual controls, quantitative metrics, and a perceptual study. We also provide temporal and spatial module analysis to examine the mechanisms and necessity of key components of our framework.

Guided upsampling is an effective approach for accelerating high-resolution image processing. In this paper, we propose a simple yet effective guided upsampling method. Each pixel in the high-resolution image is represented as a linear interpolation of two low-resolution pixels, whose indices and weights are optimized to minimize the upsampling error. The downsampling can be jointly optimized in order to prevent missing small isolated regions. Our method can be derived from the color line model and local color transformations. Compared to previous methods, our method can better preserve detail effects while suppressing artifacts such as bleeding and blurring. It is efficient, easy to implement, and free of sensitive parameters. We evaluate the proposed method with a wide range of image operators, and show its advantages through quantitative and qualitative analysis. We demonstrate the advantages of our method for both interactive image editing and real-time high-resolution video processing. In particular, for interactive editing, the joint optimization can be precomputed, thus allowing for instant feedback without hardware acceleration.

Neural implicit representation is a promising approach for reconstructing surfaces from point clouds. Existing methods combine various regularization terms, such as the Eikonal and Laplacian energy terms, to enforce the learned neural function to possess the properties of a Signed Distance Function (SDF). However, inferring the actual topology and geometry of the underlying surface from poor-quality unoriented point clouds remains challenging. In accordance with Differential Geometry, the Hessian of the SDF is singular for points within the differential thin-shell space surrounding the surface. Our approach enforces the Hessian of the neural implicit function to have a zero determinant for points near the surface. This technique aligns the gradients for a near-surface point and its on-surface projection point, producing a rough but faithful shape within just a few iterations. By annealing the weight of the singular-Hessian term, our approach ultimately produces a high-fidelity reconstruction result. Extensive experimental results demonstrate that our approach effectively suppresses ghost geometry and recovers details from unoriented point clouds with better expressiveness than existing fitting-based methods.

Estimating normals with globally consistent orientations for a raw point cloud has many downstream geometry processing applications. Despite tremendous efforts in the past decades, it remains challenging to deal with an unoriented point cloud with various imperfections, particularly in the presence of data sparsity coupled with nearby gaps or thin-walled structures. In this paper, we propose a smooth objective function to characterize the requirements of an acceptable winding-number field, which allows one to find the globally consistent normal orientations starting from a set of completely random normals. By taking the vertices of the Voronoi diagram of the point cloud as examination points, we consider the following three requirements: (1) the winding number is either 0 or 1, (2) the occurrences of 1 and the occurrences of 0 are balanced around the point cloud, and (3) the normals align with the outside Voronoi poles as much as possible. Extensive experimental results show that our method outperforms the existing approaches, especially in handling sparse and noisy point clouds, as well as shapes with complex geometry/topology.

Most of the existing point-to-mesh distance query solvers, such as Proximity Query Package (PQP), Embree and Fast Closest Point Query (FCPW), are based on bounding volume hierarchy (BVH). The hierarchical organizational structure enables one to eliminate the vast majority of triangles that do not help find the closest point. In this paper, we develop a totally different algorithmic paradigm, named P2M , to speed up point-to-mesh distance queries. Our original intention is to precompute a KD tree (KDT) of mesh vertices to approximately encode the geometry of a mesh surface containing vertices, edges and faces. However, it is very likely that the closest primitive to the query point is an edge e (resp., a face f ), but the KDT reports a mesh vertex υ instead. We call υ an interceptor of e (resp., f ). The main contribution of this paper is to invent a simple yet effective interception inspection rule and an efficient flooding interception inspection algorithm for quickly finding out all the interception pairs. Once the KDT and the interception table are precomputed, the query stage proceeds by first searching the KDT and then looking up the interception table to retrieve the closest geometric primitive. Statistics show that our query algorithm runs many times faster than the state-of-the-art solvers.

Caustics are interesting patterns caused by the light being focused when reflecting off glossy materials. Rendering them in computer graphics is still challenging: they correspond to high luminous intensity focused over a small area. Finding the paths that contribute to this small area is difficult, and even more difficult when using camera-based path tracing instead of bidirectional approaches. Recent improvements in path guiding are still unable to compute efficiently the light paths that contribute to a caustic. In this paper, we present a novel path guiding approach to enable reliable rendering of caustics. Our approach relies on computing representative specular paths, then extending them using a chain of spherical Gaussians. We use these extended paths to estimate the incident radiance distribution and guide path tracing. We combine this approach with several practical strategies, such as spatial reusing and parallax-aware representation for arbitrarily curved reflectors. Our path-guided algorithm using extended specular paths outperforms current state-of-the-art methods and handles multiple bounces of light and a variety of scenes.

Abstract Wang tiles, also known as Wang dominoes, are a jigsaw puzzle system with matching edges. Due to their compactness and expressiveness in representing variations, they have become a popular tool in the procedural synthesis of textures, height fields, 3D printing and representing other large and non‐repetitive data. Multi‐scale tiles created from low‐level tiles allow for a higher tiling efficiency, although they face the problem of combinatorial explosion. In this paper, we propose a generation method for multi‐scale Wang tiles that aims at minimizing the amount of needed tiles while still resembling a tiling appearance similar to low‐level tiles. Based on a set of representative multi‐scale Wang tiles, we use a dynamic generation algorithm for this purpose. Our method can be used for rapid texture synthesis and image halftoning. Respecting physical constraints, our tiles are connected, lightweight, independent of the fabrication scale, able to tile larger areas with image contents and contribute to “mass customization”.

Convolutional layers are the core building blocks of Convolutional Neural Networks (CNNs). In this paper, we propose to augment a convolutional layer with an additional depthwise convolution, where each input channel is convolved with a different 2D kernel. The composition of the two convolutions constitutes an over-parameterization, since it adds learnable parameters, while the resulting linear operation can be expressed by a single convolution layer. We refer to this depthwise over-parameterized convolutional layer as DO-Conv, which is a novel way of over-parameterization. We show with extensive experiments that the mere replacement of conventional convolutional layers with DO-Conv layers boosts the performance of CNNs on many classical vision tasks, such as image classification, detection, and segmentation. Moreover, in the inference phase, the depthwise convolution is folded into the conventional convolution, reducing the computation to be exactly equivalent to that of a convolutional layer without over-parameterization. As DO-Conv introduces performance gains without incurring any computational complexity increase for inference, we advocate it as an alternative to the conventional convolutional layer. We open sourced an implementation of DO-Conv in Tensorflow, PyTorch and GluonCV at https://github.com/yangyanli/DO-Conv.

Wrapping objects using ropes is a common practice in our daily life. However, it is difficult to design and tie ropes on a 3D object with complex topology and geometry features while ensuring wrapping security and easy operation. In this article, we propose to compute a rope net that can tightly wrap around various 3D shapes. Our computed rope net not only immobilizes the object but also maintains the load balance during lifting. Based on the key observation that if every knot of the net has four adjacent curve edges, then only a single rope is needed to construct the entire net. We reformulate the rope net computation problem into a constrained curve network optimization. We propose a discrete-continuous optimization approach, where the topological constraints are satisfied in the discrete phase and the geometrical goals are achieved in the continuous stage. We also develop a hoist planning to pick anchor points so that the rope net equally distributes the load during hoisting. Furthermore, we simulate the wrapping process and use it to guide the physical rope net construction process. We demonstrate the effectiveness of our method on 3D objects with varying geometric and topological complexity. In addition, we conduct physical experiments to demonstrate the practicability of our method.

The task of explicit surface reconstruction is to generate a surface mesh by interpolating a given point cloud. Explicit surface reconstruction is necessary when the point cloud is required to appear exactly on the surface. However, for a non-perfect input, such as lack of normals, low density, irregular distribution, thin and tiny parts, and high genus, a robust explicit reconstruction method that can generate a high-quality manifold triangulation is missing. We propose a robust explicit surface reconstruction method that starts from an initial simple surface mesh, alternately performs a Filmsticking step and a Sculpting step of the initial mesh, and converges when the surface mesh interpolates all input points (except outliers) and remains stable. The Filmsticking is to minimize the geometric distance between the surface mesh and the point cloud through iteratively performing a restricted Voronoi diagram technique on the surface mesh, whereas the Sculpting is to bootstrap the Filmsticking iteration from local minima by applying appropriate geometric and topological changes of the surface mesh. Our algorithm is fully automatic and produces high-quality surface meshes for non-perfect inputs that are typically considered to be challenging for prior state of the art. We conducted extensive experiments on simulated scans and real scans to validate the effectiveness of our approach.

In this paper, we propose to compute Voronoi diagrams over mesh surfaces driven by an arbitrary geodesic distance solver, assuming that the input is a triangle mesh as well as a collection of sites P = { Pi } m i =1 on the surface. We propose two key techniques to solve this problem. First, as the partition is determined by minimizing the m distance fields, each of which rooted at a source site, we suggest keeping one or more distance triples, for each triangle, that may help determine the Voronoi bisectors when one uses a mark-and-sweep geodesic algorithm to predict the multi-source distance field. Second, rather than keep the distance itself at a mesh vertex, we use the squared distance to characterize the linear change of distance field restricted in a triangle, which is proved to induce an exact VD when the base surface reduces to a planar triangle mesh. Specially, our algorithm also supports the Euclidean distance, which can handle thin-sheet models (e.g. leaf) and runs faster than the traditional restricted Voronoi diagram (RVD) algorithm. It is very extensible to deal with various variants of surface-based Voronoi diagrams including (1) surface-based power diagram, (2) constrained Voronoi diagram with curve-type breaklines, and (3) curve-type generators. We conduct extensive experimental results to validate the ability to approximate the exact VD in different distance-driven scenarios.

Feature lines are important geometric cues in characterizing the structure of a CAD model. Despite great progress in both explicit reconstruction and implicit reconstruction, it remains a challenging task to reconstruct a polygonal surface equipped with feature lines, especially when the input point cloud is noisy and lacks faithful normal vectors. In this paper, we develop a multistage algorithm, named RFEPS , to address this challenge. The key steps include (1) denoising the point cloud based on the assumption of local planarity, (2) identifying the feature-line zone by optimization of discrete optimal transport, (3) augmenting the point set so that sufficiently many additional points are generated on potential geometry edges, and (4) generating a polygonal surface that interpolates the augmented point set based on restricted power diagram. We demonstrate through extensive experiments that RFEPS, benefiting from the edge-point augmentation and the feature preserving explicit reconstruction, outperforms state of the art methods in terms of the reconstruction quality, especially in terms of the ability to reconstruct missing feature lines.

This article presents a simple yet effective method for computing geodesic distances on triangle meshes. Unlike the popular window propagation methods that partition mesh edges into intervals of varying lengths, our method places evenly-spaced, source-independent Steiner points on edges. Given a source vertex, our method constructs a Steiner-point graph that partitions the surface into mutually exclusive tracks, called geodesic tracks. Inside each triangle, the tracks form sub-regions in which the change of distance field is approximately linear. Our method does not require any pre-computation, and can effectively balance speed and accuracy. Experimental results show that with 5 Steiner points on each edge, the mean relative error is less than 0.3 % for common 3D models used in the graphics community. We propose a set of effective filtering rules to eliminate a large amount of useless broadcast events. For a 1000K-face model, our method runs 10 times faster than the conventional Steiner point method that examines a complete graph of Steiner points in each triangle. We also observe that using more Steiner points increases the accuracy at only a small extra computational cost. Our method works well for meshes with poor triangulation and non-manifold configuration, which often poses challenges to the existing PDE methods. We show that geodesic tracks, as a new data structure that encodes rich information of discrete geodesics, support accurate geodesic path and isoline tracing, and efficient distance query. Our method can be easily extended to meshes with non-constant density functions and/or anisotropic metrics.

Colormapping is an effective and popular visualization technique for analyzing patterns in scalar fields. Scientists usually adjust a default colormap to show hidden patterns by shifting the colors in a trial-and-error process. To improve efficiency, efforts have been made to automate the colormap adjustment process based on data properties (e.g., statistical data value or histogram distribution). However, as the data properties have no direct correlation to the spatial variations, previous methods may be insufficient to reveal the dynamic range of spatial variations hidden in the data. To address the above issues, we conduct a pilot analysis with domain experts and summarize three requirements for the colormap adjustment process. Based on the requirements, we formulate colormap adjustment as an objective function, composed of a boundary term and a fidelity term, which is flexible enough to support interactive functionalities. We compare our approach with alternative methods under a quantitative measure and a qualitative user study (25 participants), based on a set of data with broad distribution diversity. We further evaluate our approach via three case studies with six domain experts. Our method is not necessarily more optimal than alternative methods of revealing patterns, but rather is an additional color adjustment option for exploring data with a dynamic range of spatial variations.

A common task for scatterplots is communicating trends in bivariate data. However, the ability of people to visually estimate these trends is under-explored, especially when the data violate assumptions required for common statistical models, or visual trend estimates are in conflict with statistical ones. In such cases, designers may need to intervene and de-bias these estimations, or otherwise inform viewers about differences between statistical and visual trend estimations. We propose data-driven mark orientation as a solution in such cases, where the directionality of marks in the scatterplot guide participants when visual estimation is otherwise unclear or ambiguous. Through a set of laboratory studies, we investigate trend estimation across a variety of data distributions and mark directionalities, and find that data-driven mark orientation can help resolve ambiguities in visual trend estimates.

RGB-D semantic segmentation has attracted increasing attention over the past few years. Existing methods mostly employ homogeneous convolution operators to consume the RGB and depth features, ignoring their intrinsic differences. In fact, the RGB values capture the photometric appearance properties in the projected image space, while the depth feature encodes both the shape of a local geometry as well as the base (whereabout) of it in a larger context. Compared with the base, the shape probably is more inherent and has a stronger connection to the semantics, and thus is more critical for segmentation accuracy. Inspired by this observation, we introduce a Shape-aware Convolutional layer (ShapeConv) for processing the depth feature, where the depth feature is firstly decomposed into a shape-component and a base-component, next two learnable weights are introduced to cooperate with them independently, and finally a convolution is applied on the re-weighted combination of these two components. ShapeConv is model-agnostic and can be easily integrated into most CNNs to replace vanilla convolutional layers for semantic segmentation. Extensive experiments on three challenging indoor RGB-D semantic segmentation benchmarks, i.e., NYU-Dv2(-13,-40), SUN RGB-D, and SID, demonstrate the effectiveness of our ShapeConv when employing it over five popular architectures. Moreover, the performance of CNNs with ShapeConv is boosted without introducing any computation and memory increase in the inference phase. The reason is that the learnt weights for balancing the importance between the shape and base components in ShapeConv become constants in the inference phase, and thus can be fused into the following convolution, resulting in a network that is identical to one with vanilla convolutional layers.

Scribble-supervised semantic segmentation has gained much attention recently for its promising performance without high-quality annotations. Due to the lack of supervision, confident and consistent predictions are usually hard to obtain. Typically, people handle these problems by either adopting an auxiliary task with the well-labeled dataset or incorporating a graphical model with additional requirements on scribble annotations. Instead, this work aims to achieve semantic segmentation by scribble annotations directly without extra information and other limitations. Specifically, we propose holistic operations, including minimizing entropy and a network embedded random walk on the neural representation to reduce uncertainty. Given the probabilistic transition matrix of a random walk, we further train the network with self-supervision on its neural eigenspace to impose consistency on predictions between related images. Comprehensive experiments and ablation studies verify the proposed approach, which demonstrates superiority over others; it is even comparable to some full-label supervised ones and works well when scribbles are randomly shrunk or dropped.

We propose a decentralized, learning-based solution to the challenging problem of unlabeled multi-agent navigation among obstacles, where robots need to simultaneously tackle the problems of goal assignment, local collision avoidance, and navigation. Our method has each robot infer their desired action by communicating with each other as well as a set of position-fixed routers. The inference is carried out on a graph neural network (GNN) with both robot and router nodes. We train our GNN using imitation learning on a small group of robots, where we modify the centralized version of the concurrent goal assignment and planning algorithm (CAPT) as our expert. By sharing weights among all robots and routers, our model can scale to unseen environments with any number of possibly kinodynamic agents during test time. We have achieved a success rate of 91.2% and 85.6% for point and car-like robots, respectively. Source code will be publicly available upon the publication of the work.

Abstract Depth of field is one of the critical reasons to limit the richness of image information. Usually, in a scene with multiple targets, when the distance between each target and the lens is different, the clear scene image can be get within a certain distance range. This situation restricts the further image processing, such as semantic segmentation, object recognition and 3D reconstruction. Multi‐focus image fusion uses two or more images focused on different targets to fuse scene information, which can solve this problem to a great extent. In general, two or more multi‐focus images can cover almost all near/far targets. The fusion of more than two multi‐focus images can be accomplished by cascading the fusion results of the previous two images and the next image to be processed many times. Therefore, the paper focus on the fusion of two multi‐focus images. Inspired by this, new Pseudo‐Siamese neural network with several residual atrous convolution pyramids with multi‐level perception ability to perceive the multi‐level features and consistency relations of multi‐focus image pairs is proposed, and multi‐layer residual blocks are used to fuse the extracted features. In this process, the residual of the groundtruth and the generated image will be learned. Finally, a fully focused image without blur will be generated. After several ablation experiments and comparison experiments with other methods, the results show that the performance of the method proposed in this paper is state‐of‐the‐art, and overall better than other methods, which are advanced.

Motivated by the fact that the medial axis transform is able to encode the shape completely, we propose to use as few medial balls as possible to approximate the original enclosed volume by the boundary surface. We progressively select new medial balls, in a top-down style, to enlarge the region spanned by the existing medial balls. The key spirit of the selection strategy is to encourage large medial balls while imposing given geometric constraints. We further propose a speedup technique based on a provable observation that the intersection of medial balls implies the adjacency of power cells (in the sense of the power crust).We further elaborate the selection rules in combination with two closely related applications. One application is to develop an easy-to-use ball-stick modeling system that helps non-professional users to quickly build a shape with only balls and wires, but any penetration between two medial balls must be suppressed. The other application is to generate porous structures with convex, compact (with a high isoperimetric quotient) and shape-aware pores where two adjacent spherical pores may have penetration as long as the mechanical rigidity can be well preserved.

Learning structures of 3D shapes is a fundamental problem in the field of computer graphics and geometry processing. We present a simple yet interpretable unsupervised method for learning a new structural representation in the form of 3D structure points. The 3D structure points produced by our method encode the shape structure intrinsically and exhibit semantic consistency across all the shape instances with similar structures. This is a challenging goal that has not fully been achieved by other methods. Specifically, our method takes a 3D point cloud as input and encodes it as a set of local features. The local features are then passed through a novel point integration module to produce a set of 3D structure points. The chamfer distance is used as reconstruction loss to ensure the structure points lie close to the input point cloud. Extensive experiments have shown that our method outperforms the state-of-the-art on the semantic shape correspondence task and achieves comparable performance with the state-of-the-art on the segmentation label transfer task. Moreover, the PCA based shape embedding built upon consistent structure points demonstrates good performance in preserving the shape structures. Code is available at https://github.com/NolenChen/3DStructurePoints.

Abstract The problem of seamless parametrization of surfaces is of interest in the context of structured quadrilateral mesh generation and spline‐based surface approximation. It has been tackled by a variety of approaches, commonly relying on continuous numerical optimization to ultimately obtain suitable parameter domains. We present a general combinatorial seamless parameter domain construction, free from the potential numerical issues inherent to continuous optimization techniques in practice. The domains are constructed as abstract polygonal complexes which can be embedded in a discrete planar grid space, as unions of unit squares. We ensure that the domain structure matches any prescribed parametrization singularities (cones) and satisfies seamlessness conditions. Surfaces of arbitrary genus are supported. Once a domain suitable for a given surface is constructed, a seamless and locally injective parametrization over this domain can be obtained using existing planar disk mapping techniques, making recourse to Tutte's classical embedding theorem.

One major branch of saliency object detection methods are diffusion-based which construct a graph model on a given image and diffuse seed saliency values to the whole graph by a diffusion matrix. While their performance is sensitive to specific feature spaces and scales used for the diffusion matrix definition, little work has been published to systematically promote the robustness and accuracy of salient object detection under the generic mechanism of diffusion. In this work, we firstly present a novel view of the working mechanism of the diffusion process based on mathematical analysis, which reveals that the diffusion process is actually computing the similarity of nodes with respect to the seeds based on diffusion maps. Following this analysis, we propose super diffusion, a novel inclusive learning-based framework for salient object detection, which makes the optimum and robust performance by integrating a large pool of feature spaces, scales and even features originally computed for non-diffusion-based salient object detection. A closed-form solution of the optimal parameters for the integration is determined through supervised learning. At the local level, we propose to promote each individual diffusion before the integration. Our mathematical analysis reveals the close relationship between saliency diffusion and spectral clustering. Based on this, we propose to re-synthesize each individual diffusion matrix from the most discriminative eigenvectors and the constant eigenvector (for saliency normalization). The proposed framework is implemented and experimented on prevalently used benchmark datasets, consistently leading to state-of-the-art performance.

Arrangements of geometric objects refer to the spatial partitions formed by the objects, and they serve as an underlining structure of motion design, analysis, and planning in CAD/CAM, robotics, molecular modeling, manufacturing, and computer-assisted radio-surgery. Arrangements are especially useful to collision detection, which is a key task in various applications such as computer animation, virtual reality, computer games, robotics, CAD/CAM, and computational physics. Ellipsoids are commonly used as bounding volumes in approximating complex geometric objects in collision detection. In this article, we present an in-depth study on the arrangements formed by two ellipsoids. Specifically, we present a classification of these arrangements and propose an efficient algorithm for determining the arrangement formed by any particular pair of ellipsoids. A stratification diagram is also established to show the connections among all the arrangements formed by two ellipsoids. Our results, for the first time, elucidate all possible relative positions between two arbitrary ellipsoids and provide an efficient and robust algorithm for determining the relative position of any two given ellipsoids, therefore providing the necessary foundation for developing practical and trustworthy methods for processing ellipsoids for collision analysis or simulation in various applications.

We present a generative neural network that enables us to generate plausible 3D indoor scenes in large quantities and varieties, easily and highly efficiently. Our key observation is that indoor scene structures are inherently hierarchical . Hence, our network is not convolutional; it is a recursive neural network, or RvNN. Using a dataset of annotated scene hierarchies, we train a variational recursive autoencoder , or RvNN-VAE, which performs scene object grouping during its encoding phase and scene generation during decoding. Specifically, a set of encoders are recursively applied to group 3D objects based on support, surround, and co-occurrence relations in a scene, encoding information about objects’ spatial properties, semantics , and relative positioning with respect to other objects in the hierarchy. By training a variational autoencoder (VAE), the resulting fixed-length codes roughly follow a Gaussian distribution. A novel 3D scene can be generated hierarchically by the decoder from a randomly sampled code from the learned distribution. We coin our method GRAINS, for Generative Recursive Autoencoders for INdoor Scenes. We demonstrate the capability of GRAINS to generate plausible and diverse 3D indoor scenes and compare with existing methods for 3D scene synthesis. We show applications of GRAINS including 3D scene modeling from 2D layouts, scene editing, and semantic scene segmentation via PointNet whose performance is boosted by the large quantity and variety of 3D scenes generated by our method.

In this paper, we propose an approximate Voronoi base domain method to address constrained texture mapping problem. In particular, we generate approximate Voronoi base domains on the input texture image plane and planar embedding of mesh surface. Then, we propose to leverage the triangulations of constraint points on both sides, and yield the same topology for the two approximate Voronoi base domains. Based on the equivalent topology, we are able to employ generalized barycentric coordinates between pairwise Voronoi cells of the two approximate Voronoi base domains. The proposed method is highly efficient, and it allows to edit constraints in real time. Experimental results show the improved effectiveness and robustness of the proposed method for constraint texture mapping.

We propose to synthesize feasible caging grasps for a target object through computing Caging Loops, a closed curve defined in the shape embedding space of the object. Different from the traditional methods, our approach decouples caging loops from the surface geometry of target objects through working in the embedding space. This enables us to synthesize caging loops encompassing multiple topological holes, instead of always tied with one specific handle which could be too small to be graspable by the robot gripper. Our method extracts caging loops through a topological analysis of the distance field defined for the target surface in the embedding space, based on a rigorous theoretical study on the relation between caging loops and the field topology. Due to the decoupling, our method can tolerate incomplete and noisy surface geometry of an unknown target object captured on-the-fly. We implemented our method with a robotic gripper and demonstrate through extensive experiments that our method can synthesize reliable grasps for objects with complex surface geometry and topology and in various scales.

Deep Neural Networks (DNNs) have recently shown state of the art performance on semantic segmentation tasks, however, they still suffer from problems of poor boundary localization and spatial fragmented predictions. The difficulties lie in the requirement of making dense predictions from a long path model all at once since details are hard to keep when data goes through deeper layers. Instead, in this work, we decompose this difficult task into two relative simple sub-tasks: seed detection which is required to predict initial predictions without the need of wholeness and preciseness, and similarity estimation which measures the possibility of any two nodes belong to the same class without the need of knowing which class they are. We use one branch network for one sub-task each, and apply a cascade of random walks base on hierarchical semantics to approximate a complex diffusion process which propagates seed information to the whole image according to the estimated similarities. The proposed DifNet consistently produces improvements over the baseline models with the same depth and with the equivalent number of parameters, and also achieves promising performance on Pascal VOC and Pascal Context dataset. OurDifNet is trained end-to-end without complex loss functions.

We present an automatic algorithm for subtractive manufacturing of freeform 3D objects using high-speed machining (HSM) via CNC. A CNC machine operates a cylindrical cutter to carve off material from a 3D shape stock, following a tool path, to "expose" the target object. Our method decomposes the input object's surface into a small number of patches each of which is fully accessible and machinable by the CNC machine, in continuous fashion, under a fixed cutter-object setup configuration. This is achieved by covering the input surface with a minimum number of accessible regions and then extracting a set of machinable patches from each accessible region. For each patch obtained, we compute a continuous, space-filling, and iso-scallop tool path which conforms to the patch boundary, enabling efficient carving with high-quality surface finishing. The tool path is generated in the form of connected Fermat spirals , which have been generalized from a 2D fill pattern for layered manufacturing to work for curved surfaces. Furthermore, we develop a novel method to control the spacing of Fermat spirals based on directional surface curvature and adapt the heat method to obtain iso-scallop carving. We demonstrate automatic generation of accessible and machinable surface decompositions and iso-scallop Fermat spiral carving paths for freeform 3D objects. Comparisons are made to tool paths generated by commercial software in terms of real machining time and surface quality.

The aspect ratio of a line chart heavily influences the perception of the underlying data. Different methods explore different criteria in choosing aspect ratios, but so far, it was still unclear how to select aspect ratios appropriately for any given data. This paper provides a guideline for the user to choose aspect ratios for any input 1D curves by conducting an in-depth analysis of aspect ratio selection methods both theoretically and experimentally. By formulating several existing methods as line integrals, we explain their parameterization invariance. Moreover, we derive a new and improved aspect ratio selection method, namely the -LOR (local orientation resolution), with a certain degree of parameterization invariance. Furthermore, we connect different methods, including AL (arc length based method), the banking to 45 principle, RV (resultant vector) and AS (average absolute slope), as well as -LOR and AO (average absolute orientation). We verify these connections by a comparative evaluation involving various data sets, and show that the selections by RV and -LOR are complementary to each other for most data. Accordingly, we propose the dual-scale banking technique that combines the strengths of RV and -LOR, and demonstrate its practicability using multiple real-world data sets.

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This paper presents a novel approach to quadrangulate a sequence of meshes with global optimization method, generating consistent quad meshes expressing global topological and geometric characteristics during animation. The key contribution is that our method first proposes a grouping strategy to extract the geometric and topological features of the sequence in animation quadrangulation. Animation sequence is firstly divided into groups through picked key frames. Then analyze the local deformation of each group and detect the surface feature for each reference frame, inducing a set of hard and soft constraints for each key frame of every subgroup, next smooth the cross field of each reference frame and combine them through singularities for the whole sequence, finally compute a field guided global parametrization and quad meshes extraction with an off-the-shelf method. It is effective and easy to implement, and experiment results and comparisons show that our method achieves better quality.

Human 3D pose estimation from a single image is a challenging task with numerous applications. Convolutional Neural Networks (CNNs) have recently achieved superior performance on the task of 2D pose estimation from a single image, by training on images with 2D annotations collected by crowd sourcing. This suggests that similar success could be achieved for direct estimation of 3D poses. However, 3D poses are much harder to annotate, and the lack of suitable annotated training images hinders attempts towards end-to-end solutions. To address this issue, we opt to automatically synthesize training images with ground truth pose annotations. Our work is a systematic study along this road. We find that pose space coverage and texture diversity are the key ingredients for the effectiveness of synthetic training data. We present a fully automatic, scalable approach that samples the human pose space for guiding the synthesis procedure and extracts clothing textures from real images. Furthermore, we explore domain adaptation for bridging the gap between our synthetic training images and real testing photos. We demonstrate that CNNs trained with our synthetic images out-perform those trained with real photos on 3D pose estimation tasks.

We present a new approach for constructing the 3D panorama for an indoor environment by joining together aligned submaps. For each submap, the trajectory of the moving camera is estimated based on the Kanade-Lucas-Tomasi (KLT) features. Our method can update the feature set status by adding new features and removing expiring ones adaptively to accommodate scene changes. The accuracy of the estimated poses is further improved through sparse bundle adjustment. Furthermore, we utilize a linear optimization framework to align all submaps to obtain a consistently extended 3D panorama and to refine the visual odometry at the same time. We evaluated our approach on publicly available benchmark datasets. The experiments demonstrate that the proposed method achieves low translational drift and is robust even when the camera moves very fast.

This article presents a new method to optimally partition a geometric domain with capacity constraints on the partitioned regions. It is an important problem in many fields, ranging from engineering to economics. It is known that a capacity-constrained partition can be obtained as a power diagram with the squared L2 metric. We present a method with super-linear convergence for computing optimal partition with capacity constraints that outperforms the state-of-the-art in an order of magnitude. We demonstrate the efficiency of our method in the context of three different applications in computer graphics and geometric processing: displacement interpolation of function distribution, blue-noise point sampling, and optimal convex decomposition of 2D domains. Furthermore, the proposed method is extended to capacity-constrained optimal partition with respect to general cost functions beyond the squared Euclidean distance.

We develop a new kind of "space-filling" curves, connected Fermat spirals , and show their compelling properties as a tool path fill pattern for layered fabrication. Unlike classical space-filling curves such as the Peano or Hilbert curves, which constantly wind and bind to preserve locality, connected Fermat spirals are formed mostly by long, low-curvature paths. This geometric property, along with continuity, influences the quality and efficiency of layered fabrication. Given a connected 2D region, we first decompose it into a set of sub-regions, each of which can be filled with a single continuous Fermat spiral. We show that it is always possible to start and end a Fermat spiral fill at approximately the same location on the outer boundary of the filled region. This special property allows the Fermat spiral fills to be joined systematically along a graph traversal of the decomposed sub-regions. The result is a globally continuous curve. We demonstrate that printing 2D layers following tool paths as connected Fermat spirals leads to efficient and quality fabrication, compared to conventional fill patterns.

The original depth map captured by low-cost depth cameras such as Kinect suffers from problems of depth missing and noise, which restrict its further application. In this paper, we propose a novel recovery method of Kinect-like depth map utilizing the corresponding color image. The proposed method consists of two steps: hole-filling by image in painting and denoising by fast guided filter. Experiments show that our method gives satisfactory result.

Abstract We introduce a novel method for enabling stereoscopic viewing of a scene from a single pre‐segmented image. Rather than attempting full 3D reconstruction or accurate depth map recovery, we hallucinate a rough approximation of the scene's 3D model using a number of simple depth and occlusion cues and shape priors. We begin by depth‐sorting the segments, each of which is assumed to represent a separate object in the scene, resulting in a collection of depth layers. The shapes and textures of the partially occluded segments are then completed using symmetry and convexity priors. Next, each completed segment is converted to a union of generalized cylinders yielding a rough 3D model for each object. Finally, the object depths are refined using an iterative ground fitting process. The hallucinated 3D model of the scene may then be used to generate a stereoscopic image pair, or to produce images from novel viewpoints within a small neighborhood of the original view. Despite the simplicity of our approach, we show that it compares favorably with state‐of‐the‐art depth ordering methods. A user study was conducted showing that our method produces more convincing stereoscopic images than existing semi‐interactive and automatic single image depth recovery methods.

The emergence of low-cost 3D printers steers the investigation of new geometric problems that control the quality of the fabricated object. In this paper, we present a method to reduce the material cost and weight of a given object while providing a durable printed model that is resistant to impact and external forces. We introduce a hollowing optimization algorithm based on the concept of honeycomb-cells structure. Honeycombs structures are known to be of minimal material cost while providing strength in tension. We utilize the Voronoi diagram to compute irregular honeycomb-like volume tessellations which define the inner structure. We formulate our problem as a strength--to--weight optimization and cast it as mutually finding an optimal interior tessellation and its maximal hollowing subject to relieve the interior stress. Thus, our system allows to build-to-last 3D printed objects with large control over their strength-to-weight ratio and easily model various interior structures. We demonstrate our method on a collection of 3D objects from different categories. Furthermore, we evaluate our method by printing our hollowed models and measure their stress and weights.

Coarse piecewise linear approximation of surfaces causes undesirable polygonal appearance of silhouettes. We present an efficient method for smoothing the silhouettes of coarse triangle meshes using efficient 3D curve reconstruction and simple local re-meshing. It does not assume the availability of a fine mesh and generates only moderate amount of additional data at run time. Furthermore, polygonal feature edges are also smoothed in a unified framework. Our method is based on a novel interpolation scheme over silhouette triangles and this ensures that smooth silhouettes are faithfully reconstructed and always change continuously with respect to continuous movement of the view point or objects. We speed up computation with GPU assistance to achieve real-time rendering of coarse meshes with the smoothed silhouettes. Experiments show that this method outperforms previous methods for silhouette smoothing.

In manufacturing grid, a lot of applications and resources in manufacturing enterprises are encapsulated as Web services and a cooperative work environment is provided. Applying Web service composition and workflow technologies, services are integrated into a composite service to represent a cooperative business process. Therefore the enterprise cooperation can be implemented by executing and monitoring the composite service. According to the characteristics of manufacturing, this paper presents a composite service modeling solution based on BPEL4WS and discusses how this solution support BPEL4WS during the whole modeling process. The solution includes dynamic service discovery and service selection to support a flexible binding with the partners' services. This paper also describes how to execute and monitor the composite service

We present new results on classifying the morphology of the nonsingular intersection curve of two quadrics by studying the roots of the characteristic equation, or the discriminant, of the pencil spanned by the two quadrics. The morphology of a nonsingular algebraic curve means the structural (or topological) information about the curve, such as the number of disjoint connected components of the curve in P/spl Ropf//sup 3/ (the 3D real projective space), and whether a particular component is a compact set in any affine realization of P/spl Ropf//sup 3/. For example, we show that two quadrics intersect along a nonsingular space quartic curve in P/spl Ropf//sup 3/ with one connected component if and only if their characteristic equation has two distinct real roots and a pair of complex conjugate roots. Since the number of the real roots of the characteristic equation can be counted robustly with exact arithmetic, our results can be used to obtain structural information reliably before computing the parameterization of the intersection curve; thus errors in the subsequent computation that is most likely done using floating point arithmetic will not lead to erroneous topological classification of the intersection curve. The key technique used to prove our results is to reduce two quadrics into simple forms using a projective transformation, a technique equivalent to the simultaneous block diagonalization of two real symmetric matrices, a topic that has been studied in matrix algebra.