Multi-view video reconstruction plays a vital role in computer vision, enabling applications in film production, virtual reality, and motion analysis. While recent advances such as 3D Gaussian Splatting have demonstrated impressive capabilities in dynamic scene reconstruction, they typically rely on the assumption that input video streams are temporally synchronized. However, in real-world scenarios, this assumption often fails due to factors like camera trigger delays, frame rate discrepancies, or independent recording setups, leading to temporal misalignment across views and reduced reconstruction quality. To address this challenge, a novel temporal alignment strategy is proposed for high-quality 4DGS reconstruction from unsynchronized multi-view videos. Our method features a coarse-to-fine alignment module that estimates and compensates for each camera's time shift. The method first determines a coarse, frame-level offset and then refines it to achieve sub-frame accuracy. This strategy can be integrated as a plug-and-play module into existing 4DGS frameworks, enhancing their robustness when handling asynchronous data. Experiments show that this approach effectively processes temporally misaligned videos and significantly enhances baseline methods.

Creating compelling 3D character animations typically requires either expert use of professional software or expensive motion capture systems operated by skilled actors. We present DancingBox, a lightweight, vision-based system that makes motion capture accessible to novices by reimagining the process as digital puppetry. Instead of tracking precise human motions, DancingBox captures the approximate movements of everyday objects manipulated by users with a single webcam. These coarse proxy motions are then refined into realistic character animations by conditioning a generative motion model on bounding-box representations, enriched with human motion priors learned from large-scale datasets. To overcome the lack of paired proxy–animation data, we synthesize training pairs by converting existing motion capture sequences into proxy representations. A user study demonstrates that DancingBox enables intuitive and creative character animation using diverse proxies, from plush toys to bananas, lowering the barrier to entry for novice animators.

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.

Articulation modeling aims to infer movable parts and their motion parameters for a 3D object, enabling interactive animation, simulation, and shape editing. In this paper, we present Sketch2Arti , the first sketch-based articulation modeling system for CAD objects. Our key observation is that designers naturally communicate articulation intent through lightweight sketches ( e.g. , arrows and strokes) that indicate how parts should move, yet translating such sketches into articulated 3D models remains largely manual. Sketch2Arti bridges this gap by enabling users to specify articulation through simple 2D sketches drawn from a chosen viewpoint. Given a CAD model and user sketches, our approach automatically discovers the corresponding movable parts and predicts their motion parameters, allowing iterative modeling of multiple articulations on complex objects with fine-grained control. Importantly, Sketch2Arti is trained in a category-agnostic manner without requiring object category information, leading to strong generalization to diverse objects beyond existing articulation datasets. Moreover, for shell models lacking interior structures, Sketch2Arti supports controllable internal completion guided by user sketches, generating plausible internal components consistent with the existing geometry and predicted motion constraints. Comprehensive experiments and user evaluations demonstrate the effectiveness, controllability, and generalization of Sketch2Arti. The code, dataset, and the prototype system are at https://arlo-yang.github.io/Sketch2Arti.

This work presents a novel framework for few-shot 3D part segmentation. Recent advances have demonstrated the significant potential of 2D foundation models for low-shot 3D part segmentation. However, it is still an open problem that how to effectively aggregate 2D knowledge from foundation models to 3D. Existing methods either ignore geometric structures for 3D feature learning or neglects the high-quality grouping clues from SAM, leading to under-segmentation and inconsistent part labels. We devise a novel SAM segment graph-based propagation method, named SegGraph, to explicitly learn geometric features encoded within SAM's segmentation masks. Our method encodes geometric features by modeling mutual overlap and adjacency between segments while preserving intra-segment semantic consistency. We construct a segment graph, conceptually similar to an atlas, where nodes represent segments and edges capture their spatial relationships (overlap/adjacency). Each node adaptively modulates 2D foundation model features, which are then propagated via a graph neural network to learn global geometric structures. To enforce intra-segment semantic consistency, we map segment features to 3D points with a novel view-direction-weighted fusion attenuating contributions from low-quality segments. Extensive experiments on PartNet-E demonstrate that our method outperforms all competing baselines by at least 6.9% mIoU. Further analysis reveals that SegGraph achieves particularly strong performance on small components and part boundaries, demonstrating its superior geometric understanding.

The use of pretrained backbones with fine-tuning has shown success for 2D vision and natural language processing tasks, with advantages over task-specific networks. In this paper, we introduce a pretrained 3D backbone, called Swin3d, for 3D indoor scene understanding. We designed a 3D Swin Transformer as our backbone network, which enables efficient self-attention on sparse voxels with linear memory complexity, making the backbone scalable to large models and datasets. We also introduce a generalized contextual relative positional embedding scheme to capture various irregularities of point signals for improved network performance. We pretrained a large Swin3d model on a synthetic Structured3D dataset, which is an order of magnitude larger than the ScanNet dataset. Our model pretrained on the synthetic dataset not only generalizes well to downstream segmentation and detection on real 3D point datasets but also outperforms state-of-the-art methods on downstream tasks with +2.3 mIoU and +2.2 mIoU on S3DIS Area5 and 6-fold semantic segmentation, respectively, +1.8 mIoU on ScanNet segmentation (val), +1.9 [email protected] on ScanNet detection, and +8.1 [email protected] on S3DIS detection. A series of extensive ablation studies further validated the scalability, generality, and superior performance enabled by our approach.

Neural implicit representations are increasingly used to depict three-dimensional (3D) shapes owing to their inherent smoothness and compactness, contrasting with traditional discrete representations. Yet, the multilayer perceptron–based neural representation, because of its smooth nature, rounds sharp corners or edges, rendering it unsuitable for representing objects with sharp features like computer-aided design (CAD) models. Moreover, neural implicit representations need long training times to fit 3D shapes. While previous works address these issues separately, we present a unified neural implicit representation called Patch-Grid , which efficiently fits complex shapes, preserves sharp features delineating different patches, and can also represent surfaces with open boundaries and thin geometric features. Patch-Grid learns a signed distance field (SDF) to approximate an encompassing surface patch of the shape with a learnable patch feature volume. To form sharp edges and corners in a CAD model, Patch-Grid merges the learned SDFs via the constructive solid geometry (CSG) approach. Core to the merging process is a novel merge grid design that organizes different patch feature volumes in a common octree structure. This design choice ensures robust merging of multiple learned SDFs by confining the CSG operations to localized regions. Additionally, it drastically reduces the complexity of the CSG operations in each merging cell, allowing the proposed method to be trained in seconds to fit a complex shape at high fidelity. Experimental results demonstrate that the proposed Patch-Grid representation is capable of accurately reconstructing shapes with complex sharp features, open boundaries, and thin geometric elements, achieving state-of-the-art reconstruction quality with high computational efficiency within seconds.

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.

Man-made 3D shapes are naturally organized in parts and hierarchies; such structures provide important constraints for shape reconstruction and generation. Modeling shape structures is difficult, because there can be multiple hierarchies for a given shape, causing ambiguity, and across different categories, the shape structures are correlated with semantics, limiting generalization. We present StructRe , a structure rewriting system, as a novel approach to structured shape modeling. Given a 3D object represented by points and components, StructRe can rewrite it upward into more concise structures, or downward into more detailed structures; by iterating the rewriting process, hierarchies are obtained. Such a localized rewriting process enables probabilistic modeling of ambiguous structures and robust generalization across object categories. We train StructRe on PartNet data and show its generalization to cross-category and multiple object hierarchies, and test its extension to ShapeNet. We also demonstrate the benefits of probabilistic and generalizable structure modeling for shape reconstruction, generation and editing tasks.

Reverse engineering CAD models from raw geometry is a classic but challenging research problem. In particular, reconstructing the CAD modeling sequence from point clouds provides great interpretability and convenience for editing. Analyzing previous work, we observed that a CAD modeling sequence represented by tokens and processed by a generative model does not have an immediate geometric interpretation. To improve upon this problem, we introduce geometric guidance into the reconstruction network. Our proposed model, PS-CAD, reconstructs the CAD modeling sequence one step at a time as illustrated in Figure 1 . At each step, we provide three forms of geometric guidance. First, we provide the geometry of surfaces where the current reconstruction differs from the complete model as a point cloud. This helps the framework to focus on regions that still need work. Second, we use geometric analysis to extract a set of planar prompts, that correspond to candidate surfaces where a CAD extrusion step could be started. Third, we present a step-wise sampling to generate multiple complete candidate CAD modeling steps instead of single-tokens without direct geometric interpretation. Our framework has three major components. Geometric guidance computation extracts the first two types of geometric guidance. Single-step reconstruction computes a single candidate CAD modeling step for each provided prompt. Single-step selection selects among the candidate CAD modeling steps. The process continues until the reconstruction is completed. Our quantitative results show a significant improvement across all metrics. For example, on the dataset DeepCAD, PS-CAD improves upon the best published SOTA method by reducing the geometry errors (CD and HD) by 10%, and the structural error (ECD metric) by about 13%.

CAD programs are a popular way to compactly encode shapes as a sequence of operations that are easy to para-metrically modify. However, without sufficient semantic comments and structure, such programs can be challenging to understand, let alone modify. We introduce the problem of semantic commenting CAD programs, wherein the goal is to segment the input program into code blocks corresponding to semantically meaningful shape parts and assign a semantic label to each block. We solve the problem by combining program parsing with visual-semantic analysis afforded by recent advances in foundational language and vision models. Specifically, by executing the input programs, we create shapes, which we use to generate conditional photorealistic images to make use of semantic annotators for such images. We then distill the information across the images and link back to the original programs to semantically comment on them. Additionally, we collected and annotated a benchmark dataset, CADTalk, consisting of 5,288 machine-made programs and 45 human-made programs with ground truth semantic comments. We exten-sively evaluated our approach, compared it to a GPT-based baseline, and an open-set shape segmentation baseline, and reported an 83.24% accuracy on the new CADTalk dataset. Code and data: https://enigma-li.github.io/CADTalk/.

Masked autoencoders (MAE) have recently been introduced to 3D self-supervised pretraining for point clouds due to their great success in NLP and computer vision. Unlike MAEs used in the image domain, where the pretext task is to restore features at the masked pixels, such as colors, the existing 3D MAE works reconstruct the missing geometry only, i.e, the location of the masked points. In contrast to previous studies, we advocate that point location recovery is inessential and restoring intrinsic point features is much superior. To this end, we propose to ignore point position reconstruction and recover high-order features at masked points including surface normals and surface variations, through a novel attention-based decoder which is independent of the encoder design. We validate the effectiveness of our pretext task and decoder design using different encoder structures for 3D training and demonstrate the advantages of our pretrained networks on various point cloud analysis tasks.

Differentiable rendering is a key ingredient for inverse rendering and machine learning, as it allows to optimize scene parameters (shape, materials, lighting) to best fit target images. Differentiable rendering requires that each scene parameter relates to pixel values through differentiable operations. While 3D mesh rendering algorithms have been implemented in a differentiable way, these algorithms do not directly extend to Constructive-Solid-Geometry (CSG), a popular parametric representation of shapes, because the underlying boolean operations are typically performed with complex black-box mesh-processing libraries. We present an algorithm, DiffCSG, to render CSG models in a differentiable manner. Our algorithm builds upon CSG rasterization, which displays the result of boolean operations between primitives without explicitly computing the resulting mesh and, as such, bypasses black-box mesh processing. We describe how to implement CSG rasterization within a differentiable rendering pipeline, taking special care to apply antialiasing along primitive intersections to obtain gradients in such critical areas. Our algorithm is simple and fast, can be easily incorporated into modern machine learning setups, and enables a range of applications for computer-aided design, including direct and image-based editing of CSG primitives. Code and data: https://yyyyyhc.github.io/DiffCSG/.

Point clouds acquired by 3D scanning devices are often sparse, noisy, and non-uniform, causing a loss of geometric features. To facilitate the usability of point clouds in downstream applications, given such input, we present a learning-based point upsampling method, i.e., iPUNet, which generates dense and uniform points at arbitrary ratios and better captures sharp features. To generate feature-aware points, we introduce cross fields that are aligned to sharp geometric features by self-supervision to guide point generation. Given cross field defined frames, we enable arbitrary ratio upsampling by learning at each input point a local parameterized surface. The learned surface consumes the neighboring points and 2D tangent plane coordinates as input, and maps onto a continuous surface in 3D where arbitrary ratios of output points can be sampled. To solve the non-uniformity of input points, on top of the cross field guided upsampling, we further introduce an iterative strategy that refines the point distribution by moving sparse points onto the desired continuous 3D surface in each iteration. Within only a few iterations, the sparse points are evenly distributed and their corresponding dense samples are more uniform and better capture geometric features. Through extensive evaluations on diverse scans of objects and scenes, we demonstrate that iPUNet is robust to handle noisy and non-uniformly distributed inputs, and outperforms state-of-the-art point cloud upsampling methods.

Volumetric data abounds in medical imaging and other fields. With the improved imaging quality and the increased resolution, volumetric datasets are getting so large that the existing tools have become inadequate for processing and analyzing the data. Here we consider the problem of computing tetrahedral meshes to represent large volumetric datasets with labeled multiple materials, which are often encountered in medical imaging or microscopy optical slice tomography. Such tetrahedral meshes are a more compact and expressive geometric representation so are in demand for efficient visualization and simulation of the data, which are impossible if the original large volumetric data are used directly due to the large memory requirement. Existing methods for meshing volumetric data are not scalable for handling large datasets due to their sheer demand on excessively large run-time memory or failure to produce a tet-mesh that preserves the multi-material structure of the original volumetric data. In this article we propose a novel approach, called Marching Windows, that uses a moving window and a disk-swap strategy to reduce the run-time memory footprint, devise a new scheme that guarantees to preserve the topological structure of the original dataset, and adopt an error-guided optimization technique to improve both geometric approximation error and mesh quality. Extensive experiments show that our method is capable of processing very large volumetric datasets beyond the capability of the existing methods and producing tetrahedral meshes of high quality.

Understanding dynamic hand motions and actions from egocentric RGB videos is a fundamental yet challenging task due to self-occlusion and ambiguity. To address occlusion and ambiguity, we develop a transformer-based framework to exploit temporal information for robust estimation. Noticing the different temporal granularity of and the semantic correlation between hand pose estimation and action recognition, we build a network hierarchy with two cascaded transformer encoders, where the first one exploits the short-term temporal cue for hand pose estimation, and the latter aggregates per-frame pose and object information over a longer time span to recognize the action. Our approach achieves competitive results on two first-person hand action benchmarks, namely FPHA and H2O. Extensive ablation studies verify our design choices.

Vector graphics (VG) are ubiquitous in industrial designs. In this paper, we address semantic segmentation of a typical VG, i.e., roughcast floorplans with bare wall structures, whose output can be directly used for further applications like interior furnishing and room space modeling. Previous semantic segmentation works mostly process well-decorated floorplans in raster images and usually yield aliased boundaries and outlier fragments in segmented rooms, due to pixel-level segmentation that ignores the regular elements (e.g. line segments) in vector floor-plans. To overcome these issues, we propose to fully utilize the regular elements in vector floorplans for more integral segmentation. Our pipeline predicts room segmentation from vector floorplans by dually classifying line segments as room boundaries, and regions partitioned by line segments as room segments. To fully exploit the structural relationships between lines and regions, we use two-stream graph neural networks to process the line segments and partitioned regions respectively, and devise a novel modulated graph attention layer to fuse the heterogeneous information from one stream to the other. Extensive experiments show that by directly operating on vector floorplans, we outper-form image-based methods in both mIoU and mAcc. In addition, we propose a new metric that captures room integrity and boundary regularity, which confirms that our method produces much more regular segmentations. Source code is available at https://github.com/DrZiji/VecFloorSeg.

Although the recent rapid evolution of 3D generative neural networks greatly improves 3D shape generation, it is still not convenient for ordinary users to create 3D shapes and control the local geometry of generated shapes. To address these challenges, we propose a diffusion-based 3D generation framework --- locally attentional SDF diffusion , to model plausible 3D shapes, via 2D sketch image input. Our method is built on a two-stage diffusion model. The first stage, named occupancy-diffusion , aims to generate a low-resolution occupancy field to approximate the shape shell. The second stage, named SDF-diffusion , synthesizes a high-resolution signed distance field within the occupied voxels determined by the first stage to extract fine geometry. Our model is empowered by a novel view-aware local attention mechanism for image-conditioned shape generation, which takes advantage of 2D image patch features to guide 3D voxel feature learning, greatly improving local controllability and model generalizability. Through extensive experiments in sketch-conditioned and category-conditioned 3D shape generation tasks, we validate and demonstrate the ability of our method to provide plausible and diverse 3D shapes, as well as its superior controllability and generalizability over existing work.

The freeform architectural modeling process often involves two important stages: concept design and digital modeling. In the first stage, architects usually sketch the overall 3D shape and the panel layout on a physical or digital paper briefly. In the second stage, a digital 3D model is created using the sketch as a reference. The digital model needs to incorporate geometric requirements for its components, such as the planarity of panels due to consideration of construction costs, which can make the modeling process more challenging. In this work, we present a novel sketch-based system to bridge the concept design and digital modeling of freeform roof-like shapes represented as planar quadrilateral (PQ) meshes. Our system allows the user to sketch the surface boundary and contour lines under axonometric projection and supports the sketching of occluded regions. In addition, the user can sketch feature lines to provide directional guidance to the PQ mesh layout. Given the 2D sketch input, we propose a deep neural network to infer in real-time the underlying surface shape along with a dense conjugate direction field, both of which are used to extract the final PQ mesh. To train and validate our network, we generate a large synthetic dataset that mimics architect sketching of freeform quadrilateral patches. The effectiveness and usability of our system are demonstrated with quantitative and qualitative evaluation as well as user studies.

We propose a method for self-supervised image representation learning under the guidance of 3D geometric consistency. Our intuition is that 3D geometric consistency priors such as smooth regions and surface discontinuities may imply consistent semantics or object boundaries, and can act as strong cues to guide the learning of 2D image representations without semantic labels. Specifically, we introduce 3D geometric consistency into a contrastive learning framework to enforce the feature consistency within image views. We propose to use geometric consistency sets as constraints and adapt the InfoNCE loss accordingly. We show that our learned image representations are general. By fine-tuning our pre-trained representations for various 2D image-based downstream tasks, including semantic segmentation, object detection, and instance segmentation on real-world indoor scene datasets, we achieve superior performance compared with state-of-the-art methods.

We present a novel implicit representation ---neural halfspace representation(NH-Rep), to convert manifold B-Rep solids to implicit representations. NH-Rep is a Boolean tree built on a set of implicit functions represented by the neural network, and the composite Boolean function is capable of representing solid geometry while preserving sharp features. We propose an efficient algorithm to extract the Boolean tree from a manifold B-Rep solid and devise a neural network-based optimization approach to compute the implicit functions. We demonstrate the high quality offered by our conversion algorithm on ten thousand manifold B-Rep CAD models that contain various curved patches including NURBS, and the superiority of our learning approach over other representative implicit conversion algorithms in terms of surface reconstruction, sharp feature preservation, signed distance field approximation, and robustness to various surface geometry, as well as a set of applications supported by NH-Rep.

We view the reconstruction of CAD models in the boundary representation (B-Rep) as the detection of geometric primitives of different orders, i.e. , vertices, edges and surface patches, and the correspondence of primitives, which are holistically modeled as a chain complex, and show that by modeling such comprehensive structures more complete and regularized reconstructions can be achieved. We solve the complex generation problem in two steps. First, we propose a novel neural framework that consists of a sparse CNN encoder for input point cloud processing and a tri-path transformer decoder for generating geometric primitives and their mutual relationships with estimated probabilities. Second, given the probabilistic structure predicted by the neural network, we recover a definite B-Rep chain complex by solving a global optimization maximizing the likelihood under structural validness constraints and applying geometric refinements. Extensive tests on large scale CAD datasets demonstrate that the modeling of B-Rep chain complex structure enables more accurate detection for learning and more constrained reconstruction for optimization, leading to structurally more faithful and complete CAD B-Rep models than previous results.

CAD modeling, despite being the industry-standard, remains restricted to usage by skilled practitioners due to two key barriers. First, the user must be able to mentally parse a final shape into a valid sequence of supported CAD commands; and second, the user must be sufficiently conversant with CAD software packages to be able to execute the corresponding CAD commands. As a step towards addressing both these challenges, we present Free2CAD wherein the user can simply sketch the final shape and our system parses the input strokes into a sequence of commands expressed in a simplified CAD language. When executed, these commands reproduce the sketched object. Technically, we cast sketch-based CAD modeling as a sequence-to-sequence translation problem, for which we leverage the powerful Transformers neural network architecture. Given the sequence of pen strokes as input, we introduce the new task of grouping strokes that correspond to individual CAD operations. We combine stroke grouping with geometric fitting of the operation parameters, such that intermediate groups are geometrically corrected before being reused, as context, for subsequent steps in the sequence inference. Although trained on synthetically-generated data, we demonstrate that Free2CAD generalizes to sketches created from real-world CAD models as well as to sketches drawn by novice users. Code and data are at https://github.com/Enigma-li/Free2CAD.

Point set is a flexible and lightweight representation widely used for 3D deep learning. However, their discrete nature prevents them from representing continuous and fine geometry, posing a major issue for learning-based shape generation. In this work, we turn the discrete point sets into smooth surfaces by introducing the well-known implicit moving least-squares (IMLS) surface formulation, which naturally defines locally implicit functions on point sets. We incorporate IMLS surface generation into deep neural networks for inheriting both the flexibility of point sets and the high quality of implicit surfaces. Our IMLSNet predicts an octree structure as a scaffold for generating MLS points where needed and characterizes shape geometry with learned local priors. Furthermore, our implicit function evaluation is independent of the neural network once the MLS points are predicted, thus enabling fast runtime evaluation. Our experiments on 3D object reconstruction demonstrate that IMLSNets outperform state-of-the-art learning-based methods in terms of reconstruction quality and computational efficiency. Extensive ablation tests also validate our network design and loss functions.

We present a novel approach for completing and reconstructing 3D shapes from incomplete scanned data by using deep neural networks. Rather than being trained on supervised completion tasks and applied on a testing shape, the network is optimized from scratch on the single testing shape to fully adapt to the shape and complete the missing data using contextual guidance from the known regions. The ability to complete missing data by an untrained neural network is usually referred to as the deep prior . In this article, we interpret the deep prior from a neural tangent kernel (NTK) perspective and show that the completed shape patches by the trained CNN are naturally similar to existing patches, as they are proximate in the kernel feature space induced by NTK. The interpretation allows us to design more efficient network structures and learning mechanisms for the shape completion and reconstruction task. Being more aware of structural regularities than both traditional and other unsupervised learning-based reconstruction methods, our approach completes large missing regions with plausible shapes and complements supervised learning-based methods that use database priors by requiring no extra training dataset and showing flexible adaptation to a particular shape instance.

Surface meshes are widely used shape representations and capture finer geometry data than point clouds or volumetric grids, but are challenging to apply CNNs directly due to their non-Euclidean structure. We use parallel frames on surface to define PFCNNs that enable effective feature learning on surface meshes by mimicking standard convolutions faithfully. In particular, the convolution of PFCNN not only maps local surface patches onto flat tangent planes, but also aligns the tangent planes such that they locally form a flat Euclidean structure, thus enabling recovery of standard convolutions. The alignment is achieved by the tool of locally flat connections borrowed from discrete differential geometry, which can be efficiently encoded and computed by parallel frame fields. In addition, the lack of canonical axis on surface is handled by sampling with the frame directions. Experiments show that for tasks including classification, segmentation and registration on deformable geometric domains, as well as semantic scene segmentation on rigid domains, PFCNNs achieve robust and superior performances without using sophisticated input features than state-of-the-art surface based CNNs.

We present a sketch-based CAD modeling system, where users create objects incrementally by sketching the desired shape edits, which our system automatically translates to CAD operations. Our approach is motivated by the close similarities between the steps industrial designers follow to draw 3D shapes, and the operations CAD modeling systems offer to create similar shapes. To overcome the strong ambiguity with parsing 2D sketches, we observe that in a sketching sequence, each step makes sense and can be interpreted in the context of what has been drawn before. In our system, this context corresponds to a partial CAD model, inferred in the previous steps, which we feed along with the input sketch to a deep neural network in charge of interpreting how the model should be modified by that sketch. Our deep network architecture then recognizes the intended CAD operation and segments the sketch accordingly, such that a subsequent optimization estimates the parameters of the operation that best fit the segmented sketch strokes. Since there exists no datasets of paired sketching and CAD modeling sequences, we train our system by generating synthetic sequences of CAD operations that we render as line drawings. We present a proof of concept realization of our algorithm supporting four frequently used CAD operations. Using our system, participants are able to quickly model a large and diverse set of objects, demonstrating Sketch2CAD to be an alternate way of interacting with current CAD modeling systems.

3D mesh models created by human users and shared through online platforms and datasets flourish recently. While the creators generally have spent large efforts in modeling the visually appealing shapes with both large scale structures and intricate details, a majority of the meshes are unfortunately flawed in terms of having duplicate faces, mis-oriented regions, disconnected patches, etc., due to multiple factors involving both human errors and software inconsistencies. All these artifacts have severely limited the possible low-level and high-level processing tasks that can be applied to the rich datasets. In this work, we present a novel approach to fix these man-made meshes such that the outputs are guaranteed to be oriented manifold meshes that preserve the original structures, big and small, as much as possible. Our key observation is that the models all visually look meaningful, which leads to our strategy of repairing the flaws while always preserving the visual quality. We apply local refinements and removals only where necessary to achieve minimal intrusion of the original meshes, and global adjustments through robust optimization to ensure the outputs are valid manifold meshes with optimal connections. We test the approach on large-scale 3D datasets, and obtain quality meshes that are more readily usable for further geometry processing tasks.

Sketching provides an intuitive user interface for communicating free form shapes. While human observers can easily envision the shapes they intend to communicate, replicating this process algorithmically requires resolving numerous ambiguities. Existing sketch-based modeling methods resolve these ambiguities by either relying on expensive user annotations or by restricting the modeled shapes to specific narrow categories. We present an approach for modeling generic freeform 3D surfaces from sparse, expressive 2D sketches that overcomes both limitations by incorporating convolution neural networks (CNN) into the sketch processing workflow. Given a 2D sketch of a 3D surface, we use CNNs to infer the depth and normal maps representing the surface. To combat ambiguity we introduce an intermediate CNN layer that models the dense curvature direction, or flow, field of the surface, and produce an additional output confidence map along with depth and normal. The flow field guides our subsequent surface reconstruction for improved regularity; the confidence map trained unsupervised measures ambiguity and provides a robust estimator for data fitting. To reduce ambiguities in input sketches users can refine their input by providing optional depth values at sparse points and curvature hints for strokes. Our CNN is trained on a large dataset generated by rendering sketches of various 3D shapes using non-photo-realistic line rendering (NPR) method that mimics human sketching of free-form shapes. We use the CNN model to process both single- and multi-view sketches. Using our multi-view framework users progressively complete the shape by sketching in different views, generating complete closed shapes. For each new view, the modeling is assisted by partial sketches and depth cues provided by surfaces generated in earlier views. The partial surfaces are fused into a complete shape using predicted confidence levels as weights. We validate our approach, compare it with previous methods and alternative structures, and evaluate its performance with various modeling tasks. The results demonstrate our method is a new approach for efficiently modeling freeform shapes with succinct but expressive 2D sketches.

Sketch-based modeling provides a powerful paradigm for geometric modeling. Recent research had shown, sketch based modeling methods are most effective when targeting a specific family of surfaces. A large and growing arsenal of sketching tools is available for different types of geometries and different target user populations. Our work augments this arsenal with a new and powerful tool for modeling complex freeform shapes by sketching sparse 2D strokes; our method complements existing approaches in enabling the generation of surfaces with complex curvature patterns that are challenging to produce with existing methods. To model a desired surface patch with our technique, the user sketches the patch boundary as well as a small number of strokes representing the major bending directions of the shape. Our method uses this input to generate a curvature field that conforms to the user strokes and then uses this field to derive a freeform surface with the desired curvature pattern. To infer the surface from the strokes we first disambiguate the convex versus concave bending directions indicated by the strokes and estimate the surface bending magnitude along the strokes. We subsequently construct a curvature field based on these estimates, using a non-orthogonal 4-direction field coupled with a scalar magnitude field, and finally construct a surface whose curvature pattern reflects this field through an iterative sequence of simple linear optimizations. Our framework is well suited for single-view modeling, but also supports multi-view interaction, necessary to model complex shapes portions of which can be occluded in many views. It effectively combines multi-view inputs to obtain a coherent 3D shape. It runs at interactive speed allowing for immediate user feedback. We demonstrate the effectiveness of the proposed method through a large collection of complex examples created by both artists and amateurs. Our framework provides a useful complement to the existing sketch-based modeling methods.

Mosaics are widely used for surface decoration to produce appealing visual effects. We present a method for synthesizing digital surface mosaics with irregularly shaped tiles, which are a type of tiles often used for mosaics design. Our method employs both continuous optimization and combinatorial optimization to improve tile arrangement. In the continuous optimization step, we iteratively partition the base surface into approximate Voronoi regions of the tiles and optimize the positions and orientations of the tiles to achieve a tight fit. Combination optimization performs tile permutation and replacement to further increase surface coverage and diversify tile selection. The alternative applications of these two optimization steps lead to rich combination of tiles and high surface coverage. We demonstrate the effectiveness of our solution with extensive experiments and comparisons.

We propose a new approach for automatic surfacing of 3D curve networks, a long standing computer graphics problem which has garnered new attention with the emergence of sketch based modeling systems capable of producing such networks. Our approach is motivated by recent studies suggesting that artist-designed curve networks consist of descriptive curves that convey intrinsic shape properties, and are dominated byrepresentative flow linesdesigned to convey the principal curvature lines on the surface. Studies indicate that viewers complete the intended surface shape by envisioning a surface whose curvature lines smoothly blend these flow-line curves. Following these observations we design a surfacing framework that automatically aligns the curvature lines of the constructed surface with the representative flow lines and smoothly interpolates these representative flow, or curvature directions while minimizing undesired curvature variation. Starting with an initial triangle mesh of the network, we dynamically adapt the mesh to maximize the agreement between the principal curvature direction field on the surface and a smoothflow fieldsuggested by the representative flow-line curves. Our main technical contribution is a framework for curvature-based surface modeling, that facilitates the creation of surfaces with prescribed curvature characteristics. We validate our method via visual inspection, via comparison to artist created and ground truth surfaces, as well as comparison to prior art, and confirm that our results are well aligned with the computed flow fields and with viewer perception of the input networks.

Masonry structures must be compressively self-supporting; designing such surfaces forms an important topic in architecture as well as a challenging problem in geometric modeling. Under certain conditions, a surjective mapping exists between a power diagram , defined by a set of 2D vertices and associated weights, and the reciprocal diagram that characterizes the force diagram of a discrete self-supporting network. This observation lets us define a new and convenient parameterization for the space of self-supporting networks. Based on it and the discrete geometry of this design space, we present novel geometry processing methods including surface smoothing and remeshing which significantly reduce the magnitude of force densities and homogenize their distribution.

We present a new method for modeling discrete constant mean curvature (CMC) surfaces, which arise frequently in nature and are highly demanded in architecture and other engineering applications. Our method is based on a novel use of the CVT ( centroidal Voronoi tessellation ) optimization framework. We devise a CVT-CMC energy function defined as a combination of an extended CVT energy and a volume functional. We show that minimizing the CVT-CMC energy is asymptotically equivalent to minimizing mesh surface area with a fixed volume, thus defining a discrete CMC surface. The CVT term in the energy function ensures high mesh quality throughout the evolution of a CMC surface in an interactive design process for form finding. Our method is capable of modeling CMC surfaces with fixed or free boundaries and is robust with respect to input mesh quality and topology changes. Experiments show that the new method generates discrete CMC surfaces of improved mesh quality over existing methods.

Centroidal Voronoi Tessellation (CVT) is a widely used geometric structure in applications including mesh generation, vector quantization and image processing. Global optimization of the CVT function is important in these applications. With numerical evidences, we show that the CVT function is highly nonconvex and has many local minima and therefore the global optimization of the CVT function is nontrivial. We apply the method of Monte Carlo with Minimization (MCM) to optimizing the CVT function globally and demonstrate its efficacy in producing much improved results compared with two other global optimization methods.