While 3D Gaussian Splatting (3DGS) excels at real-time rendering of standard scenes, it struggles to reconstruct underwater environments due to severe challenges such as light scattering, color attenuation, and sparse coverage of Gaussian kernels in far-field aqueous regions. To address this, we introduce AquaSplatting, a hybrid framework that combines explicit and implicit modeling methods for robust underwater scene reconstruction. Our dual-branch architecture employs 3DGS in a geometry-guided branch to model solid surfaces like the seabed, while a medium-aware branch uses a compact, view-dependent MLP to represent volumetric water effects. Furthermore, a neural underwater hybrid rendering mechanism adaptively fuses these two representations based on accumulated opacity. Thanks to this dual-branch framework, our method can also synthesize restored images without water medium. To enhance efficiency, our proposed engagement-based pruning (EBP) strategy quantifies each Gaussian's contribution by accumulating its image-space gradients over multiple frames, enabling the principled removal of primitives with negligible impact. The entire framework is optimized using a comprehensive loss function that integrates photometric, exposure, semantic, and depth priors to maximize visual fidelity. Experiments on challenging underwater datasets demonstrate that AquaSplatting achieves the state-of-the-art in reconstruction quality surpassing prior methods while maintaining real-time performance.

Computing-in-Memory (CIM) demonstrates exceptional performance on edge AI applications, owing to its in-situ computation capability with minimal data transfer consumption. However, volatile CIMs suffer from inevitable data retention power overhead, while non-volatile MRAM-CIMs still necessitate periodic weight updates constrained by limited memory space, diminishing the intrinsic advantage of CIMs. In this work, we propose a digital SOT-MRAM CIM accelerator with circuit-architecture-operator cross-layer design, achieving double bit density and full utilization of both data transmission bandwidth and computing throughput, thereby satisfying the stringent hardware demands for edge AI applications. Firstly, we propose a refined 2T-1MTJ non-complementary memory cell with an XOR-integrated pre-charged sense amplifier (X-SA), which significantly promotes the storage density and consumes only 6.284 fJ per read-based XOR operation. Then, we devise a channel-flatten data mapping (CFDM) scheme and an operator-aware residual fusion (OARF) structure to full utilize the storage and computing resources. Furthermore, an operator fusion method towards non-linear layers is proposed, achieving an 89.84% size reduction in non-binary parameters. System-level simulations at 40nm demonstrate that our work achieves 284.25 TOPS/W energy efficiency and 5.41 TOPS/mm2area efficiency with an accuracy of 98.72% (87.78%) on MNIST (CIFAR-10) dataset.

Polycube-maps play a critical role in computer graphics, especially for generating high-quality hexahedral meshes. Existing polycube validity conditions, primarily based on Steinitz and Eppstein’s approach, are limited to 3-connected graphs. Extending polycube-maps to handle higher connectivity graphs is crucial for practical applications. In this work, we introduce Validity-Augmented Topological Conditions (VAT conditions) based on the Gauss–Bonnet theorem. These conditions offer both global and local topological criteria, enabling the solvability of k-connected graphs, non-manifold structures, and meshes with voids. Our VAT conditions allow models that do not meet traditional polycube validity criteria but are still valid polycube polyhedra in practice. Additionally, we propose an Immune Genetic Algorithm (ImGA) tailored to our VAT conditions to enhance the robustness of polycube-map generation. We evaluate our method using the Thingi10k and ABC datasets. Results demonstrate that our VAT conditions expands the solvable space of polycubes and achieves higher quality all-hexahedral meshing for higher-connectivity or more complex models. Furthermore, we discuss the limitations associated with our proposed method.

Optimal transport (OT) has gained significant attention in deep learning as a powerful mathematical tool for transforming distributions. Specifically, in deep generative models, the incorporation of OT helps address issues such as training instability, vanishing gradients, and mode collapse. However, in these models, most of the OT mappings learned by neural networks are typically implicit, making it difficult to explicitly model the relationship between the source and target domains. This limitation reduces the interpretability of the model and hinders its applicability in conditional generation tasks. To address this issue, we introduce Nesterov's smoothing technique to smooth the Brenier potential, enabling the derivation of an explicit OT mapping that serves as the foundation for constructing an advanced generative model. The proposed model offers the following advantages. First, it explicitly captures the mapping between the source and target domains, thereby enhancing the interpretability of the generative process and enabling a novel pathway for conditional sample generation based on a smoothed approximation of OT mapping. Second, the model can generate new samples directly through an explicit OT mapping, eliminating the need for interpolation and rejection sampling commonly seen in traditional methods, thereby improving generation efficiency. Moreover, extensive experiments show that our proposed model achieves superior performance in both unconditional and conditional generation tasks.

Traditional variational models often fail to segment images in the presence of inhomogeneity or weak boundaries, partly due to their reliance on unreliable region metrics that quantify inhomogeneity based on a single mean value or a smoothed image serving as a mean function. The former, such as variance-based methods, are highly sensitive to image inhomogeneity, whereas the latter, such as local convolution-based approaches, lack a global receptive field. To address these issues, we employ an optimal transport-based data fidelity term in our segmentation objective functional. This term accounts for global differences between regions, resolving problems arising from local convolutions. It can also adaptively seek an optimized match between two probability density functions, proving more robust than relying solely on their mean values. Our proposed functional is minimized by gradually performing region merging. Experimental results demonstrate that our model outperforms state-of-the-art variational and deep learning models.

Unsigned distance fields (UDFs) provide a versatile framework for representing a diverse array of 3D shapes, encompassing both watertight and non-watertight geometries. Traditional UDF learning methods typically require extensive training on large 3D shape datasets, which is costly and necessitates re-training for new datasets. This paper presents a novel neural framework, LoSF-UDF, for reconstructing surfaces from 3D point clouds by leveraging local shape functions to learn UDFs. We observe that 3D shapes manifest simple patterns in localized regions, prompting us to develop a training dataset of point cloud patches characterized by mathematical functions that represent a continuum from smooth surfaces to sharp edges and corners. Our approach learns features within a specific radius around each query point and utilizes an attention mechanism to focus on the crucial features for UDF estimation. Despite being highly lightweight, with only 653 KB of trainable parameters and a modest-sized training dataset with 0.5 GB storage, our method enables efficient and robust surface reconstruction from point clouds without requiring for shape-specific training. Furthermore, our method exhibits enhanced resilience to noise and outliers in point clouds compared to existing methods. We conduct comprehensive experiments and comparisons across various datasets, including synthetic and real-scanned point clouds, to validate our method’s efficacy. Notably, our lightweight framework offers rapid and reliable initialization for other unsupervised iterative approaches, improving both the efficiency and accuracy of their reconstructions. Our project and code are available at https://jbhu67.github.io/LoSF-UDF.github.io/.

Adversarial attacks exploit the vulnerability of deep models against adversarial samples. Existing point cloud attackers are tailored to specific models, iteratively optimizing perturbations based on gradients in either a white-box or black-box setting. Despite their promising attack performance, they often struggle to produce transferable adversarial samples due to overfitting to the specific parameters of surrogate models. To overcome this issue, we shift our focus to the data distribution itself and introduce a novel approach named NoPain, which employs optimal transport (OT) to identify the inherent singular boundaries of the data manifold for cross-network point cloud attacks. Specifically, we first calculate the OT mapping from noise to the target feature space, then identify singular boundaries by locating non-differentiable positions. Finally, we sample along singular boundaries to generate adversarial point clouds. Once the singular boundaries are determined, NoPain can efficiently produce adversarial samples without the need of iterative updates or guidance from the surrogate classifiers. Extensive experiments demonstrate that the proposed end-to-end method outperforms baseline approaches in terms of both transferability and efficiency, while also maintaining notable advantages even against defense strategies. Code and model are available at https://github.com/cognaclee/nopain.

Abstract Topological properties play a crucial role in the analysis, reconstruction, and generation of 3D shapes. Yet, most existing research focuses primarily on geometric features, due to the lack of effective representations for topology. In this paper, we introduce TopoGen , a method that extracts both discrete and continuous topological descriptors–Betti numbers and persistence points–using persistent homology. These features provide robust characterizations of 3D shapes in terms of their topology. We incorporate them as conditional guidance in generative models for 3D shape synthesis, enabling topology‐aware generation from diverse inputs such as sparse and partial point clouds, as well as sketches. Furthermore, by modifying persistence points, we can explicitly control and alter the topology of generated shapes. Experimental results demonstrate that TopoGen enhances both diversity and controllability in 3D generation by embedding global topological structure into the synthesis process.

Existing level set models employ regularization based only on gradient information, 1D curvature or 2D curvature. For 3D image segmentation, however, an appropriate curvature-based regularization should involve a well-defined 3D curvature energy. This is the first paper to introduce a regularization energy that incorporates 3D scalar curvature for 3D image segmentation, inspired by the Einstein-Hilbert functional. To derive its Euler-Lagrange equation, we employ a two-step gradient descent strategy, alternately updating the level set function and its gradient. The paper also establishes the existence and uniqueness of the viscosity solution for the proposed model. Experimental results demonstrate that our proposed model outperforms other state-of-the-art models in 3D image segmentation.

Quad meshes are essential in geometric modeling and computational mechanics. Although learning-based methods for triangle mesh demonstrate considerable advancements, quad mesh generation remains less explored due to the challenge of ensuring coplanarity, convexity, and quad-only meshes. In this paper, we presentPoint2Quad, the first learning-based method for quad-only mesh generation from point clouds. The key idea is learning to identify quad mesh with fused pointwise and facewise features. Specifically, Point2Quad begins with a k-NN-based candidate generation considering the coplanarity and squareness. Then, two encoders are followed to extract geometric and topological features that address the challenge of quad-related constraints, especially by combining in-depth quadrilaterals-specific characteristics. Subsequently, the extracted features are fused to train the classifier with a designed compound loss. The final results are derived after the refinement by a quad-specific post-processing. Extensive experiments on both clear and noise data demonstrate the effectiveness and superiority of Point2Quad, compared to baseline methods under comprehensive metrics. The code and dataset are available athttps://github.com/cognaclee/Point2Quad.

Semi-supervised learning leverages insights from unlabeled data to enhance generalizability of the model, thereby decreasing the dependence on extensive labeled datasets. Most existing methods overly focus on local representations while neglecting the learning of global structures. On the one hand, given that labeled and unlabeled images are presumed to originate from the same distribution, it is probable that similar regional features observed in both types of images correspond to the same label. Current label propagation techniques, which predominantly propagate label information through the construction of graph structures or similarity matrices, heavily depend on localized information and are prone to converge to local optima. In contrast, optimal transport considers the entire distribution. This facilitates more comprehensive and efficient label propagation. On the other hand, current consistency regularization-based methods focus on the local view, we believe learning from a global geometric view may capture more information. Geometric moment information of the sample itself can constrain the overall geometric structure. Inspired by these observations, this paper introduces a semi-supervised medical image segmentation framework that integrates optimal transport and central moment consistency regularization (OTCMC) from a global perspective. Firstly, we pass label information from labeled data to unlabeled data by optimal transport. Secondly, we incorporate central moment consistency regularization to focus the network on the geometric structure of images. Our method achieves the state-of-the-art (SOTA) performance on a series of datasets, including the NIH pancreas, left atrium, brain tumor, and skin lesion dermoscopy datasets.

Recent CLIP-guided 3D generation methods have achieved promising results but struggle with generating faithful 3D shapes that conform with input text due to the gap between text and image embeddings. To this end, this paper proposes HOTS3D which makes the first attempt to effectively bridge this gap by aligning text features to the image features with spherical optimal transport (SOT). However, in high-dimensional situations, solving the SOT remains a challenge. To obtain the SOT map for high-dimensional features obtained from CLIP encoding of two modalities, we mathematically formulate and derive the solution based on Villani's theorem, which can directly align two hyper-sphere distributions without manifold exponential maps. Furthermore, we implement it by leveraging input convex neural networks (ICNNs) for the optimal Kantorovich potential. With the optimally mapped features, a diffusion-based generator is utilized to decode them into 3D shapes. Extensive quantitative and qualitative comparisons with state-of-the-art methods demonstrate the superiority of HOTS3D for text-to-3D generation, especially in the consistency with text semantics.

This paper presents a novel point cloud compression method COT-PCC by formulating the task as a constrained optimal transport (COT) problem. COT-PCC takes the bitrate of compressed features as an extra constraint of optimal transport (OT) which learns the distribution transformation between original and reconstructed points. Specifically, the formulated COT is implemented with a generative adversarial network (GAN) and a bitrate loss for training. The discriminator measures the Wasserstein distance between input and reconstructed points, and a generator calculates the optimal mapping between distributions of input and reconstructed point cloud. Moreover, we introduce a learnable sampling module for downsampling in the compression procedure. Extensive results on both sparse and dense point cloud datasets demonstrate that COT-PCC outperforms state-of-the-art methods in terms of both CD and PSNR metrics. Source codes are available at https://github.com/cognaclee/PCC-COT.

This paper introduces a novel method for reconstructing meshes from sparse point clouds by predicting edge connection. Existing implicit methods usually produce superior smooth and watertight meshes due to the isosurface extraction algorithms (e.g., Marching Cubes). However, these methods become memory and computationally intensive with increasing resolution. Explicit methods are more efficient by directly forming the face from points. Nevertheless, the challenge of selecting appropriate faces from enormous candidates often leads to undesirable faces and holes. Moreover, the reconstruction performance of both approaches tends to degrade when the point cloud gets sparse. To this end, we propose MEsh Reconstruction via edGE (MergeNet), which converts mesh reconstruction into local connectivity prediction problems. Specifically, MergeNet learns to extract the features of candidate edges and regress their distances to the underlying surface. Consequently, the predicted distance is utilized to filter out edges that lay on surfaces. Finally, the meshes are reconstructed by refining the triangulations formed by these edges. Extensive experiments on synthetic and real-scanned datasets demonstrate the superiority of MergeNet to SoTA explicit methods.

Optimal transport (OT) studies the most economical transformation of one probability measure into another, attracting attention across diverse fields and inspiring various OT-solving algorithms. However, adjusting the probability measure according to specific application requirements, such as achieving unbiased generated images or generating images with specific attributes, necessitates recalculating the OT mapping. This process may result in inefficiency and limited usage flexibility of existing algorithms. To address this, we propose a measure-driven neural solver for OT, the key of which is to construct a network module to learn Brenier’s height representation, and then compute the gradient of Brenier’s potential to derive the OT mapping. Our algorithm has two main advantages: i) It enables direct calculation or fine-tuning of the OT mapping when the target sample measure changes, enhancing efficiency. ii) For unbiased image generation or attribute-specific face generation, adjusting the posterior probability measure of the latent space in the pre-trained model suffices, without the need for additional auxiliary components, this highlights the flexibility of our algorithm. Extensive experiments demonstrate the excellent performance of our algorithm in debiased generation and controllable generation, and its flexibility and efficiency. In addition, both of these generation ways can enhance the classification performance of minority groups.

Designing thin-shell structures that are diverse, lightweight, and physically viable is a challenging task for traditional heuristic methods. To address this challenge, we present a novel parametric design framework for engraving regular, irregular, and customized patterns on thin-shell structures. Our method optimizes pattern parameters such as size and orientation, to ensure structural stiffness while minimizing material consumption. Our method is unique in that it works directly with shapes and patterns represented by functions, and can engrave patterns through simple function operations. By eliminating the need for remeshing in traditional FEM methods, our method is more computationally efficient in optimizing mechanical properties and can significantly increase the diversity of shell structure design. Quantitative evaluation confirms the convergence of the proposed method. We conduct experiments on regular, irregular, and customized patterns and present 3D printed results to demonstrate the effectiveness of our approach.

Intelligent Mesh Generation (IMG) represents a novel and promising field of research, utilizing machine learning techniques to generate meshes. Despite its relative infancy, IMG has significantly broadened the adaptability and practicality of mesh generation techniques, delivering numerous breakthroughs and unveiling potential future pathways. However, a noticeable void exists in the contemporary literature concerning comprehensive surveys of IMG methods. This paper endeavors to fill this gap by providing a systematic and thorough survey of the current IMG landscape. With a focus on 113 preliminary IMG methods, we undertake a meticulous analysis from various angles, encompassing core algorithm techniques and their application scope, agent learning objectives, data types, targeted challenges, as well as advantages and limitations. We have curated and categorized the literature, proposing three unique taxonomies based on key techniques, output mesh unit elements, and relevant input data types. This paper also underscores several promising future research directions and challenges in IMG.

Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent progress in designing fast samplers for DPMs achieves a trade-off between sampling speed and sample quality by knowledge distillation or adjusting the variance schedule or the denoising equation. However, it can’t be optimal in both aspects and often suffer from mode mixture in short steps. To tackle this problem, we innovatively regard inverse diffusion as an optimal transport (OT) problem between latents at different stages and propose the DPM-OT, a unified learning framework for fast DPMs with a direct expressway represented by OT map, which can generate high-quality samples within around 10 function evaluations. By calculating the semi-discrete optimal transport map between the data latents and the white noise, we obtain an expressway from the prior distribution to the data distribution, while significantly alleviating the problem of mode mixture. In addition, we give the error bound of the proposed method, which theoretically guarantees the stability of the algorithm. Extensive experiments validate the effectiveness and advantages of DPM-OT in terms of speed and quality (FID and mode mixture), thus representing an efficient solution for generative modeling. Source codes are available at https://github.com/cognaclee/DPM-OT.

Abstract Efficiently optimizing the internal structure of 3D printing models is a critical focus in the field of industrial manufacturing, particularly when designing self‐supporting structures that offer high stiffness and lightweight characteristics. To tackle this challenge, this research introduces a novel approach featuring a self‐supporting polyhedral structure and an efficient optimization algorithm. Specifically, the internal space of the model is filled with a combination of self‐supporting octahedrons and tetrahedrons, strategically arranged to maximize structural integrity. Our algorithm optimizes the wall thickness of the polyhedron elements to satisfy specific stiffness requirements, while ensuring efficient alignment of the filled structures in finite element calculations. Our approach results in a considerable decrease in optimization time. The optimization process is stable, converges rapidly, and consistently delivers effective results. Through a series of experiments, we have demonstrated the effectiveness and efficiency of our method in achieving the desired design objectives.

Optimal transport (OT) plays an essential role in various areas like machine learning and deep learning. However, computing discrete optimal transport plan for large scale problems with adequate accuracy and efficiency is still highly challenging. Recently, methods based on the Sinkhorn algorithm add an entropy regularizer to the prime problem and get a trade off between efficiency and accuracy. In this paper, we propose a novel algorithm to further improve the efficiency and accuracy based on Nesterov's smoothing technique. Basically, the non-smooth c-transform of the Kantorovich potential is approximated by the smooth Log-Sum-Exp function, which finally smooths the original non-smooth Kantorovich dual functional. The smooth Kantorovich functional can be optimized by the fast proximal gradient algorithm (FISTA) efficiently. Theoretically, the computational complexity of the proposed method is lower than current estimation of the Sinkhorn algorithm in terms of the precision. Empirically, compared with the Sinkhorn algorithm, our experimental results demonstrate that the proposed method achieves faster convergence and better accuracy with the same parameter.

3D medical images consist of voxels with points, edges, faces, and volumes. A fascinating question is how to compute the shortest basis of the first homology group of a 3D image. The fastest time complexity known for this question is O($n^{\omega}+n^{2}$g), where n is the size of voxels and $\omega \lt$ 2.3728639 is a quantity so that two n×n matrices can be multiplied in O($n^{\omega}$) time. But it is still slow in practical applications. We first construct a hexahedral mesh of an arbitrary domain of a 3D image and second propose an approximate algorithm with time complexity O($n^{\omega}$) to calculate the minimal homology basis for the 3D images. Experiments show that our approximate algorithm is very close to the exact algorithm. We demonstrate the effectiveness of our algorithm in segmenting the semicircular canals, the organ with complex topology.

Existing learning-based methods usually train a point cloud upsampling model with synthesized, paired sparse-dense point clouds. However, the distribution gap between synthesized and real data limits the performance and generalization. To solve this problem, we innovatively regard the upsamplig task as an optimal transport (OT) problem from sparse to dense point cloud. Further we propose PU-CycGAN, a cycle network that consists of a Densifier, Sparsifier and two discriminators. It can be directly trained for upsampling with unpaired real sparse point clouds, so that the distribution gap can be filled via the learning. Especially, quadratic Wasserstein distance is introduced for the stable training. Extensive experiments on both synthetic and real-scanned datasets validate the effectiveness and advantages in terms of distribution uniformity, underlying surface representation and applicability to real data. The source code is available at https://github.com/cognaclee/PU-CycGAN.

An optimal transportation map finds the most economical way to transport one probability measure to the other. It has been applied in a broad range of applications in vision, deep learning and medical images. By Brenier theory, computing the optimal transport map is equivalent to solving a Monge-Ampère equation. Due to the highly non-linear nature, the computation of optimal transportation maps in large scale is very challenging.This work proposes a simple but powerful method, the FFT-OT algorithm, to tackle this difficulty based on three key ideas. First, solving Monge-Ampère equation is converted to a fixed point problem; Second, the obliqueness property of optimal transportation maps are reformulated as Neumann boundary conditions on rectangular domains; Third, FFT is applied in each iteration to solve a Poisson equation in order to improve the efficiency.Experiments on surfaces captured from 3D scanning and reconstructed from medical imaging are conducted, and compared with other existing methods. Our experimental results show that the proposed FFT-OT algorithm is simple, general and scalable with high efficiency and accuracy.

Shape analysis has been playing an important role in early diagnosis and prognosis of neurodegenerative diseases such as Alzheimer's diseases (AD). However, obtaining effective shape representations remains challenging. This paper proposes to use the Alexandrov polyhedra as surface-based shape signatures for cortical morphometry analysis. Given a closed genus-0 surface, its Alexandrov polyhedron is a convex representation that encodes its intrinsic geometry information. We propose to compute the polyhedra via a novel spherical optimal transport (OT) computation. In our experiments, we observe that the Alexandrov polyhedra of cortical surfaces between pathology-confirmed AD and cognitively unimpaired individuals are significantly different. Moreover, we propose a visualization method by comparing local geometry differences across cortical surfaces. We show that the proposed method is effective in pinpointing regional cortical structural changes impacted by AD.

Optimal transportation plays a fundamental role in many fields in engineering and medicine, including surface parameterization in graphics, registration in computer vision, and generative models in deep learning. For quadratic distance cost, optimal transportation map is the gradient of the Brenier potential, which can be obtained by solving the Monge-Ampère equation. Furthermore, it is induced to a geometric convex optimization problem. The Monge-Ampère equation is highly non-linear, and during the solving process, the intermediate solutions have to be strictly convex. Specifically, the accuracy of the discrete solution heavily depends on the sampling pattern of the target measure. In this work, we propose a self-adaptive sampling algorithm which greatly reduces the sampling bias and improves the accuracy and robustness of the discrete solutions. Experimental results demonstrate the efficiency and efficacy of our method.

Neural network pruning is widely applied to various mobile applications. Previous pruning methods mainly leverage ad-hoc criteria to evaluate channel importance. In this paper, we propose an effective metaheuristic sub-structure selection (MetaSelection) method for neural network pruning. MetaSelection exploits evolutionary algorithm (EA) to search the proper sub-structure satisfying the resource constraints. In comparison with previous AutoML based methods, MetaSelection can automatically achieve the pruning rate and channel selection at the same time instead of hand-crafted criteria in a cascaded way. Regarding the tremendous search space of channel selection as a combinatorial optimization problem, we further utilize a coarse-to-fine strategy and the novel probability distribution crossover (PDC) to speed up the search procedure. Besides, MetaSelection prunes the network globally rather than in a layer-by-layer way. We evaluate MetaSelection on several appealing deep neural networks, achieving superior results with adaptive depth and width. Concretely, on ImageNet, MetaSelection achieves a top-1 accuracy of 71.5% on MobileNetV2 under 70% FLOPs constraint and a FLOPs reduction of 30% with 76.4% top-1 accuracy for ResNet50.

Abstract Based on mesh deformation, we present a unified mesh parametrization algorithm for both planar and spherical domains. Our approach can produce intermediate frames from the original meshes to the targets. We derive and define a novel geometric flow: ‘unit normal flow (UNF)’ and prove that if UNF converges, it will deform a surface to a constant mean curvature (CMC) surface, such as planes and spheres. Our method works by deforming meshes of disk topology to planes, and spherical meshes to spheres. Our algorithm is robust, efficient, simple to implement. To demonstrate the robustness and effectiveness of our method, we apply it to hundreds of models of varying complexities. Our experiments show that our algorithm can be a competing alternative approach to other state‐of‐the‐art mesh parametrization methods. The unit normal flow also suggests a potential direction for creating CMC surfaces.

In the maintenance work of tunnels, images are often used to detect diseases, but collections of tunnel images are limited by the tunnel environment and working time. Three-dimensional laser scanning technology can acquire high-precision tunnel information efficiently, and the main problem to be solved by using this technology to collect tunnel inner wall images is the dimensionality reduction of the laser tunnel point cloud data. This letter proposes a tunnel surface parameterization algorithm based on a harmonic map, where a 3-D tunnel point cloud is used as a data source to reconstruct a triangle mesh model of the tunnel and then generate a harmonic map depth map of the tunnel inner wall on the triangle mesh. We can obtain the spatial distribution and position information of the appendages and detect whether there are cracks, water leakage, falling pieces, and other diseases by the depth images. The results of this study indicate that the proposed algorithm is suitable for tunnels of various shapes and has low area distortion, which can better avoid the loss of information during dimensionality reduction. Compared with other existing methods, the algorithm has higher efficiency and applicability.

Skull registration plays a fundamental role in forensic science and is crucial for craniofacial reconstruction. The complicated topology, lack of anatomical features, and low quality reconstructed mesh make skull registration challenging. In this work, we propose an automatic skull registration method based on the discrete uniformization theory, which can handle complicated topologies and is robust to low quality meshes. We apply dynamic Yamabe flow to realize discrete uniformization, which modifies the mesh combinatorial structure during the flow and conformally maps the multiply connected skull surface onto a planar disk with circular holes. The 3D surfaces can be registered by matching their planar images using harmonic maps. This method is rigorous with theoretic guarantee, automatic without user intervention, and robust to low mesh quality. Our experimental results demonstrate the efficiency and efficacy of the method.

Abstract There are many methods proposed for generating polycube polyhedrons, but it lacks the study about the possibility of generating polycube polyhedrons. In this paper, we prove a theorem for characterizing the necessary condition for the skeleton graph of a polycube polyhedron, by which Steinitz's theorem for convex polyhedra and Eppstein's theorem for simple orthogonal polyhedra are generalized to polycube polyhedra of any genus and with non‐simply connected faces. Based on our theorem, we present a faster linear algorithm to determine the dimensions of the polycube shape space for a valid graph, for all its possible polycube polyhedrons. We also propose a quadratic optimization method to generate embedding polycube polyhedrons with interactive assistance. Finally, we provide a graph‐based framework for polycube mesh generation, quadrangulation, and all‐hex meshing to demonstrate the utility and applicability of our approach.

Polycube construction and deformation are essential problems in computer graphics. In this paper, we present a robust, simple, efficient, and automatic algorithm to deform the meshes of arbitrary shapes into polycube form. We derive a clear relationship between a mesh and its corresponding polycube shape. Our algorithm is edge-preserving, and works on surface meshes with or without boundaries. Our algorithm outperforms previous ones with respect to speed, robustness, and efficiency. Our method is simple to implement. To demonstrate the robustness and effectivity of our method, we have applied it to hundreds of models of varying complexity and topology. We demonstrate that our method compares favorably to other state-of-the-art polycube deformation methods.

3D dynamic surface tracking is an important research problem and plays a vital role in many computer vision and medical imaging applications. However, it is still challenging to efficiently register surface sequences which has large deformations and strong noise. In this paper, we propose a novel automatic method for non-rigid 3D dynamic surface tracking with surface Ricci flow and Teichmüller map methods. According to quasi-conformal Teichmüller theory, the Techmüller map minimizes the maximal dilation so that our method is able to automatically register surfaces with large deformations. Besides, the adoption of Delaunay triangulation and quadrilateral meshes makes our method applicable to low quality meshes. In our work, the 3D dynamic surfaces are acquired by a high speed 3D scanner. We first identified sparse surface features using machine learning methods in the texture space. Then we assign landmark features with different curvature settings and the Riemannian metric of the surface is computed by the dynamic Ricci flow method, such that all the curvatures are concentrated on the feature points and the surface is flat everywhere else. The registration among frames is computed by the Teichmüller mappings, which aligns the feature points with least angle distortions. We apply our new method to multiple sequences of 3D facial surfaces with large expression deformations and compare them with two other state-of-the-art tracking methods. The effectiveness of our method is demonstrated by the clearly improved accuracy and efficiency.

This work introduces a novel surface registration method based on foliation. A foliation decomposes the surface into a family of closed loops, such that the decomposition has local tensor product structure. By projecting each loop to a point, the surface is collapsed into a graph. Two homeomorphic surfaces with consistent foliations can be registered by first matching their foliation graphs, then matching the corresponding leaves. This foliation based method is capable of handling surfaces with complicated topologies and large non-isometric deformations, rigorous with solid theoretic foundation, easy to implement, robust to compute. The result mapping is diffeomorphic. Our experimental results show the efficiency and efficacy of the proposed method.

Robot Coverage Path planning (i.e., the process of providing full coverage of a given domain by one or multiple robots) is a classical problem in the field of robotics and motion planning. The goal of such planning is to provide nearly full coverage while also minimize duplicately visited area. In this paper, we focus on the scenario of path planning on general surface, including planar domains with complex topology, complex terrain, and general surface in 3D space. Our approach described in this paper adopts a natural, intrinsic and global parametrization of the surface for robot path planning, namely the holomorphic quadratic differentials. We give each point on the surface a uv-coordinates naturally represented by a complex number, except for a small number of zero points (singularities). We show that natural, efficient robot paths can be obtained by using such coordinate systems. The method is based on intrinsic geometry and thus can be adapted to general surface exploration in 3D.

Whereas traditional finite element methods use meshes to define domain geometry, weighted extended B-spline finite element methods rely on a weight function. A weight function is a smooth, strictly positive function which vanishes at the domain boundary at an appropriate rate. We describe a method for generating weight functions for a general class of domains based on A-splines. We demonstrate this approach and address the relationship between weight function quality and error in the resulting finite element solutions.