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Neuron morphology reconstruction from high-resolution imaging data is essential for understanding the structure and function of the brain in neuroscience. However, previous methods cannot achieve both water-tight and high performance in surface mesh reconstruction of large-scale neurons. Thus, this paper proposes a novel neuronal surface mesh reconstruction algorithm based on isosurface extraction, virtual memory management, and parallel computation. The space of a neuron is firstly divided into blocks, and they are organized as a sparse octree to handle large-scale neurons with long projection. We then perform voxelization and isosurface extraction on valid blocks based on the skeleton model of the neuron to ensure the generated mesh that is water-tightness, and the quality and the density of the mesh are controllable. Since each block is processed independently, the reconstruction can be performed in parallel for high performance and partially for interactive modification during neuron proofreading. Experiments demonstrate that the proposed algorithm can generate water-tight neuronal surface meshes effectively and satisfy the needs of interactive visualization and correction. [ABSTRACT FROM AUTHOR]

Slicing 3D polygonal meshes is a fundamental operation in various applications such as virtual surgery, garment simulation, and game development. Existing methods primarily slice meshes using either a single line or a set of line segments approximating a smooth curve. This paper introduces a novel approach to freely slice a triangle mesh using a freeform curve without discretizing it into line segments. The user draws a stroke on the screen, defining the desired cutting trajectory. Subsequently, a freeform curve approximating this stroke is generated and extended into a ruled surface in the user's viewing direction. To efficiently compute intersections between the ruled surface and a triangle mesh, the Line–Surface Intersection (LSI) problem is broken down into two subproblems: Plane–Curve Intersection (PCI) followed by Line–Line Intersection (LLI). Intersection points are then connected to form polylines, effectively cutting the mesh into multiple submeshes. To ensure the solidity of the submeshes, cross-sections are generated by trimming the ruled surface along the polylines and merged with the corresponding submeshes. Our method empowers users to slice triangle meshes along arbitrary trajectories encompassing both straight and freely curved paths while preserving efficiency and accuracy. The effectiveness of the proposed approach is demonstrated through experimental results showing various examples of mesh slicing. [ABSTRACT FROM AUTHOR]

Slicing 3D polygonal meshes is a fundamental operation in various applications such as virtual surgery, garment simulation, and game development. Existing methods primarily slice meshes using either a single line or a set of line segments approximating a smooth curve. This paper introduces a novel approach to freely slice a triangle mesh using a freeform curve without discretizing it into line segments. The user draws a stroke on the screen, defining the desired cutting trajectory. Subsequently, a freeform curve approximating this stroke is generated and extended into a ruled surface in the user’s viewing direction. To efficiently compute intersections between the ruled surface and a triangle mesh, the Line–Surface Intersection (LSI) problem is broken down into two subproblems: Plane–Curve Intersection (PCI) followed by Line–Line Intersection (LLI). Intersection points are then connected to form polylines, effectively cutting the mesh into multiple submeshes. To ensure the solidity of the submeshes, cross-sections are generated by trimming the ruled surface along the polylines and merged with the corresponding submeshes. Our method empowers users to slice triangle meshes along arbitrary trajectories encompassing both straight and freely curved paths while preserving efficiency and accuracy. The effectiveness of the proposed approach is demonstrated through experimental results showing various examples of mesh slicing.

In recent years, high-fidelity three-dimensional (3D) oracle bone models (3D-OBMs) have received extensive attention from oracle bone experts due to their unparalleled reducibility to real oracle bone. In the research process of 3D-OBMs, the first procedure is to extract oracle bone inscriptions (OBIs) from the model to form individual oracle bone characters (OBCs). However, the manual extraction of OBIs is a time-consuming and labor-intensive task that relies heavily on oracle bone knowledge. To address these problems, we propose a texture-mapping-based OBI extractor (tm-OBIE), which leverages the symmetrical characteristics of the texture mapping process and is able to extract 3D-OBIs from 3D-OBMs saved as a wavefront file. The OBIs in the texture file were first located using a trained 2D object detector. After that, the 3D mesh area, where the OBIs are located, was obtained using an inverse texture mapping method. Thirdly, a specific 2D plane was fitted using the centroid of triangular faces in the flat regions of the mesh via a singular value decomposition (SVD) method. Finally, by measuring the distances between the triangle meshes and the fitted plane, the meshes of the 3D-OBIs were obtained. This paper verifies the feasibility of this method via experiments and analyzes the possibility of using the algorithm framework for extracting other ancient characters from their corresponding 3D models. [ABSTRACT FROM AUTHOR]

Multi-view Stereo (MVS) meshes suffer from occlusions or missing data, making most surface reconstruction methods invalid. Due to data imperfections, existing methods, just like PolyFit, have made a trade-off between reconstruction accuracy and time consumption. We propose a novel approach that automatically reconstructs a building surface model from raw triangular mesh with data incompleteness. Unlike existing methods that extract high-quality primitives, our method focuses on assemblies of primitives to control the level of geometric detail in the reconstructed models. We design a topological relationship of the primitives to form a plane connection graph. To be precise, we first combine the scalability of shapes with plane primitives. Then strong and soft connections between primitives are constructed by calculating the confidence of the plane intersection in space. Furthermore, the topological relations of all primitives are encoded into an undirected graph. Finally, a watertight and manifold model is extracted from the faces of a candidate set by energy minimization. Experiments on the Helsinki 3D dataset demonstrate the superiority of our method in time consumption and reconstruction error, as measured by Hausdorff distance. Our method outperforms other primitive-based algorithms in handling non-planar structures. Even when dealing with imperfect data, a watertight model is still obtained. [Display omitted] • Due to the occlusion caused by various reasons such as trees, we designed a lightweight data structure and general strategy to rectify the building data defects. A confidence strategy combining graph structure is proposed, which reduces the time consumption compared with the state-of-art methods and captures more accurate geometric details within the reconstruction pipeline to generate building models with higher levels of detail. [ABSTRACT FROM AUTHOR]

In recent years, high-fidelity three-dimensional (3D) oracle bone models (3D-OBMs) have received extensive attention from oracle bone experts due to their unparalleled reducibility to real oracle bone. In the research process of 3D-OBMs, the first procedure is to extract oracle bone inscriptions (OBIs) from the model to form individual oracle bone characters (OBCs). However, the manual extraction of OBIs is a time-consuming and labor-intensive task that relies heavily on oracle bone knowledge. To address these problems, we propose a texture-mapping-based OBI extractor (tm-OBIE), which leverages the symmetrical characteristics of the texture mapping process and is able to extract 3D-OBIs from 3D-OBMs saved as a wavefront file. The OBIs in the texture file were first located using a trained 2D object detector. After that, the 3D mesh area, where the OBIs are located, was obtained using an inverse texture mapping method. Thirdly, a specific 2D plane was fitted using the centroid of triangular faces in the flat regions of the mesh via a singular value decomposition (SVD) method. Finally, by measuring the distances between the triangle meshes and the fitted plane, the meshes of the 3D-OBIs were obtained. This paper verifies the feasibility of this method via experiments and analyzes the possibility of using the algorithm framework for extracting other ancient characters from their corresponding 3D models.

The 3D refinement modeling of the orebody provides an important guarantee for the estimation of the resources and reserves of an ore deposit. Implicit modeling techniques can effectively improve the efficiency of orebody modeling and facilitate the dynamic updating of the model. However, due to the problems of ambiguity and missing features during implicit surface interpolation and implicit surface reconstruction, the mesh models of orebodies obtained by means of implicit modeling techniques do not easily snap to the geological feature points and feature polylines obtained based on geological sampling data. In essence, all models are inaccurate, but geological sampling data are very useful and valuable, which should be accurately and effectively involved in the orebody modeling process. This would help to improve the reliability of resource estimation and mining design. The main contribution of this paper is the proposal of a method for accurately snapping orebody features after implicit modeling. This method enables the orebody model to snap accurately to the geological feature points and feature polylines and realizes the accurate clipping of the model boundary. We tested the method with real geological datasets. The results showed that the method is applicable and effective when the geological feature points and feature polylines are close to those of the orebody mesh model and the shape trend changes little, and the model can thus meet the practical application requirements of mines. [ABSTRACT FROM AUTHOR]

Convolutionalneural networks (CNNs) have made great breakthroughs in two-dimensional (2D) computer vision. However, their irregular structure makes it hard to harness the potential of CNNs directly on meshes. A subdivision surface provides a hierarchical multi-resolution structure in which each face in a closed 2-manifold triangle mesh is exactly adjacent to three faces. Motivated by these two observations, this article presents SubdivNet, an innovative and versatile CNN framework for three-dimensional (3D) triangle meshes with Loop subdivision sequence connectivity. Making an analogy between mesh faces and pixels in a 2D image allows us to present a mesh convolution operator to aggregate local features from nearby faces. By exploiting face neighborhoods, this convolution can support standard 2D convolutional network concepts, e.g., variable kernel size, stride, and dilation. Based on the multi-resolution hierarchy, we make use of pooling layers that uniformly merge four faces into one and an upsampling method that splits one face into four. Thereby, many popular 2D CNN architectures can be easily adapted to process 3D meshes. Meshes with arbitrary connectivity can be remeshed to have Loop subdivision sequence connectivity via self-parameterization, making SubdivNet a general approach. Extensive evaluation and various applications demonstrate SubdivNet's effectiveness and efficiency. [ABSTRACT FROM AUTHOR]

Archaeological steles having a rough surface due to long periods of weathering make recognizing the inscription difficult. In this paper, we propose a machine learning-based method to extract reliefs for the inscription from a rough stele surface. Relief candidate segments are initially obtained by using a curvature-based method, which include not only actual reliefs but also noises such as dents and scratches. Then, relief segments are selected using a support vector machine classifier that is trained with various features extracted from relief candidate segments. While conventional methods using a single geometric feature easily fail to detect reliefs from the rough surface, the proposed method utilizes 79-dimensional features consisting of appearance-based, cross section-based, and local extrema-based characteristics of each candidate segment to determine whether the segment is relief or not. Using the proposed method, the inscription of the stele Musul-ojakbi made during the Silla Dynasty AD578 were completely recognized. The experimental results demonstrate that the proposed method accurately extracts reliefs and achieves the highest performance on the rough stele data. The performance of the proposed method is about 8.95% and 10.4% higher than the best of the conventional methods in terms of the F1-score and the SIRI, respectively.

Ancient stelae are considered important historical sources. However, it is a challenge to recognize the inscriptions carved on stelae that have rough surfaces due to prolonged weathering. In this paper, we propose a deep learning-based method to extract engraved regions from the 3D scanned mesh of a stela. First, the uneven distribution of vertices in the mesh is transformed using a mesh subdivision method such that the vertices in the mesh are uniformly distributed. Then, surface features (depth, concave features, and local surface features) are extracted from the subdivided mesh. The depth represents the basic shape of the mesh and is obtained from the aligned mesh. The concave features effectively represent concave regions by using a Frangi filter, and the local surface features have the spin image technique applied to describe the fine shapes of neighboring vertices relative to a vertex. The mesh and the surface features are rasterized into feature images, and engraved regions are segmented from the feature images by using a FC-DenseNet. Our experiments confirm that the proposed method effectively extracts engraved regions of the inscriptions from the rough surface of a stela and it shows robustness to noisy and extremely abraded characters. The proposed method outperformed the second-best method, obtaining an F1 score, IoU, and SIRI of approximately 2.95%, 3.65%, and 7.53%, respectively.

In metal additive manufacturing, geometries with high aspect ratio (AR) features are often associated with defects caused by thermal stresses and other related build failures. Ideally, excessively high AR features would be detected and removed in the design phase to avoid unwanted failure during manufacture. However, AR is scale and orientation independent and identifying features across all scales and orientations is exceptionally challenging. Furthermore, not all high AR features are as easy to recognise as thin walls and fine needles. There is therefore a pressing need for further development in the field of problematic features detection for additive manufacturing processes. In this work, a dimensionless ratio (D1/D2) based on two distance metrics that are extracted from triangulated mesh geometries is proposed. Based on this method, geometries with different features (e.g. thin wall, helices and polyhedra) were generated and evaluated to produce metrics that are similar to AR. The prediction results are compared with known theoretical AR values of typical geometries.By combining this metric with mesh segmentation, this method was further extended to analyse the geometry with complex features. The proposed method provides a powerful, general and promising way to automatically detect high AR features and tackle the relevant defect issues prior to manufacture. [ABSTRACT FROM AUTHOR]

3D models are commonly used in computer vision and graphics. With the wider availability of mesh data, an efficient and intrinsic deep learning approach to processing 3D meshes is in great need. Unlike images, 3D meshes have irregular connectivity, requiring careful design to capture relations in the data. To utilize the topology information while staying robust under different triangulations, we propose to encode mesh connectivity using Laplacian spectral analysis, along with mesh feature aggregation blocks (MFABs) that can split the surface domain into local pooling patches and aggregate global information amongst them. We build a mesh hierarchy from fine to coarse using Laplacian spectral clustering, which is flexible under isometric transformations. Inside the MFABs there are pooling layers to collect local information and multi-layer perceptrons to compute vertex features of increasing complexity. To obtain the relationships among different clusters, we introduce a Correlation Net to compute a correlation matrix, which can aggregate the features globally by matrix multiplication with cluster features. Our network architecture is flexible enough to be used on meshes with different numbers of vertices. We conduct several experiments including shape segmentation and classification, and our method outperforms state-of-the-art algorithms for these tasks on the ShapeNet and COSEG datasets. [ABSTRACT FROM AUTHOR]

The topology optimization methodology is widely applied in industrial engineering to design lightweight and efficient components. Despite that, many techniques based on structural optimization return a digital model that is far from being directly manufactured, mainly because of surface noise given by spikes and peaks on the component. For this reason, mesh post-processing is needed. Surface smoothing is one of the numerical procedures that can be applied to a triangulated mesh file to return a more appealing geometry. In literature, there are many smoothing algorithms available, but especially those based on the modification of vertex position suffer from high mesh shrinkage and loss of important geometry features like holes and surface planarity. For these reasons, an improved vertex-based algorithm based on Vollmer's surface smoothing has been developed and introduced in this work along with two case studies included to evaluate its performances compared with existent algorithms. The innovative approach herein developed contains some sub-routines to mitigate the issues of common algorithms, and confirms to be efficient and useful in a real-life industrial context. Thanks to the developed functions able to recognize the geometry feature to be frozen during the smoothing process, the user's intervention is not required to guide the procedure to get proper results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel approach that reconstructs the indoor scene in a structure-aware manner and produces two meshes with different levels of abstraction. To be precise, we start from the raw triangular mesh of indoor scene and decompose it into two parts: structure and non-structure objects. On the one hand, structure objects are defined as significant permanent parts in the indoor environment such as floors, ceilings and walls. In the proposed algorithm, structure objects are abstracted by planar primitives and assembled into a polygonal structure mesh. This step produces a compact structure-aware watertight model that decreases the complexity of original mesh by three orders of magnitude. On the other hand, non-structure objects are movable objects in the indoor environment such as furniture and interior decoration. Meshes of these objects are repaired and simplified according to their relationship with respect to structure primitives. Finally, the union of all the non-structure meshes and structure mesh comprises the scene mesh. Note that structure mesh and scene mesh preserve various levels of abstraction and can be used for different applications according to user preference. Our experiments on both LIDAR and RGBD data scanned from simple to large scale indoor scenes indicate that the proposed framework generates structure-aware results while being robust and scalable. It is also compared qualitatively and quantitatively against popular mesh approximation, floorplan generation and piecewise-planar surface reconstruction methods to demonstrate its performance. [ABSTRACT FROM AUTHOR]

• The irregularity and complexity of mesh data make shape segmentation challenging. • Mesh data are similar to point cloud data in spatial property so shape segmentation can be treated as a pointwise labeling problem. • Spatial information of mesh data is able to be learned by a point based network architecture by transforming shapes into point sets. • A simple and effective shape segmentation method which treats mesh segmentation as point labeling by converting each face into its barycenter and normal vector per shape with the spatial information of given shape preserving. • A intuitive and efficient operation, called Barycentric Dual Graph Edge Convolution (BDGEC), extracts edge features by operating over the nodes of Barycentric Dual Graph (BDG) intrinsic for the given shape. • A novel point based DNN, named LGCP Net, is proposed for mesh segmentation which can capture local and global features of shape efficient to obtain satisfying segmentation performance. [Display omitted] Segmenting 3D shapes represented by meshes remains a challenging problem, due to the irregularity and complexity of meshes. Point cloud, on the other hand, can be considered as the simplest no-frills approximation for meshes. Therefore, in this paper, we regard the shape segmentation problem as a point labeling task: Given a shape, we first transform it into points encoding barycenters and normal vectors of faces. Then we construct a Barycentric Dual Graph (BDG) on the transformed points, and propose a Barycentric Dual Graph Edge Convolution (BDGEC) to extract features from the graph. Based on the BDGEC, we further propose a novel point-based deep neural network (DNN) named local-global combined point-based network (LGCPNet). Our LGCPNet consists of three modules, of which the Local Module and Global Module capture local and global features respectively, while the Fusion Module uses a gate mechanism to aggregate local features and global features, and obtain the point labeling result. Comprehensive experimental results on various datasets demonstrate that the proposed network inherits the merits of point-based DNNs and achieves the state-of-the-art performance. [ABSTRACT FROM AUTHOR]

The 3D refinement modeling of the orebody provides an important guarantee for the estimation of the resources and reserves of an ore deposit. Implicit modeling techniques can effectively improve the efficiency of orebody modeling and facilitate the dynamic updating of the model. However, due to the problems of ambiguity and missing features during implicit surface interpolation and implicit surface reconstruction, the mesh models of orebodies obtained by means of implicit modeling techniques do not easily snap to the geological feature points and feature polylines obtained based on geological sampling data. In essence, all models are inaccurate, but geological sampling data are very useful and valuable, which should be accurately and effectively involved in the orebody modeling process. This would help to improve the reliability of resource estimation and mining design. The main contribution of this paper is the proposal of a method for accurately snapping orebody features after implicit modeling. This method enables the orebody model to snap accurately to the geological feature points and feature polylines and realizes the accurate clipping of the model boundary. We tested the method with real geological datasets. The results showed that the method is applicable and effective when the geological feature points and feature polylines are close to those of the orebody mesh model and the shape trend changes little, and the model can thus meet the practical application requirements of mines.

This article presents a way of optimizing the conduction topology for heat-generating structures by means of transformable triangular mesh (TTM) algorithm which is implemented in an explicit and geometrical way. Unlike the traditional optimization approaches, the proposed method capitalizes on the use of a special morphing algorithm to generate optimal topologies from a genus zero surface. In this method, the initial geometry is firstly converted into triangular mesh and stored as a half-edge data structure. Then, the mesh operations (i.e., subdivision, split, and refinement) are employed to activate the geometry to move, split, and deform upon the underlying finite element mesh so that the conduction topology can be achieved by optimizing the positions and orientations of the triangular grids. The unique feature of the mesh operation is the split, which makes the geometries have different number of faces, edges, vertices as the initial one, and therefore different genus number between these geometries. This method renders the optimization process more flexibility. Finally, some examples with verification results are presented to demonstrate that TTM algorithm is capable of proposing solutions having almost the same cooling effectiveness with less computing resources compared with the commonly used density approaches. [ABSTRACT FROM AUTHOR]

• We present co-skeletons, a new method that computes consistent curve skeletons for 3D shapes from a given family. • We compute co-skeletons in terms of sampling density and semantic relevance, while preserving the desired characteristics of traditional, per-shape curve skeletonization approaches. • Our approach achieves more concise and family-consistent skeletons when compared to traditional per-shape methods. • We show the utility of our method by using co-skeletons for shape segmentation and shape blending on benchmark data. We present co-skeletons, a new method that computes consistent curve skeletons for 3D shapes from a given family. We compute co-skeletons in terms of sampling density and semantic relevance, while preserving the desired characteristics of traditional, per-shape curve skeletonization approaches. We take the curve skeletons extracted by traditional approaches for all shapes from a family as input, and compute semantic correlation information of individual skeleton branches to guide an edge-pruning process via skeleton-based descriptors, clustering, and a voting algorithm. Our approach achieves more concise and family-consistent skeletons when compared to traditional per-shape methods. We show the utility of our method by using co-skeletons for shape segmentation and shape blending on real-world data. [ABSTRACT FROM AUTHOR]

Scanning electron microscopy (SEM) has been frequently used for size and shape measurements of particles. SEM images offer twodimensional (2D) information about a particle's lateral dimensions. Unfortunately, information about the particle's three-dimensional (3D) size and shape remains unavailable. To resolve this issue, I propose a new concept in SEM: 3D particle metrology obtained by applying structure-from-motion (SfM) algorithms to multiple rotational SEM images of particles deposited onto a cylindrical substrate to generate a 3D model from which size and shape information can be extracted. Particles can have any size that is suitable for SEM imaging. SEM images of the sample can be acquired from 0° to 360° using a rotational-tip SEM substage. Here, I will discuss the concept and, for clarity, illustrate it with aquarium gravel particles that are glued onto a craft roll and imaged optically before generating the 3D model of that handmade craft. Future work will include the experimental SEM realization, as well as further development of the SfM algorithms. In my view, this proposed concept may become an integral part of SEM-based particle metrology. [ABSTRACT FROM AUTHOR]

Simplicial complexes are widely used to discretize shapes. In low dimensions, a 3D shape is represented by discretizing its boundary surface, encoded as a triangle mesh, or by discretizing the enclosed volume, encoded as a tetrahedral mesh. High‐dimensional simplicial complexes have recently found their application in topological data analysis. Topological data analysis aims at studying a point cloud P, possibly embedded in a high‐dimensional metric space, by investigating the topological characteristics of the simplicial complexes built on P. Analysing such complexes is not feasible due to their size and dimensions. To this aim, the idea of simplifying a complex while preserving its topological features has been proposed in the literature. Here, we consider the problem of efficiently simplifying simplicial complexes in arbitrary dimensions. We provide a new definition for the edge contraction operator, based on a top‐based data structure, with the objective of preserving structural aspects of a simplicial shape (i.e., its homology), and a new algorithm for verifying the link condition on a top‐based representation. We implement the simplification algorithm obtained by coupling the new edge contraction and the link condition on a specific top‐based data structure, that we use to demonstrate the scalability of our approach. [ABSTRACT FROM AUTHOR]

Creating realistic digital 3D avatars has been getting more attention thanks to the introduction of new multimedia formats such as augmented and virtual reality. An important factor making avatars realistic is clothes. In this paper, we investigate a new method to reconstruct realistic garments from a set of images and body information. Early methods working on realistic images struggle to faithfully reconstruct the garment details. As deep learning is increasingly applied to geometric data which can conveniently represent garments, we devise a novel deep learning-based solution to the garment reconstruction problem. We offer a new perspective on the reconstruction problem and treat it as a reversion of the smoothing diffusion process. To achieve this goal, we propose to deform the smoothed human mesh into a clothed human via a Double Reverse Diffusion (DReD) process. For the first reverse diffusion, we introduce a novel operator called Graph Long Short-Term Memory (GraphLSTM) which recursively diffuses features to produce a deformed mesh by modeling the relationships between vertices. Then, the output mesh can be repeatedly upsampled and deformed by the above pipeline to obtain finer garment details, which can be seen as another reverse diffusion process. To obtain features for the reverse diffusion, we extract pixel-aligned features transferred from images and explore to incorporate the visibility of garments from the image viewpoints. Through detailed experiments on two public datasets, we demonstrate that DReD synthesizes more realistic wrinkled garments with lower errors and offers faster inference than previous methods. [ABSTRACT FROM AUTHOR]

Body surface area (BSA) measurement is important in engineering and medicine fields to determine parameters for various applications. Three-dimensional scanning techniques may be used to acquire the BSA directly. Nevertheless, the raw data obtained from 3D scanning usually requires some manual post-processing which is time-consuming and requires technical expertise. Automated post-processing of 3D scans enables expedient BSA calculation with minimal technical expertise. The purpose of this research was to compare the accuracy and reliability of three different automated post-processing techniques including Stitched Puppet (SP), Poisson surface reconstruction (PSR), and screened Poisson surface reconstruction (SPSR) using manual post-processing as the criterion. Twenty-nine participants were scanned twice, and raw data were processed with the manual operation and automated techniques to acquire BSAs separately. The reliability of BSAs acquired from these approaches was represented by the relative technical error of measurements (TEM). Pearson's regressions were applied to correct BSAs acquired from the automated techniques. The limits of agreement (LOA) were used to quantify the accuracy of BSAs acquired from the automated techniques and corrected by regression models. The reliability (relative TEM) of BSAs obtained from PSR, SPSR and SP were 0.32, 0.30 and 0.82% respectively. After removing bias with the regression models, the LOA for PSR, SPSR and SP were (−0.0134 m2, 0.0135 m2), (−0.0130 m2, 0.0132 m2), (−0.0573 m2, 0.0572 m2) respectively. It is concluded that PSR and SPSR are good alternative approaches to manual post-processing for applications that need reliable and accurate measurements of BSAs with large populations. [ABSTRACT FROM AUTHOR]

The development of the patchwise partial differential equation (PDE) framework a few years ago has paved the way for the PDE method to be used in mesh signal processing. In this paper, we, for the first time, extend the use of the PDE method to progressive mesh compression and mesh denoising. We, meanwhile, upgrade the existing patchwise PDE method in patch merging, mesh partitioning, and boundary extraction to accommodate mesh signal processing. In our new method, an arbitrary mesh model is partitioned into patches, each of which can be represented by a small set of coefficients of its PDE spectral solution. Since low-frequency components contribute more to the reconstructed mesh than high-frequency ones, we can achieve progressive mesh compression and mesh denoising by manipulating the frequency terms of the PDE solution. Experimental results demonstrate the feasibility of our method in both progressive mesh compression and mesh denoising. [ABSTRACT FROM AUTHOR]

A fully automatic mesh segmentation scheme using heterogeneous graphs is presented. We introduce a spectral framework where local geometry affinities are coupled with surface patch affinities. A heterogeneous graph is constructed combining two distinct graphs: a weighted graph based on adjacency of patches of an initial over-segmentation, and the weighted dual mesh graph. The partitioning relies on processing each eigenvector of the heterogeneous graph Laplacian individually, taking into account the nodal set and nodal domain theory. Experiments on standard datasets show that the proposed unsupervised approach outperforms the state-of-the-art unsupervised methodologies and is comparable to the best supervised approaches. [ABSTRACT FROM PUBLISHER]

Discrete exterior calculus (DEC) is a numerical method for solving partial differential equations on meshes with applications in computer graphics, numerics, and physical simulations. It discretizes PDEs in a way such that important integral theorems hold exactly instead of being approximated. The drawback of the method is that it has strong requirements on the mesh. While the narrow range of admissible meshes mentioned in the original work could be widened, current methods still exclude an essential category of meshes, i.e., meshes with concyclic triangle pairs. Such meshes are common, as many synthetic meshes, e.g., triangulations of CAD models, handcrafted 3D models, and even results of surface meshing algorithms, contain such triangle pairs. Our paper describes an approach that allows us to use meshes with arbitrary triangulations that may contain concyclic triangle pairs by defining DEC operators for concyclic polygons. • Lifting one of the last mesh requirements for using DEC. • Allows for using circumcentric duality in meshes with degenerate dual edges. • The method only requires minor changes in existing DEC codes. [ABSTRACT FROM AUTHOR]

This article introduces a method that generates a hexahedral-dominant mesh from an input tetrahedral mesh. It follows a three-step pipeline similar to the one proposed by Carrier Baudoin et al.: (1) generate a frame field, (2) generate a pointset P that is mostly organized on a regular grid locally aligned with the frame field, and (3) generate the hexahedral-dominant mesh by recombining the tetrahedra obtained from the constrained Delaunay triangulation of P. For step (1), we use a state-of-the-art algorithm to generate a smooth frame field. For step (2), we introduce an extension of Periodic Global Parameterization to the volumetric case. As compared with other global parameterization methods (such as CubeCover), our method relaxes some global constraints to avoid creating degenerate elements, at the expense of introducing some singularities that are meshed using non-hexahedral elements. For step (3), we build on the formalism introduced by Meshkat and Talmor, fill in a gap in their proof, and provide a complete enumeration of all the possible recombinations, as well as an algorithm that efficiently detects all the matches in a tetrahedral mesh. The method is evaluated and compared with the state of the art on a database of examples with various mesh complexities, varying from academic examples to real industrial cases. Compared with the method of Carrier-Baudoin et al., the method results in better scores for classical quality criteria of hexahedral-dominant meshes (hexahedral proportion, scaled Jacobian, etc.). The method also shows better robustness than CubeCover and its derivatives when applied to complicated industrial models. [ABSTRACT FROM AUTHOR]

Folding planar sheets to make 3D shapes from is an ancient practice with many new applications, ranging from personal fabrication of customized items to design of surgical instruments for minimally invasive surgery in self-folding machines. Given a polyhedral mesh, unfolding is an operation of cutting and flattening the mesh. The flattened polyhedral nets are then cut out of planar materials and folded back to 3D. Unfolding a polyhedral mesh into planar nets usually require segmentation. Either used as a preprocessing step to simplify the mesh and provide semantics or as the result of unfolding to avoid overlapping, the segmentation and the unfolding operations are decoupled. Consequently, segmented components may not be unfoldable and unfolded nets usually provide no semantic meaning and make folding difficult. In this paper, we propose a strategy that tightly couples unfolding and segmentation. We show that the proposed method produces unfoldable segmentation that resembles carefully designed paper craft. The key idea that enables this capability is an algorithm that learns from failed unfoldings. [ABSTRACT FROM AUTHOR]

In this paper, we present a method for 3D mesh segmentation based on sparse non-negative matrix factorization (NMF). Image analysis techniques based on NMF have been shown to decompose images into semantically meaningful local features. Since the features and coefficients are represented in terms of non-negative values, the features contribute to the resulting images in an intuitive, additive fashion. Like spectral mesh segmentation, our method relies on the construction of an affinity matrix which depends on the geometric properties of the mesh. We show that segmentation based on the NMF is simpler to implement, and can result in more meaningful segmentation results than spectral mesh segmentation. [ABSTRACT FROM AUTHOR]

This paper presents a novel 3D shape descriptor which explicitly captures the local geometry and encodes it using an efficient representation. Our method consists of multiple evolving fronts which are realized by a set of growing spheres on the surface. At the core of this method is a simple intersection operator between the spheres and the shape's surface. Intersection curves yield a discrete sampling of the surface at different positions and scales. Our key idea is to define a shape descriptor that captures the continuous local geometry of the surface in an efficient and consistent representation by intersecting the surface with multiple spheres and transforming the intersection curve to frequency domain. To evaluate our descriptor, we define shape similarity metric and perform shape matching on the SHREC11 non-rigid benchmark and other classes. [ABSTRACT FROM AUTHOR]