Mesh Compression Research Articles

A metric-based adaptive mesh refinement criterion under constrain for solving elliptic problems on quad/octree grids

In this work we propose and investigate the performance of a metric-based refinement criteria for adaptive meshing used for improving the numerical solution of an elliptic problem. We show that in general, when solving elliptic equations such as the Poisson-Helmholtz equation, the minimization of the interpolation error often used as local refinement criteria does not always guarantee the minimization of the total numerical error. Numerical and theoretical arguments are given to unveil the critical role of the mesh compression – the size aspect ratio between the finest cell size and the mean cell size of an adapted mesh – to determine whether the estimated error is purely local meaning that the interpolation error is a good enough error model for the total error or if other, non-local, sources of error need to be accounted for. We show through particular examples that a slightly sub-optimal mesh in terms of interpolation error may significantly reduce the total error of a numerical solution, depending on the value of the compression ratio and not on the number of grid points. Based on this observation, we propose a new method to exclude the grids where non-local errors can control the accuracy of the solution. This is achieved by an automatic estimation of the optimal compression ratio, which is imposed as an additional constraint in the minimal element size during the mesh adaptation process. The method is tested on quadtree and octree grids, showing very satisfactory performances in reducing the total numerical error despite the additional constrain imposed.

Mesh Compression Algorithm for Geometrical Coordinates in Computational Meshes

Application of advanced mesh based methods, including adaptive finite element method, is impossible without theoretical elaboration and practical realization of a model for organization and functionality of computational mesh. One of the most basic mesh functionality is storing and providing geometrical coordinates for vertices and other mesh entities. New algorithm for this task based on on-the-fly recreation of coordinates was developed. Conducted tests are proving that, for selected cases, it can be orders of magnitude faster than naive approach or other similar algorithms.

Paper] Enhancement of Motion Field Coding by Integrating Duplicated Vertices in Dynamic Mesh Compression

Paper] Enhancement of Motion Field Coding by Integrating Duplicated Vertices in Dynamic Mesh Compression

GMM-ICQ: A GMM vertex-optimization-based implicitly-connected quadrilateral format for 3D mesh storage

3D meshes are commonly utilized and may be considered to be the most popular surface representation in computer graphics due to their simplicity, efficiency and flexibility. However, the explicit storage of mesh vertices and connectivity, as in widely-used PLY and OBJ file formats, leads to substantial memory consumption. This, in turn, directly affects the processing and transmission in downstream applications. Though mesh simplification and mesh compression are common strategies to lessen memory consumption, they exhibit inherent limitations either in maintaining a balance between accuracy, efficiency, memory usage and mesh quality, or breaking the simplicity of explicit storage and struggling with optimizing the trade-off between compression performance and computational resource consumption. To overcome these limitations, inspired by the Gaussian Mixture Model (GMM), this paper proposes a GMM vertex-optimization-based implicitly-connected quadrilateral format for 3D mesh storage, named GMM-ICQ. Extensive qualitative and quantitative evaluations demonstrate that the GMM-ICQ format achieves efficient compression by retaining only a small amount of vertex information, while preserving sharp features and maintaining relatively high mesh quality. It also exhibits a certain degree of robustness in the presence of noise interference. Furthermore, benefiting from the inherent grid-based connectivity, the GMM-ICQ format maintains the simplicity of explicit storage and can be implemented as a progressive variant without incurring additional computational overhead.

Graphs in computer graphics

This paper provides an overview of the main ideas of graph theory used in computer graphics. Applications include mesh compression, animation, visibility determination, rendering optimization, shape recognition, and navigation. We present both success and failure cases from the most cited works and recent publications. Related work review reveals a trend in using graphs for extracting the essential information from a given context, which directly manifests itself in various compression schemes and efficient querying data structures.

Progressive Compression of Triangle Meshes

This paper details the first publicly available implementation of the progressive mesh compression algorithm described in the paper entitled "Compressed Progressive Meshes" [R. Pajarola and J. Rossignac, IEEE Transactions on Visualization and Computer Graphics, 6 (2000), pp. 79-93]. Our implementation is generic, modular, and includes several improvements in the stopping criteria and final encoding. Given an input 2-manifold triangle mesh, an iterative simplification is performed, involving batches of edge collapse operations guided by an error metric. During this compression step, all the information necessary for the reconstruction (at the decompression step) is recorded and compressed using several key features: geometric quantization, prediction, and spanning tree encoding. Our implementation allowed us to carry out an experimental comparison of several settings for the key parameters of the algorithm: the local error metric, the position type of the resulting vertex (after collapse), and the geometric predictor.

Dynamic Reconstruction and Mesh Compression of 4D Volumetric Model Using Correspondence-Based Deformation for Streaming Service.

A sequence of 3D models generated using volumetric capture has the advantage of retaining the characteristics of dynamic objects and scenes. However, in volumetric data, since 3D mesh and texture are synthesized for every frame, the mesh of every frame has a different shape, and the brightness and color quality of the texture is various. This paper proposes an algorithm to consistently create a mesh of 4D volumetric data using dynamic reconstruction. The proposed algorithm comprises remeshing, correspondence searching, and target frame reconstruction by key frame deformation. We make non-rigid deformation possible by applying the surface deformation method of the key frame. Finally, we propose a method of compressing the target frame using the target frame reconstructed using the key frame with error rates of up to 98.88% and at least 20.39% compared to previous studies. The experimental results show the proposed method's effectiveness by measuring the geometric error between the deformed key frame and the target frame. Further, by calculating the residual between two frames, the ratio of data transmitted is measured to show a compression performance of 18.48%.

Priority‐based encoding of triangle mesh connectivity for a known geometry

AbstractIn certain practical situations, the connectivity of a triangle mesh needs to be transmitted or stored given a fixed set of 3D vertices that is known at both ends of the transaction (encoder/decoder). This task is different from a typical mesh compression scenario, in which the connectivity and geometry (vertex positions) are encoded either simultaneously or in reversed order (connectivity first), usually exploiting the freedom in vertex/triangle re‐indexation. Previously proposed algorithms for encoding the connectivity for a known geometry were based on a canonical mesh traversal and predicting which vertex is to be connected to the part of the mesh that is already processed. In this paper, we take this scheme a step further by replacing the fixed traversal with a priority queue of open expansion gates, out of which in each step a gate is selected that has the most certain prediction, that is one in which there is a candidate vertex that exhibits the largest advantage in comparison with other possible candidates, according to a carefully designed quality metric. Numerical experiments demonstrate that this improvement leads to a substantial reduction in the required data rate in comparison with the state of the art.

Volumetric Rendering on Wavelet-Based Adaptive Grid

Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve localized structures of the solution on dynamically adaptive computational meshes, make it feasible to perform large-scale numerical simulations of a variety of physical systems on a dynamically adaptive computational mesh that changes both in space and time. Volumetric visualization of the solution is an essential part of scientific computing, yet the existing volumetric visualization techniques do not take full advantage of multi-resolution wavelet analysis and are not fully tailored for visualization of a compressed solution on the wavelet-based adaptive computational mesh. Our objective is to explore the alternatives for the visualization of time-dependent data on space-time varying adaptive mesh using volume rendering while capitalizing on the available sparse data representation. Two alternative formulations are explored. The first one is based on volumetric ray casting of multi-scale datasets in wavelet space. Rather than working with the wavelets at the finest possible resolution, a partial inverse wavelet transform is performed as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a solution in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these coarse scaling functions. Additional details are added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet coefficient magnitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. The second approach is based on complementing of wavelet-based adaptive mesh to the traditional Adaptive Mesh Refinement (AMR) mesh. Both algorithms are illustrated and compared to the existing volume visualization software for Rayleigh-Benard thermal convection and electron density data sets in terms of rendering time and visual quality for different data compression of both wavelet-based and AMR adaptive meshes.

Survey on Deep Learning-Based Point Cloud Compression

Point clouds are becoming essential in key applications with advances in capture technologies leading to large volumes of data. Compression is thus essential for storage and transmission. In this work, the state of the art for geometry and attribute compression methods with a focus on deep learning based approaches is reviewed. The challenges faced when compressing geometry and attributes are considered, with an analysis of the current approaches to address them, their limitations and the relations between deep learning and traditional ones. Current open questions in point cloud compression, existing solutions and perspectives are identified and discussed. Finally, the link between existing point cloud compression research and research problems to relevant areas of adjacent fields, such as rendering in computer graphics, mesh compression and point cloud quality assessment, is highlighted.

Compression and Visualization Interactive of 3D Mesh

The combination of compression and visualization is mentioned as perspective, very few articles treat with this problem. Indeed, in this paper, we proposed a new approach to multiresolution visualization based on a combination of segmentation and multiresolution mesh compression. For this, we proposed a new segmentation method that benefits the organization of faces of the mesh followed by a progressive local compression of regions of mesh to ensure the refinement local of the three-dimensional object. Thus, the quantization precision is adapted to each vertex during the encoding /decoding process to optimize the rate-distortion compromise. The optimization of the treated mesh geometry improves the approximation quality and the compression ratio at each level of resolution. The experimental results show that the proposed algorithm gives competitive results compared to the previous works dealing with the rate-distortion compromise and very satisfactory visual results.

Error estimate FEM for the Nikol’skij–Lizorkin problem with degeneracy

This paper discusses the finite element approximation of the Nikol’skij–Lizorkin problem with degeneracy on the entire boundary of the domain. The triangulation of the domain with a special compression of nodes to the boundary of the domain was carried out. It was established that the approximation to the exact solution has first-order convergence in the norm of the Sobolev weighted space W2,α1(Ω) at special exponent of the degree of mesh compression. Numerical experiments confirmed the established estimate of the convergence rate.

Surgical Management of Sinus Pericranii With Crouzon Syndrome.

Sinus pericranii (SP) is a rare vascular malformation which connects the intracranial dural sinuses to the extracranial venous drainage system. Although the majority of SP cases are caused by trauma, some of them are congenital. Furthermore, a few SP cases have been reported in association with craniosynostosis. The authors' objective is to discuss the surgical management of SP with Crouzon's syndrome in children. Three-Dimensional reconstruction with enhanced CT scan was used for evaluate the condition of SP with Crouzon's syndrome in all 4 cases. Two cases with small single-hole defect on skull were only treated by cranioplasty with distraction osteogenesis. In the management of the other 2 SP patients with large skull defect, titanium mesh was used for compression of dilated venous sinus to inhabit filling and promote shrinking. Four cases of SP with Crouzon's syndrome were treated in the authors' department. With cranioplasty with distraction osteogenesis only, 2 patients with single-hole skull defect experienced SP spontaneous involution at 4 to 6 months postoperatively. With titanium mesh compression, SP with large skull defect shrank significantly without clinical recurrence, but long-term follow-up was still in need. For small single-hole skull defect in SP patient with Crouzon's syndrome, the only application of cranioplasty for decreasing intracranial pressure can promote SP spontaneous involution. 3D printed titanium mesh compression renders a safe and efficient approach for SP with large skull defect. Long-time follow up and further accumulation of cases may establish the efficacy of the authors' management.

Data-Driven Human Modeling by Sparse Representation

Data-driven methods for modeling the realistic shapeof 3D human bodies need to access datasets that contain a large amount of 3D human models. We develop a method based on sparse representation in this paper to represent 3D human models as signals of patches. Unlike the general mesh compression approaches, all mesh models used in a data-driven human modeling framework have the same mesh connectivity. By using this property, we segment a human model into patches containing the same number of vertices. L0-learning algorithm is selected to train an overcomplete dictionary matrix, which in turn introduces sparse representation of the dataset. Patch signals of individual human models can then be extracted by using the dictionary matrix. With the ease of balance control between sparsity and accuracy that is featured by the chosen learning algorithm, a representation with high compression ratio and low shape-approximation error can be determined. The results have been compared with the widely used statistic representation based on principal component analysis (PCA) to verify the effectiveness of our approach. Moreover, the method for using sparse representation in the regression-based statistical modeling of 3D human models has been presented at the end of the paper.

Numerical modeling of nonlinear dynamic and static compression of the metal mesh

Simulation of elastoplastic compression of a symmetric fragment of a bundle of woven steel grids was carried out. The simulation was carried out under static and dynamic loading modes in ANSYS and ANSYS LS-DYNA computing systems. A porous mesh package is formed by overlaying the layers on top of each other while maintaining the directions of wires. Such a packet has a quasiperiodic structure; therefore, a certain symmetric fragment can be distinguished. The compression was carried out by a pair of absolutely rigid plates moving symmetrically towards each other. In the calculations, a multilinear plasticity model with isotropic hardening was used. The diagram of static deformation of the material was used which was obtained experimentally. The calculations were carried out according to the algorithm of a perfect symmetric contact of bodies without friction and with friction. The dynamic loading of a fragment of the mesh packet was carried out at a constant speed. The characteristics of the pulse and the loading rate correspond to those observed in previous experimental studies. The dynamic strain diagram was assumed to be similar to a static one with an increased yield strength. Calculations showed that in all loading modes there is a high level of internal stresses, and complex inhomogeneous stress-strain state. We investigated two factors that could cause differences in the behavior of the curves of deformation of a porous medium - the finite length of the acting pulse and the differences in the dynamic and static compression diagrams of the initial mesh material. The main influence on the dynamic behavior of a fragment of a porous packet of a steel mesh is exerted by the dynamic properties of the wire material. The strain curves of the porous fragment qualitatively change in accordance with the behavior observed in static and dynamic experiments. The final duration of the loading pulse and the friction between the wires for this type of mesh do not have a significant effect. The numerical dependences of the relative area of the normal and lateral through sections of the symmetric fragment of the grid packet on the compression deformation are obtained.

3D Models Recognition in Fourier Domain Using Compression of the Spherical Mesh up to the Models Surface

3D Models Recognition in Fourier Domain Using Compression of the Spherical Mesh up to the Models Surface

Compressing animated meshes with fine details using local spectral analysis and deformation transfer

Geometry-centric shape animation, usually represented as dynamic meshes with fixed connectivity and time-deforming geometry, is becoming ubiquitous in digital entertainment and other relevant graphics applications. However, digital animation with fine details, which requires more diversity of texture on meshed geometry, always consumes a significant amount of storage space, and compactly storing and efficiently transmitting these meshes still remain technically challenging. In this paper, we propose a novel key-frame-based dynamic meshes compression method, wherein we decompose the meshes into the low-frequency and high-frequency parts by applying piece-wise manifold harmonic bases to reduce spatial-temporal redundancy of primary poses and by using deformation transfer to recover high-frequency details. First of all, we partition the animated meshes into several clusters with similar poses, and the primary poses of meshes in each cluster can be characterized as a linear combination of manifold harmonic bases derived from the key-frame of that cluster. Second, we recover the geometric details on each primary pose using the deformation transfer technique which reconstructs the details from the key-frames. Thus, we only need to store a very small number of key-frames and a few harmonic coefficients for compressing time-varying meshes, which would reduce a significant amount of storage in contrast with traditional methods where bases were stored explicitly. Finally, we employ the state-of-the-art static mesh compression method to store the key-frames and apply a second-order linear prediction coding to the harmonics coefficients to further reduce the spatial-temporal redundancy. Our comprehensive experiments and thorough evaluations on various datasets have manifested that, our novel method could obtain a high compression ratio while preserving high-fidelity geometry details and guaranteeing limited human perceived distortion rate simultaneously, as quantitatively characterized by the popular Karni–Gotsman error and our newly devised local rigidity error metrics.

Motion-Aware Compression and Transmission of Mesh Animation Sequences

With the increasing demand in using 3D mesh data over networks, supporting effective compression and efficient transmission of meshes has caught lots of attention in recent years. This article introduces a novel compression method for 3D mesh animation sequences, supporting user-defined and progressive transmissions over networks. Our motion-aware approach starts with clustering animation frames based on their motion similarities, dividing a mesh animation sequence into fragments of varying lengths. This is done by a novel temporal clustering algorithm, which measures motion similarity based on the curvature and torsion of a space curve formed by corresponding vertices along a series of animation frames. We further segment each cluster based on mesh vertex coherence, representing topological proximity within an object under certain motion. To produce a compact representation, we perform intra-cluster compression based on Graph Fourier Transform (GFT) and Set Partitioning In Hierarchical Trees (SPIHT) coding. Optimized compression results can be achieved by applying GFT due to the proximity in vertex position and motion. We adapt SPIHT to support progressive transmission and design a mechanism to transmit mesh animation sequences with user-defined quality. Experimental results show that our method can obtain a high compression ratio while maintaining a low reconstruction error.

A PDE patch-based spectral method for progressive mesh compression and mesh denoising

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 ...

Error propagation control in Laplacian mesh compression

AbstractLaplacian mesh compression, also known as high‐pass mesh coding, is a popular technique for efficiently storing both static and dynamic triangle meshes that gained further recognition with the advent of perceptual mesh distortion evaluation metrics. Currently, the usual rule of thumb that drives the decision for a mesh compression algorithm is whether or not accuracy in absolute scale is required: Laplacian mesh encoding is chosen when perceptual quality is the main objective, while other techniques provide better results in terms of mechanistic error measures such as mean squared error.In this work, we present a modification of the Laplacian mesh encoding algorithm that preserves its benefits while it substantially reduces the resulting absolute error. Our approach is based on analyzing the reconstruction stage and modifying the quantization of differential coordinates, so that the decoded result stays close to the input even in areas that are distant from anchor points. In our approach, we avoid solving an overdetermined system of linear equations and thus reduce data redundancy, improve conditioning and achieve faster processing. Our approach can be directly applied to both static and dynamic mesh compression and we provide quantitative results comparing our approach with the state of the art methods.