Mesh Compression Research Articles

Sparse Approximation of 3D Meshes Using the Spectral Geometry of the Hamiltonian Operator

The discrete Laplace operator is ubiquitous in spectral shape analysis, since its eigenfunctions are provably optimal in representing smooth functions defined on the surface of the shape. Indeed, subspaces defined by its eigenfunctions have been utilized for shape compression, treating the coordinates as smooth functions defined on the given surface. However, surfaces of shapes in nature often contain geometric structures for which the general smoothness assumption may fail to hold. At the other end, some explicit mesh compression algorithms utilize the order by which vertices that represent the surface are traversed, a property which has been ignored in spectral approaches. Here, we incorporate the order of vertices into an operator that defines a novel spectral domain. We propose a method for representing 3D meshes using the spectral geometry of the Hamiltonian operator, integrated within a sparse approximation framework. We adapt the concept of a potential function from quantum physics and incorporate vertex ordering information into the potential, yielding a novel data-dependent operator. The potential function modifies the spectral geometry of the Laplacian to focus on regions with finer details of the given surface. By sparsely encoding the geometry of the shape using the proposed data-dependent basis, we improve compression performance compared to previous results that use the standard Laplacian basis and spectral graph wavelets.

A Novel Compression-Driven Lightweight Framework for Medical Skeleton Model Visualization

In the field of medical imaging, many medical image data can be rebuilt into 3-D medical models for use in medical education and analysis. In fact, the 3-D medical models help ordinary people (including patients and students) to more easily understand and learn medical knowledge. In addition, with the rapid development of Web3D technology, the demand for 3-D visualization technology based on the web browser increases. However, the limited bandwidth and low load capacity of the browser have seriously restricted the development of technology. Therefore, this paper proposes a framework to better show 3-D skeleton shapes. In particular, mesh compression is one of the most effective methods to achieve a fast transmission data process. In addition, because of the poor rendering capabilities of the browsers, it is notably difficult to render the entire model at once. Moreover, it often makes the browser crash; thus, the transmitted model data are only rendered once. In addition, a mesh segmentation algorithm is proposed to realize component-wise rendering and lightweight for shape. A voxel-based component repetition method is used to detect the repetitive components; thus, we can perform matrix transformation to finish the repetitive-component Web3D visualization, i.e., lightweight for shape. Finally, the related experiments are performed to validate our proposed framework. The results show that the proposed framework is feasible and superior.

Eigenspace compression: dynamic 3D mesh compression by restoring fine geometry to deformed coarse models

Dynamic 3D mesh compression is of great practical important issues in computer graphics and multimedia applications. In this paper, an efficient compression algorithm is proposed to represent animated mesh sequences in a compact way, so that the storage and transmission of dynamic 3D meshes can be accomplished efficiently. The focus of this paper is on the animated mesh sequences with shared connectivity. The proposed method first computes coarse models (low frequency modes) of the animated sequence using the graph Laplacian matrix. Obtained coordinate weights are used at the decoder to reconstruct the coarse models of the sequence. Then, a novel approach is proposed to extract fixed details (high frequency modes or finer features) of the animated mesh. Finally, a details restoration process is applied at the decoder to add details back to the coarse models of the reconstructed sequence. The superiority of the proposed method to the current state of the arts is demonstrated in terms of low data rates for a given degree of perceived distortion.

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 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.

A Parallel Approach to Compression and Decompression of Triangle Meshes using the GPU

AbstractMost state‐of‐the‐art compression algorithms use complex connectivity traversal and prediction schemes, which are not efficient enough for online compression of large meshes. In this paper we propose a scalable massively parallel approach for compression and decompression of large triangle meshes using the GPU. Our method traverses the input mesh in a parallel breadth‐first manner and encodes the connectivity data similarly to the well known cut‐border machine. Geometry data is compressed using a local prediction strategy. In contrast to the original cut‐border machine, we can additionally handle triangle meshes with inconsistently oriented faces. Our approach is more than one order of magnitude faster than currently used methods and achieves competitive compression rates.

Progressive Compression of 3D Mesh Geometry Using Sparse Approximations from Redundant Frame Dictionaries

The proliferation of sophisticated techniques for 3D model acquisition and graphic design in recent years is resulting in a rapid increase in the number and complexity of 3D models being produced. At the same time, the need for exchanging 3D models is also rising due to new computing paradigms (e.g., cloud computing) and an increase in collaborative applications and online social networks. This has created a need for efficient compression techniques for 3D models, which are progressive, allow high quality or even lossless reconstruction, and minimize the amount of transferred data. Most of the research on 3D model compression to date has focused on the compression of triangular surface meshes, as this is the most common representation for 3D objects. In particular, progressive compression techniques for 3D mesh models have become very popular in recent years, as they allow a mesh to be reconstructed from coarse to fine levels of detail at the decoder while the bitstream of data is still being received. Currently the best-performing progressive compression techniques seem to be those that use transform coding ideas borrowed from traditional signal and image processing. The fundamental assumption behind such techniques is that the input data can be represented as some sparse linear combination of atoms taken from a representative dictionary of atoms that constitute the new representation domain. Traditionally, these dictionaries have been chosen to be orthogonal bases; however, recent research into alternative signal representations has shown that overcomplete dictionaries, or frames, may be able to produce even sparser representations than orthogonal bases can. In the field of 3D mesh compression, the idea of using redundant representations has only just started to surface. The main challenge here is currently the creation of a good overcomplete dictionary, particularly for mesh models with irregular connectivity that needs to be preserved. In light of this, the main objective of the work in this thesis is to develop a new method for constructing a frame, which can be applied to a manifold triangle mesh directly (i.e., with no requirement for a prior remeshing to a more regular domain) and can be used to obtain sparse approximations of the mesh geometry in a progressive compression scenario. This is the main contribution of this thesis. The frames that we propose are constructed from the unit-norm eigenvectors of a combinatorial mesh Laplacian matrix, plus a large number of redundant linear combinations of these eigenvectors. A sparse synthesis of the input mesh geometry is achieved by selecting atoms from the frame using the Matching Pursuit algorithm. The proposed frames can be applied directly to a manifold mesh with arbitrary topology and connectivity type, as long as the mesh can be represented as a connected graph. Our experimental results for a variety of different mesh models indicate that, for a given reconstruction quality, a sparser approximation of the input mesh geometry can be obtained with the proposed…

Editorial Issue 27.6

This issue contains four papers. In the first paper, Mingfei Wang, Jinyuan Jia, Ning Xie, and Chenxi Zhang, from Tongji University in Shanghai, China, aim to solve the challenging problems of choosing the data supplier for data-dispatching services in distributed virtual environments based on peer-to-peer networks. They propose a dynamic node-organizing mechanism that aims by applying the avatar's behavioral characteristics to the neighbor maintenance mechanism and scene data transmission. They have conducted extensive simulation experiments that simulate avatar behaviors in a popular online game. The results show that their proposed mechanism achieved a substantial alleviation of neighbor churn and reduced information exchange, which improves the transmission efficiency in DVEs. In the second paper, Masaki Oshita, from the Kyushu Institute of Technology, Japan, proposes an interactive character motion control interface that uses hands. Using their hands and fingers, the user can control a large number of degrees of freedom (DOFs) at the same time. The author applied principal component analysis (PCA) to a set of sample poses and assigned the extracted principal components to each DOF of the hands (such as the hand positions and finger bending/extending angles). The author developed methods for computing the feature vector, for applying PCA, and for pose and action synthesis. In addition, he introduced a pose transition method for performing a step motion when necessary to prevent foot sliding. He presents his experimental results and demonstrates the effectiveness of his interface. In the third paper, Wenwu Yang, Xun Wang, Wangbin Kou, Bailin Yang, and Guozheng Wang, from Zhejiang Gongshang University, Hangzhou, China, present a topology-aware method based on moving least squares (MLS) deformation approach for 2D characters. First, a Laplace equation is solved to obtain a set of weights, which are called as harmonic weights. Then, the MLS deformation is performed by using the harmonic weights as the deformation influence of the user-specified controls. Finally, the possible distortion in the traditional MLS deformation can be effectively avoided, since the harmonic weights spread the deformation of the controls in a localized and topology-aware way. In addition, a simple but effective area-preserving variant of MLS deformation is proposed, which is suitable for the editing of incompressible objects. Mohammadali Hajizadeh and Hossein Ebrahimnezhad, from Sahand University of Technology, Islamic Republic of Iran, propose a key frame-based technique for 3D dynamic mesh compression. First, key frames are extracted from the animated sequence. Extracted key frames are then linearly combined using blending weights to predict the vertex locations of the other frames. These blending weights play a key role in the proposed algorithm since the prediction performance and the required number of key frames are greatly dependent on these weights. They present a novel method in order to compute the optimum blending weight, which makes it possible to predict location of the vertices of the non-key frames with the minimum number of key frames. The residual prediction errors are finally quantized and encoded using Huffman coding and another heuristic method. Experimental results on different test sequences with various sizes, topologies, and geometries demonstrate the privileged performance of the proposed method compared to the previous techniques.

Multi-layer compression algorithm for 3D deformed mesh based on multi library wavelet neural network architecture

We propose in this paper a 3D mesh compression algorithm for 3D deformation objects to facilitate the transmission of deformed object to another. This algorithm allows eliminating an object in the sequence of deformed objects and reducing the information needed to represent the geometry of a mesh sequence. In our approach, we used Multi Library Wavelet Neural Network architecture (MLWNN) to align features of mesh and minimize distortion with fixed features. The introduced method minimizes the sum of the distances between all the corresponding vertices. It computes deformed ROI (Region Of Interest), updates and optimizes it to align the mesh features. First, our compression was performed using spherical geometrical image obtained by our trust region spherical parameterization. Geometrical images also facilitate compression and level-of-detail control. Second, the spherical wavelet transformation was used to decompose the geometrical image into multi-resolution sub-images characterizing the underlying functions in a local fashion in both spatial and frequency domains. Experimental results show that the progressive compression algorithm yields efficient compression capabilities with minimal set of features used to have good deformation scheme.

Progressive compression of arbitrary textured meshes

AbstractIn this paper, we present a progressive compression algorithm for textured surface meshes, which is able to handle polygonal non‐manifold meshes as well as discontinuities in the texture mapping. Our method applies iterative batched simplifications, which create high quality levels of detail by preserving both the geometry and the texture mapping. The main features of our algorithm are (1) generic edge collapse and vertex split operators suited for polygonal non‐manifold meshes with arbitrary texture seam configurations, and (2) novel geometry‐driven prediction schemes and entropy reduction techniques for efficient encoding of connectivity and texture mapping. To our knowledge, our method is the first progressive algorithm to handle polygonal non‐manifold models. For geometry and connectivity encoding of triangular manifolds and non‐manifolds, our method is competitive with state‐of‐the‐art and even better at low/medium bitrates. Moreover, our method allows progressive encoding of texture coordinates with texture seams; it outperforms state‐of‐the‐art approaches for texture coordinate encoding. We also present a bit‐allocation framework which multiplexes mesh and texture refinement data using a perceptually‐based image metric, in order to optimize the quality of levels of detail.

Multiresolution and fast decompression for optimal web-based rendering

Limited bandwidth is a strong constraint when efficient transmission of 3D data to Web clients and mobile applications is needed. In this paper we present a novel multi-resolution WebGL based rendering algorithm which combines progressive loading, view-dependent resolution and mesh compression, providing high frame rates and a decoding speed of million of triangles per second in JavaScript. The method is parallelizable and scalable to very large models.The algorithm is based on the local multi-resolution approaches provided by the community, but ad-hoc solutions had to be studied and implemented to provide adequate performances. In particular, a compression mechanism that reached very high compression rate without impact on rendering performance was implemented. Moreover, the data partition strategy was modified in order to be able to load different types of data (i.e. point clouds) and better adapt to the potentials and limitations of web-based rendering.

3D Mesh Compression and Transmission for Mobile Robotic Applications

Mobile robots are useful for environment exploration and rescue operations. In such applications, it is crucial to accurately analyse and represent an environment, providing appropriate inputs for motion planning in order to support robot navigation and operations. 2D mapping methods are simple but cannot handle multilevel or multistory environments. To address this problem, 3D mapping methods generate structural 3D representations of the robot operating environment and its objects by 3D mesh reconstruction. However, they face the challenge of efficiently transmitting those 3D representations to system modules for 3D mapping, motion planning, and robot operation visualization. This paper proposes a quality-driven mesh compression and transmission method to address this. Our method is efficient, as it compresses a mesh by quantizing its transformed vertices without the need to spend time constructing an a-priori structure over the mesh. A visual distortion function is developed to govern the level of quantization, allowing mesh transmission to be controlled under different network conditions or time constraints. Our experiments demonstrate how the visual quality of a mesh can be manipulated by the visual distortion function.

Predictive compression of animated 3D models by optimized weighted blending of key‐frames

AbstractEfficient compression techniques are required for animated mesh sequences with fixed connectivity and time‐varying geometry. In this paper, we propose a key‐frame‐based technique for three‐dimensional dynamic mesh compression. First, key‐frames are extracted from the animated sequence. Extracted key‐frames are then linearly combined using blending weights to predict the vertex locations of the other frames. These blending weights play a key role in the proposed algorithm because the prediction performance and the required number of key‐frames greatly depend on these weights. We present a novel method in order to compute the optimum blending weight that makes it possible to predict location of the vertices of the non‐key frames with the minimum number of key‐frames. The residual prediction errors are finally quantized and encoded using Huffman coding and another heuristic method. Experimental results on different test sequences with various sizes, topologies, and geometries demonstrate the privileged performance of the proposed method compared with the previous techniques. Copyright © 2015 John Wiley & Sons, Ltd.

Compressive Representation of Three-dimensional Models

Due to recent developments in data acquisition mechanisms, called 3d scanners, mesh compression has become an important tool for manipulating geometric data in several areas. In this context, a recent approach to the theory of signs called Compressive Sensing states that a signal can be recovered from far fewer samples than those provided by the classical theory. In this paper, we investigate the applicability of this new theory with the purpose of to obtain a compressive representation of geometric meshes. We developed an experiment which combines sampling, compression and reconstruction of various mesh sizes. Besides figuring compression rates, we also measured the relative error between the original mesh and the recovered mesh. We also compare two measurement techniques through their processing times, which are: the use of Gaussian matrices; and the use of Noiselet matrices. Gaussian matrices performed better in terms of processing speed, with equivalent performance in compression capacity. The results indicate that compressive sensing is very useful for mesh compression showing quite comparable results with traditional mesh compression techniques.

Dihedral angle-based maps of tetrahedral meshes

We present a geometric representation of a tetrahedral mesh that is solely based on dihedral angles. We first show that the shape of a tetrahedral mesh is completely defined by its dihedral angles. This proof leads to a set of angular constraints that must be satisfied for an immersion to exist in R 3 . This formulation lets us easily specify conditions to avoid inverted tetrahedra and multiply-covered vertices, thus leading to locally injective maps. We then present a constrained optimization method that modifies input angles when they do not satisfy constraints. Additionally, we develop a fast spectral reconstruction method to robustly recover positions from dihedral angles. We demonstrate the applicability of our representation with examples of volume parameterization, shape interpolation, mesh optimization, connectivity shapes, and mesh compression.

3D Mesh Compression

3D meshes are commonly used to represent virtual surface and volumes. However, their raw data representations take a large amount of space. Hence, 3D mesh compression has been an active research topic since the mid 1990s. In 2005, two very good review articles describing the pioneering works were published. Yet, new technologies have emerged since then. In this article, we summarize the early works and put the focus on these novel approaches. We classify and describe the algorithms, evaluate their performance, and provide synthetic comparisons. We also outline the emerging trends for future research.

Toward Real-Time and Efficient Compression of Human Time-Varying Meshes

In this paper, a novel skeleton-based approach to human time-varying mesh (H-TVM) compression is presented. The topic of TVM compression is new and has many challenges, such as handling the lack of obvious mapping of vertices across frames and handling the variable connectivity across frames, while maintaining efficiency, which are the most important ones. Very few works exist in the literature, while not all of the challenges have been addressed yet. In addition, developing an efficient and real-time solution, handling the above, obviously is a difficult task. We attempt to address the H-TVM compression problem inspired from video coding using different types of frames and trying to efficiently remove inter-frame geometric redundancy utilizing the recent advances in human skeleton tracking. The overall approach focuses on compression efficiency, low distortion, and low computation time enabling for real-time transmission of H-TVMs. It efficiently compresses geometry and vertex attributes of TVMs. In addition, this paper is the first to provide an efficient method for connectivity coding of TVMs, by introducing a modification to the state-of-the-art MPEG-4 TFAN algorithm. Experiments are conducted in the MPEG-3DGC TVM database. The method outperforms the state-of-the-art standardized static mesh coder MPEG-4 TFAN at low bit-rates, while remaining competent at high bit-rates. It gives a practical proof of concept that in the combined problem of geometry, connectivity, and vertex attribute coding of TVMs, efficient inter-frame redundancy removal is possible, establishing ground for further improvements. Finally, this paper proposes a method for motion-based coding of H-TVMs that can further enhance the overall experience when H-TVM compression is used in a tele-immersion scenario.

Hierarchical Laplacian-based compression of triangle meshes

In this paper, we present an algorithm for efficient encoding of triangle meshes. The algorithm preserves the local relations between vertices by encoding their Laplacian coordinates, while at the same time, it uses a hierarchy of additional vertex constraints that provides global rigidity and low absolute error, even for large meshes. Our scheme outperforms traversal based as well as Laplacian-based compression schemes in terms of both absolute and perceived distortion at a given data rate.

Enabling Geometry-Based 3-D Tele-Immersion With Fast Mesh Compression and Linear Rateless Coding

3-D tele-immersion (3DTI) enables participants in remote locations to share, in real time, an activity. It offers users interactive and immersive experiences, but it challenges current media-streaming solutions. Work in the past has mainly focused on the efficient delivery of image-based 3-D videos and on realistic rendering and reconstruction of geometry-based 3-D objects. The contribution of this paper is a real-time streaming component for 3DTI with dynamic reconstructed geometry. This component includes both a novel fast compression method and a rateless packet protection scheme specifically designed towards the requirements imposed by real time transmission of live-reconstructed mesh geometry. Tests on a large dataset show an encoding speed-up up to ten times at comparable compression ratio and quality, when compared with the high-end MPEG-4 SC3DMC mesh encoders. The implemented rateless code ensures complete packet loss protection of the triangle mesh object and a delivery delay within interactive bounds. Contrary to most linear fountain codes, the designed codec enables real-time progressive decoding allowing partial decoding each time a packet is received. This approach is compared with transmission over TCP in packet loss rates and latencies, typical in managed WAN and MAN networks, and heavily outperforms it in terms of end-to-end delay. The streaming component has been integrated into a larger 3DTI environment that includes state of the art 3-D reconstruction and rendering modules. This resulted in a prototype that can capture, compress transmit, and render triangle mesh geometry in real-time in realistic internet conditions as shown in experiments. Compared with alternative methods, lower interactive end-to-end delay and frame rates over three times higher are achieved.

Perception-driven adaptive compression of static triangle meshes

Mesh compression is an important task in geometry processing. It exploits geometric coherence of the data to reduce the amount of space needed to store a surface mesh. Most techniques perform compression employing a uniform data quantization over the whole surface. Research in shape perception, however, suggests that there are parts of the mesh that are visually more relevant than others. We present a novel technique that performs an adaptive compression of a static mesh, using the largest part of the bit budget on the relevant vertices while saving space on encoding the less significant ones. Our technique can be easily adapted to work with any perception-based error metric. The experiments show that our adaptive approach is at least comparable with other state-of-the-art techniques, while in some cases it provides a significant reduction of the bitrate of up to 15%. Additionally, our approach provides much faster decoding times than comparable perception-motivated compression algorithms.

Connectivity-preserving geometry images

We propose connectivity-preserving geometry images (CGIMs), which map a triangular mesh onto a rectangular regular array of an image, such that the reconstructed mesh produces no sampling errors, but merely round-off errors over the coordinates of vertices. Using permutation techniques on vertices, CGIMs first obtain a V-matrix whose elements are vertices of the original mesh, which intrinsically preserves the vertex-set and connectivity of the original mesh, and then generate a CGIM array by transforming the Cartesian coordinates of corresponding vertices of the V-matrix into RGB values. Compared with traditional geometry images (GIMs), CGIMs achieve the minimum reconstruction error with a parametrization-free algorithm. We apply CGIMs to lossy compression of meshes. Experimental results show that while CGIMs produce a lower efficiency in both encoding and decoding time and larger resolutions than traditional GIMs, CGIMs perform better peak signal-to-noise ratios and preserve details better than GIMs especially with the multi-stage base color and index map scheme, because CGIMs treat details and non-details of meshes evenly as all elements of the V-matrix.