Mesh Coding Research Articles

Teaching Series and Parallel Connections

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Contribution:</i> A new operational definition of series connections is given based on elements belonging to the same two meshes, which is properly dual to the usual definition of parallel elements being connected to the same two nodes. Furthermore, computer-based exercises have been developed and tested to teach students about such connections in gateway linear circuits courses, using color coding of nodes and meshes as a pedagogical device. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Background:</i> Series and parallel connections are a crucial but difficult concept. Existing textbooks give them limited attention, resulting in later difficulties learning circuit analysis. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Research Questions:</i> RQ1: Can an improved definition of series elements aid student understanding and student satisfaction? RQ2: Can a computer-based “game” lead to effective mastery and student satisfaction at a wide range of institutions, including minority-serving ones? <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Methodology:</i> Standard and new definitions were elaborated in a multiple-choice tutorial. A game was developed focusing on identifying series and parallel connections, with color coding of both nodes and meshes. Student learning was assessed over eight years using pretest and posttest in 14 varied institutions. Student opinions were assessed using several types of surveys. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Findings:</i> Strong learning gains were observed every semester from built-in pretest and posttest, with average scores of 28% and 87%, respectively. Large improvements were observed at every institution including five minority-serving ones. The posttest score is increased by a statistically significant amount after introducing the new definition of series elements. Students preferred the new definition of series and recommended its use, and very strongly endorsed color coding.

Scalable Wavelet-Based Coding of Irregular Meshes With Interactive Region-of-Interest Support

This paper proposes a novel functionality in wavelet-based irregular mesh coding, which is interactive region-of-interest (ROI) support. The proposed approach enables the user to define the arbitrary ROIs at the decoder side and to prioritize and decode these regions at arbitrarily high-granularity levels. In this context, a novel adaptive wavelet transform for irregular meshes is proposed, which enables: 1) varying the resolution across the surface at arbitrarily fine-granularity levels and 2) dynamic tiling, which adapts the tile sizes to the local sampling densities at each resolution level. The proposed tiling approach enables a rate-distortion-optimal distribution of rate across spatial regions. When limiting the highest resolution ROI to the visible regions, the fine granularity of the proposed adaptive wavelet transform reduces the required amount of graphics memory by up to 50%. Furthermore, the required graphics memory for an arbitrary small ROI becomes negligible compared to rendering without ROI support, independent of any tiling decisions. Random access is provided by a novel dynamic tiling approach, which proves to be particularly beneficial for large models of over 106 ~ 107 vertices. The experiments show that the dynamic tiling introduces a limited lossless rate penalty compared to an equivalent codec without ROI support. Additionally, rate savings up to 85% are observed while decoding ROIs of tens of thousands of vertices.

Benchmarking Open-Source Static 3D Mesh Codecs for Immersive Media Interactive Live Streaming

This paper provides a systematic understanding of the requirements of live 3D mesh coding, targeting (tele-) immersive media streaming applications. We thoroughly benchmark in rate-distortion and runtime performance terms, four static 3D mesh coding solutions that are openly available. Apart from mesh geometry and connectivity, our analysis includes experiments for compressing vertex normals and attributes, something scarcely found in the literature. In addition, we provide a theoretical model of the tele-immersion pipeline that calculates its expected frame rate, as well as lower and upper bounds for its end-to-end latency. In order to obtain these measures, the theoretical model takes into account the compression performance of the codecs and some indicative network conditions. Based on the results we obtained through our codec benchmarking, we used our theoretical model to calculate and provide concrete measures for these tele-immersion pipeline’s metrics and discuss on the optimal codec choice depending on the network setup. This offers deep insight into the available solutions and paves the way for future research.

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.

Scalable Feature‐Preserving Irregular Mesh Coding

AbstractThis paper presents a novel wavelet‐based transform and coding scheme for irregular meshes. The transform preserves geometric features at lower resolutions by adaptive vertex sampling and retriangulation, resulting in more accurate subsampling and better avoidance of smoothing and aliasing artefacts. By employing octree‐based coding techniques, the encoding of both connectivity and geometry information is decoupled from any mesh traversal order, and allows for exploiting the intra‐band statistical dependencies between wavelet coefficients. Improvements over the state of the art obtained by our approach are three‐fold: (1) improved rate–distortion performance over Wavemesh and IPR for both the Hausdorff and root mean square distances at low‐to‐mid‐range bitrates, most obvious when clear geometric features are present while remaining competitive for smooth, feature‐poor models; (2) improved rendering performance at any triangle budget, translating to a better quality for the same runtime memory footprint; (3) improved visual quality when applying similar limits to the bitrate or triangle budget, showing more pronounced improvements than rate–distortion curves.

View-dependent 3-D mesh coding by rate allocation with the image rendering-based distortion measures

Low-bandwidth transmission of synthetic digital content to the end user device in the form of a scene of 3-D meshes requires efficient compression of the mesh geometry. For applications in which the meshes are observed from a single viewpoint, this work explores the use of the image rendering-based distortion measures in rate allocation to their surface regions for view-dependent mesh geometry compression. It is experimentally demonstrated that the image rendering-based distortion measures yield far superior performance (the quality of the rendered image of the reconstructed scene from a viewpoint at a given rate) in optimal rate allocation than other previously proposed distortion measures. A fast rate allocation method is also proposed for use with the image rendering-based measures for real-time or interactive applications. Not only does this method have significantly lower complexity than the optimal rate allocation method due to the rendering of the images of the reconstructed meshes at only judiciously selected rate–distortion operating points, but also its coding performance is just as competitive. Further complexity reduction in rate allocation, through rendering of only the coded regions of the meshes, is also investigated.

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.

Biologic versus Synthetic Mesh Reinforcement: What are the Pros and Cons?

Preserving patients' native tissues has posed many challenges for surgeons. Increased life expectancy is leading to a proportionately older surgical population with weaker tissues. The growing population of morbidly obese patients in addition to those with multiple comorbidities which influence the native strength and perfusion of tissues compounds the surgeon's challenge. Certainly, there is a rising demand for materials to replace or augment a patient's native tissue when it has been compromised. Over time, the number of products available has increased substantially. The ideal substitute, however, is debatable. The manufacturing and processing of these materials has become more complex and this has resulted in a significant increase in cost. The composition of the mesh, clinical scenario, and operative technique all interact to impact the long-term results. Surgeons require a thorough understanding of these products to guide proper selection and use, to ensure optimal outcomes for patients, and to properly steward financial resources. This review will outline the properties of commonly used materials, highlighting the strength and weakness of each. It will then discuss recommendations regarding mesh selection, coding, and reimbursement. While general principles and trends can be highlighted, further studies of biologic versus synthetic meshes are clearly necessary.

Adaptive coding of generic 3D triangular meshes based on octree decomposition

In this paper, we present an adaptive-coding method for generic triangular meshes including both regular and irregular meshes. Though it is also based on iterative octree decomposition of the object space for the original mesh, as some prior arts, it has novelties in the following two aspects. First, it mathematically models the occupancy codes containing only a single–“1” bit for accurate initialization of the arithmetic coder at each octree level. Second, it adaptively prioritizes the bits in an occupancy code using a local surface smoothness measure that is based on triangle areas and therefore mitigates the effect of non-uniform vertex sampling over the surface. As a result, the proposed 3D mesh coder yields outstanding coding performance for both regular and irregular meshes and especially for the latter, as demonstrated by the experiments.

Context‐Based Coding of Adaptive Multiresolution Meshes

AbstractMultiresolution meshes provide an efficient and structured representation of geometric objects. To increase the mesh resolution only at vital parts of the object, adaptive refinement is widely used. We propose a lossless compression scheme for these adaptive structures that exploits the parent–child relationships inherent to the mesh hierarchy. We use the rules that correspond to the adaptive refinement scheme and store bits only where some freedom of choice is left, leading to compact codes that are free of redundancy. Moreover, we extend the coder to sequences of meshes with varying refinement. The connectivity compression ratio of our method exceeds that of state‐of‐the‐art coders by a factor of 2–7. For efficient compression of vertex positions we adapt popular wavelet‐based coding schemes to the adaptive triangular and quadrangular cases to demonstrate the compatibility with our method. Akin to state‐of‐the‐art coders, we use a zerotree to encode the resulting coefficients. Using improved context modelling we enhanced the zerotree compression, cutting the overall geometry data rate by 7% below those of the successful Progressive Geometry Compression. More importantly, by exploiting the existing refinement structure we achieve compression factors that are four times greater than those of coders which can handle irregular meshes.

Scalable Intraband and Composite Wavelet-Based Coding of Semiregular Meshes

This paper proposes novel scalable mesh coding designs exploiting the intraband or composite statistical dependencies between the wavelet coefficients. A Laplacian mixture model is proposed to approximate the distribution of the wavelet coefficients. This model proves to be more accurate when compared to commonly employed single Laplacian or generalized Gaussian distribution models. Using the mixture model, we determine theoretically the optimal embedded quantizers to be used in scalable wavelet-based coding of semiregular meshes. In this sense, it is shown that the commonly employed successive approximation quantization is an acceptable, but in general, not an optimal solution. Novel scalable intraband and composite mesh coding systems are proposed, following an information-theoretic analysis of the statistical dependencies between the coefficients. The wavelet subbands are independently encoded using octree-based coding techniques. Furthermore, context-based entropy coding employing either intraband or composite models is applied. The proposed codecs provide both resolution and quality scalability. This lies in contrast to the state-of-the-art interband zerotree-based semiregular mesh coding technique, which supports only quality scalability. Additionally, the experimental results show that, on average, the proposed codecs outperform the interband state-of-the-art for both normal and nonnormal meshes. Finally, compared with a zerotree coding system, the proposed coding schemes are better suited for software/hardware parallelism, due to the independent processing of wavelet subbands.

Feature Oriented Progressive Lossless Mesh Coding

AbstractA feature‐oriented generic progressive lossless mesh coder (FOLProM) is proposed to encode triangular meshes with arbitrarily complex geometry and topology. In this work, a sequence of levels of detail (LODs) are generated through iterative vertex set split and bounding volume subdivision. The incremental geometry and connectivity updates associated with each vertex set split and/or bounding volume subdivision are entropy coded. Due to the visual importance of sharp geometric features, the whole geometry coding process is optimized for a better presentation of geometric features, especially at low coding bitrates. Feature‐oriented optimization in FOLProM is performed in hierarchy control and adaptive quantization. Efficient coordinate representation and prediction schemes are employed to reduce the entropy of data significantly. Furthermore, a simple yet efficient connectivity coding scheme is proposed. It is shown that FOLProM offers a significant rate‐distortion (R‐D) gain over the prior art, which is especially obvious at low bitrates.

Scalable L-Infinite Coding of Meshes

The paper investigates the novel concept of local-error control in mesh geometry encoding. In contrast to traditional mesh-coding systems that use the mean-square error as target distortion metric, this paper proposes a new L-infinite mesh-coding approach, for which the target distortion metric is the L-infinite distortion. In this context, a novel wavelet-based L-infinite-constrained coding approach for meshes is proposed, which ensures that the maximum error between the vertex positions in the original and decoded meshes is lower than a given upper bound. Furthermore, the proposed system achieves scalability in L-infinite sense, that is, any decoding of the input stream will correspond to a perfectly predictable L-infinite distortion upper bound. An instantiation of the proposed L-infinite-coding approach is demonstrated for MESHGRID, which is a scalable 3D object encoding system, part of MPEG-4 AFX. In this context, the advantages of scalable L-infinite coding over L-2-oriented coding are experimentally demonstrated. One concludes that the proposed L-infinite mesh-coding approach guarantees an upper bound on the local error in the decoded mesh, it enables a fast real-time implementation of the rate allocation, and it preserves all the scalability features and animation capabilities of the employed scalable mesh codec.

Progressive Coding and Illumination and View Dependent Transmission of 3-D Meshes Using R-D Optimization

For transmitting complex 3-D models over bandwidth-limited networks, efficient mesh coding and transmission are indispensable. The state-of-the-art 3-D mesh transmission system employs a wavelet-based progressive mesh coder, which converts an irregular mesh into a semi-regular mesh and directly applies the zerotree-like image coders to compress the wavelet vectors, and view-dependent transmission, which saves the transmission bandwidth through only delivering the visible portions of a mesh model. We propose methods to improve both progressive mesh coding and transmission based on thorough rate-distortion analysis. In particular, by noticing that the dependency among the wavelet coefficients generated in remeshing is not being considered in the existing approaches, we propose to introduce a preprocessing step to scale up the wavelets so that the inherent dependency of wavelets can be truly understood by the zerotree-like image compression algorithms. The weights used in the scaling process are carefully designed through thoroughly analyzing the distortions of wavelets at different refinement levels. For the transmission part, we propose to incorporate the illumination effects into the existing view-depend progressive mesh transmission system to further improve the performance. We develop a novel distortion model that considers both illumination distortion and geometry distortion. Based on our proposed distortion model, given the viewing and lighting parameters, we are able to optimally allocate bits among different segments in real time. Simulation results show significant improvements in both progressive compression and transmission.

3D Model compression using Connectivity-Guided Adaptive Wavelet Transform built into 2D SPIHT

Connectivity-Guided Adaptive Wavelet Transform based mesh compression framework is proposed. The transformation uses the connectivity information of the 3D model to exploit the inter-pixel correlations. Orthographic projection is used for converting the 3D mesh into a 2D image-like representation. The proposed conversion method does not change the connectivity among the vertices of the 3D model. There is a correlation between the pixels of the composed image due to the connectivity of the 3D mesh. The proposed wavelet transform uses an adaptive predictor that exploits the connectivity information of the 3D model. Known image compression tools cannot take advantage of the correlations between the samples. The wavelet transformed data is then encoded using a zero-tree wavelet based method. Since the encoder creates a hierarchical bitstream, the proposed technique is a progressive mesh compression technique. Experimental results show that the proposed method has a better rate distortion performance than MPEG-3DGC/MPEG-4 mesh coder.

Reconstruction Algorithms as a Suitable Basis for Mesh Connectivity Compression

During a highly productive period running from 1995 to about 2002, the research in lossless compression of surface meshes mainly consisted in a hard battle for the best bitrates. However, for a few years, compression rates seem stabilized around 1.5 bit per vertex for the connectivity coding of usual triangular meshes, and more and more work is dedicated to remeshing, lossy compression, or gigantic mesh compression, where memory access and CPU optimizations are the new priority. However, the size of 3D models keeps growing, and many application fields keep requiring lossless compression. In this paper, we present a new contribution for single-rate lossless connectivity compression, which first brings improvement over current state of the art bitrates, and second, does not constraint the coding of the vertex positions, offering therefore a good complementarity with the best performing geometric compression methods. The initial observation having motivated this work is that very often, most of the connectivity part of a mesh can be automatically deduced from its geometric part using reconstruction algorithms. This has already been used within the limited framework of projectable objects (essentially, terrain models and GIS), but finds here its first generalization to arbitrary triangular meshes, without any limitation regarding the topological genus, the number of connected components, the manifoldness or the regularity. This can be obtained by constraining and guiding a Delaunay-based reconstruction algorithm so that it outputs the initial mesh to be coded. The resulting rates seem extremely competitive when the meshes are fully included in Delaunay, and are still good compared to the state-of-the-art in the case of scanned models.

TFAN: A low complexity 3D mesh compression algorithm

AbstractThis paper proposes a novel approach for mono‐resolution 3D mesh compression, called TFAN (Triangle Fan‐based compression). TFAN treats in a unified manner meshes of arbitrary topologies, i.e., manifold or not, oriented or not, while offering a linear computational complexity (with respect to the number of mesh vertices) for both encoding and decoding algorithms. In addition, the TFAN compressed representation is optimized for real‐time decoding applications. In order to validate the proposed approach, two databases have been considered for experimentations. The first is the MPEG‐4 test set, which includes over 3500 general purpose manifold meshes. The second, related to the French national project SEMANTIC‐3D, includes over 4000 computer assisted design (CAD) meshes of highly irregular, non‐manifold topologies. In both cases, the TFAN approach outperforms existing techniques such as MPEG‐4/3DMC (3D Mesh Coding) or Touma and Gotsman, with decoding times lower by an order of magnitude at equivalent or even better levels of compression efficiency (±10% in bitrate). In addition, when applied to non‐manifold 3D data, the compression performances are significantly enhanced (6–30% gain in bitrate). Due to its high compression performances the TFAN approach has been recently retained for ISO standardization, within the framework of the MPEG‐4/AFX standard. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Scalable Joint Source and Channel Coding of Meshes

This paper proposes a new approach for joint source and channel coding (JSCC) of meshes, simultaneously providing scalability and optimized resilience against transmission errors. An unequal error protection approach is followed, to cope with the different error-sensitivity levels characterizing the various resolution and quality layers produced by the input scalable source codec. The number of layers and the protection levels to be employed for each layer are determined by solving a joint source and channel coding problem. In this context, a novel fast algorithm for solving the optimization problem is conceived, enabling a real-time implementation of the JSCC rate-allocation. An instantiation of the proposed JSCC approach is demonstrated for MeshGrid, which is a scalable 3-D object representation method, part of MPEG-4 AFX. In this context, the L-inflnite distortion metric is employed, which is to our knowledge a unique feature in mesh coding. Numerical results show the superiority of the L-inflnite norm over the classical L-2 norm in a JSCC setting. One concludes that the proposed joint source and channel coding approach offers resilience against transmission errors, provides graceful degradation, enables a fast real-time implementation, and preserves all the scalability features and animation capabilities of the employed scalable mesh codec.

Impact of vertex clustering on registration-based 3D dynamic mesh coding

3D dynamic meshes are associated with voluminous data and need to be encoded for efficient storage and transmission. We study the impact of vertex clustering on registration-based dynamic mesh coding, where compact mesh motion representation is achieved by computing correspondences for the mesh segments from the temporal reference to obtain high compression performance. Clustering algorithms segment the mesh into smaller pieces and the compression performance is directly related to how effectively these pieces can describe the mesh motion. In this paper, we demonstrate that the use of efficient vertex clustering schemes in the compression framework can bring about a 10% improvement in compression performance.

Error Resilient 3-D Mesh Compression

An error resilient three-dimensional (3-D) mesh coding system is proposed in this paper. The encoder uses a shape adaptive data partitioning scheme to alleviate the effect of error propagation. An input mesh surface is coarsely divided into smooth and detailed regions, and each region is further divided into partitions of similar sizes. Then, those partitions are progressively compressed and their joint boundaries are compressed using the boundary edge collapse rule. At the decoder, the boundary edge collapse rule facilitates the seamless assembly of the partitions. When no data is available for a partition due to transmission errors, we employ a concealment scheme based on the projection onto convex sets (POCS) theory. Simulation results demonstrate that the proposed algorithm reconstructs 3-D mesh surfaces faithfully even in severe error prone environments