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15
ValenceDriven Connectivity Encoding for 3D Meshes
, 2001
"... In this paper, we propose a valencedriven, singleresolution encoding technique for lossless compression of triangle mesh connectivity. Building upon a valencebased approach pioneered by Touma and Gotsman 22, we design a new valencedriven conquest for arbitrary meshes that always guarantees sma ..."
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Cited by 104 (10 self)
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In this paper, we propose a valencedriven, singleresolution encoding technique for lossless compression of triangle mesh connectivity. Building upon a valencebased approach pioneered by Touma and Gotsman 22, we design a new valencedriven conquest for arbitrary meshes that always guarantees smaller compression rates than the original method. Furthermore, we provide a novel theoretical entropy study of our technique, hinting the optimality of the valencedriven approach. Finally, we demonstrate the practical efficiency of this approach (in agreement with the theoretical prediction) on a series of test meshes, resulting in the lowest compression ratios published so far, for both irregular and regular meshes, small or large.
Recent advances in compression of 3D meshes
 In Advances in Multiresolution for Geometric Modelling
, 2003
"... Summary. 3D meshes are widely used in graphic and simulation applications for approximating 3D objects. When representing complex shapes in a raw data format, meshes consume a large amount of space. Applications calling for compact storage and fast transmission of 3D meshes have motivated the multit ..."
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Cited by 70 (3 self)
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Summary. 3D meshes are widely used in graphic and simulation applications for approximating 3D objects. When representing complex shapes in a raw data format, meshes consume a large amount of space. Applications calling for compact storage and fast transmission of 3D meshes have motivated the multitude of algorithms developed to efficiently compress these datasets. In this paper we survey recent developments in compression of 3D surface meshes. We survey the main ideas and intuition behind techniques for singlerate and progressive mesh coding. Where possible, we discuss the theoretical results obtained for asymptotic behavior or optimality of the approach. We also list some open questions and directions for future research. 1
NearOptimal Connectivity Encoding of 2Manifold Polygon Meshes
, 2002
"... ... this paper we introduce a connectivity encoding method which extends these ideas to 2manifold meshes consisting of faces with arbitrary degree. The encoding algorithm exploits duality by applying valence enumeration to both the primal and dual mesh in a symmetric fashion. It generates two sequen ..."
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Cited by 54 (6 self)
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... this paper we introduce a connectivity encoding method which extends these ideas to 2manifold meshes consisting of faces with arbitrary degree. The encoding algorithm exploits duality by applying valence enumeration to both the primal and dual mesh in a symmetric fashion. It generates two sequences of symbols, vertex valences and face degrees, and encodes them separately using two contextbased arithmetic coders. This allows us to exploit vertex and/or face regularity if present. When the mesh exhibits perfect face regularity (e.g., a pure triangle or quad mesh) and/or perfect vertex regularity (valence six or four respectively) the corresponding bit rate vanishes to zero asymptotically. For triangle meshes, our technique is equivalent to earlier valence driven approaches. We report compression results for a corpus of standard meshes. In all cases we are able to show coding gains over earlier coders, sometimes as large as 50%. Remarkably, we even slightly gain over coders specialized to triangle or quad meshes. A theoretical analysis reveals that our approach is nearoptimal as we achieve the Tutte entropy bound for arbitrary planar graphs of 2 bits per edge in the worst case.
Spirale Reversi: Reverse decoding of the Edgebreaker encoding
, 2001
"... We present a simple linear time algorithm for decoding Edgebreaker encoded triangle meshes in a single traversal. The Edgebreaker encoding technique, introduced in [5], encodes the connectivity of triangle meshes homeomorphic to a sphere with a guaranteed # bits per triangle or less. The encoding a ..."
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Cited by 40 (6 self)
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We present a simple linear time algorithm for decoding Edgebreaker encoded triangle meshes in a single traversal. The Edgebreaker encoding technique, introduced in [5], encodes the connectivity of triangle meshes homeomorphic to a sphere with a guaranteed # bits per triangle or less. The encoding algorithm visits every triangle of the mesh in a depthfirst order. The original decoding algorithm [5] recreates the triangles in the same order they have been visited by the encoding algorithm and exhibits a worst case time complexity of ### # #. More recent work [6] uses the same traversal order and improves the worst case to ####. However, for meshes with handles multiple traversals are needed during both encoding and decoding. We introduce here a simpler decoding technique that performs a single traversal and recreates the triangles in reverse order.
Compressing Polygon Mesh Connectivity with Degree Duality Prediction
, 2002
"... In this paper we present a coder for polygon mesh connectivity that delivers the best connectivity compression rates meshes reported so far. Our coder is an extension of the vertexbased coder for triangle mesh connectivity by Touma and Gotsman [26]. We code polygonal connectivity as a sequence of f ..."
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Cited by 36 (13 self)
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In this paper we present a coder for polygon mesh connectivity that delivers the best connectivity compression rates meshes reported so far. Our coder is an extension of the vertexbased coder for triangle mesh connectivity by Touma and Gotsman [26]. We code polygonal connectivity as a sequence of face and vertex degrees and exploit the correlation between them for mutual predictive compression. Because lowdegree vertices are likely to be surrounded by highdegree faces and vice versa, we predict vertex degrees based on neighboring face degrees and face degrees based on neighboring vertex degrees.
Simplification and Compression of 3D Meshes
 In Proceedings of the European Summer School on Principles of Multiresolution in Geometric Modelling (PRIMUS
, 1998
"... We survey recent developments in compact representations of 3D mesh data. This includes: Methods to reduce the complexity of meshes by simplification, thereby reducing the number of vertices and faces in the mesh; Methods to resample the geometry in order to optimize the vertex distribution; Methods ..."
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Cited by 31 (5 self)
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We survey recent developments in compact representations of 3D mesh data. This includes: Methods to reduce the complexity of meshes by simplification, thereby reducing the number of vertices and faces in the mesh; Methods to resample the geometry in order to optimize the vertex distribution; Methods to compactly represent the connectivity data (the graph structure defined by the edges) of the mesh; Methods to compactly represent the geometry data (the vertex coordinates) of a mesh.
Octreebased progressive geometry encoder
 In Internet Multimedia Management Systems IV. Edited by Smith, John R.; Panchanathan, Sethuraman; Zhang, Tong. Proceedings of the SPIE
, 2003
"... Among progressive 3D mesh compression algorithms, the kdtreebased algorithm proposed by Gandoin and Devillers [1] is one of the stateoftheart algorithms. Based on the observation that this geometry coder has a large amount of overhead at high kdtree levels, we propose an octreebased geometry ..."
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Cited by 3 (0 self)
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Among progressive 3D mesh compression algorithms, the kdtreebased algorithm proposed by Gandoin and Devillers [1] is one of the stateoftheart algorithms. Based on the observation that this geometry coder has a large amount of overhead at high kdtree levels, we propose an octreebased geometry coder that demands a less amount of coding bits at high octree levels by applying selective cell subdivision at high tree levels, leading to a better ratedistortion performance for the low bit rate coding. Experimental results show that, compared with the kdtreebased coder, the proposed 3D geometry coder performs better for an expanded tree of a level less than or equal to 8 but slightly worse for the full tree expansion with 12bit quantization.
Compression and Streaming of Polygon Meshes
, 2005
"... Polygon meshes provide a simple way to represent threedimensional surfaces and are the defacto standard for interactive visualization of geometric models. Storing large polygon meshes in standard indexed formats results in files of substantial size. Such formats allow listing vertices and polygons ..."
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Cited by 3 (0 self)
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Polygon meshes provide a simple way to represent threedimensional surfaces and are the defacto standard for interactive visualization of geometric models. Storing large polygon meshes in standard indexed formats results in files of substantial size. Such formats allow listing vertices and polygons in any order so that not only the mesh is stored but also the particular ordering of its elements. Mesh compression rearranges vertices and polygons into an order that allows more compact coding of the incidence between vertices and predictive compression of their positions. Previous schemes were designed for triangle meshes and polygonal faces were triangulated prior to compression. I show that polygon models can be encoded more compactly by avoiding the initial triangulation step. I describe two compression schemes that achieve better compression by encoding meshes directly in their polygonal representation. I demonstrate that the
Algebraic analysis of highpass quantization
 ACM TOG
, 2005
"... This article presents an algebraic analysis of a meshcompression technique called highpass quantization [Sorkine et al. 2003]. In highpass quantization, a rectangular matrix based on the mesh topological Laplacian is applied to the vectors of the Cartesian coordinates of a polygonal mesh. The res ..."
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Cited by 3 (2 self)
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This article presents an algebraic analysis of a meshcompression technique called highpass quantization [Sorkine et al. 2003]. In highpass quantization, a rectangular matrix based on the mesh topological Laplacian is applied to the vectors of the Cartesian coordinates of a polygonal mesh. The resulting vectors, called δcoordinates, are then quantized. The applied matrix is a function of the topology of the mesh and the indices of a small set of mesh vertices (anchors) but not of the location of the vertices. An approximation of the geometry can be reconstructed from the quantized δcoordinates and the spatial locations of the anchors. In this article, we show how to algebraically bound the reconstruction error that this method generates. We show that the small singular value of the transformation matrix can be used to bound both the quantization error and the rounding error which is due to the use of floatingpoint arithmetic. Furthermore, we prove a bound on this singular value. The bound is a function of the topology of the mesh and of the selected anchors. We also propose a new anchorselection algorithm, inspired by this bound. We show experimentally that the method is effective and that the computed upper bound on the error is not too pessimistic.