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44
Spectral Compression of Mesh Geometry
, 2000
"... We show how spectral methods may be applied to 3D mesh data to obtain compact representations. This is achieved by projecting the mesh geometry onto an orthonormal basis derived from the mesh topology. To reduce complexity, the mesh is partitioned into a number of balanced submeshes with minimal int ..."
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Cited by 180 (6 self)
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We show how spectral methods may be applied to 3D mesh data to obtain compact representations. This is achieved by projecting the mesh geometry onto an orthonormal basis derived from the mesh topology. To reduce complexity, the mesh is partitioned into a number of balanced submeshes with minimal interaction, each of which are compressed independently. Our methods may be used for compression and progressive transmission of 3D content, and are shown to be vastly superior to existing methods using spatial techniques, if slight loss can be tolerated.
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.
Face Fixer: Compressing polygon meshes with properties
 In SIGGRAPH’00 Conference Proceedings
, 2000
"... Most schemes to compress the topology of a surface mesh have been developed for the lowest common denominator: triangulated meshes. We propose a scheme that handles the topology of arbitrary polygon meshes. It encodes meshes directly in their polygonal representation and extends to capture face grou ..."
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Cited by 88 (18 self)
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Most schemes to compress the topology of a surface mesh have been developed for the lowest common denominator: triangulated meshes. We propose a scheme that handles the topology of arbitrary polygon meshes. It encodes meshes directly in their polygonal representation and extends to capture face groupings in a natural way. Avoiding the triangulation step we reduce the storage costs for typical polygon models that have group structures and property data.
Progressive Compression for Lossless Transmission of Triangle Meshes
, 2001
"... Lossless transmission of 3D meshes is a very challenging and timely problem for many applications, ranging from collaborative design to engineering. Additionally, frequent delays in transmissions call for progressive transmission in order for the end user to receive useful successive refinements of ..."
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Cited by 86 (3 self)
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Lossless transmission of 3D meshes is a very challenging and timely problem for many applications, ranging from collaborative design to engineering. Additionally, frequent delays in transmissions call for progressive transmission in order for the end user to receive useful successive refinements of the final mesh. In this paper, we present a novel, fully progressive encoding approach for lossless transmission of triangle meshes with a very fine granularity. A new valencedriven decimating conquest, combined with patch tiling and an original strategic retriangulation is used to maintain the regularity of valence. We demonstrate that this technique leads to good mesh quality, nearoptimal connectivity encoding, and therefore a good ratedistortion ratio throughout the transmission. We also improve upon previous lossless geometry encoding by decorrelating the normal and tangential components of the surface. For typical meshes, our method compresses connectivity down to less than 3.7 bits per vertex, 40% better in average than the best methods previously reported [5, 18]; we further reduce the usual geometry bit rates by 20% in average by exploiting the smoothness of meshes. Concretely, our technique can reduce an ascii VRML 3D model down to 1.7% of its size for a 10bit quantization (2.3% for a 12bit quantization) while providing a very progressive reconstruction.
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
Progressive lossless compression of arbitrary simplicial complexes
 ACM Trans. Graphics (Proc. ACM SIGGRAPH 2002
, 2002
"... Efficient algorithms for compressing geometric data have been widely developed in the recent years, but they are mainly designed for closed polyhedral surfaces which are manifold or “nearly manifold”. We propose here a progressive geometry compression scheme which can handle manifold models as well ..."
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Cited by 66 (0 self)
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Efficient algorithms for compressing geometric data have been widely developed in the recent years, but they are mainly designed for closed polyhedral surfaces which are manifold or “nearly manifold”. We propose here a progressive geometry compression scheme which can handle manifold models as well as “triangle soups ” and 3D tetrahedral meshes. The method is lossless when the decompression is complete which is extremely important in some domains such as medical or finite element. While most existing methods enumerate the vertices of the mesh in an order depending on the connectivity, we use a kdtree technique [8] which does not depend on the connectivity. Then we compute a compatible sequence of meshes which can be encoded using edge expansion [14] and vertex split [24]. 1 The main contributions of this paper are: the idea of using the kdtree encoding of the geometry to drive the construction of a sequence of meshes, an improved coding of the edge expansion and vertex split since the vertices to split are implicitly defined, a prediction scheme which reduces the code for simplices incident to the split vertex, and a new generalization of the edge expansion operation to tetrahedral meshes. 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.
Wrap&Zip decompression of the connectivity of triangle meshes compressed with Edgebreaker
 Journal of Computational Geometry, Theory and Applications
, 1999
"... The Edgebreaker compression (Rossignac, 1999; King and Rossignac, 1999) is guaranteed to encode any unlabeled triangulated planar graph of t triangles with at most 1.84t bits. It stores the graph as a CLERS string a sequence of t symbols from the set {C, L,E,R,S}, each represented by a 1, 2 or ..."
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Cited by 41 (13 self)
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The Edgebreaker compression (Rossignac, 1999; King and Rossignac, 1999) is guaranteed to encode any unlabeled triangulated planar graph of t triangles with at most 1.84t bits. It stores the graph as a CLERS string a sequence of t symbols from the set {C, L,E,R,S}, each represented by a 1, 2 or 3 bit code. We show here that, in practice, the string can be further compressed to between 0.91t and 1.26t bits using an entropy code. These results improve over the 2.3t bits code proposed by Keeler and Westbrook (1995) and over the various 3D triangle mesh compression techniques published recently (Gumhold and Strasser, 1998; Itai and Rodeh, 1982; Naor, 1990; Touma and Gotsman, 1988; Turan, 1984), which exhibit either larger constants or cannot guarantee a linear worst case storage complexity. The decompression proposed by Rossignac (1999) is complicated and exhibits a nonlinear time complexity. The main contribution reported here is a simpler and efficient decompression algorithm, calle...
3D Compression Made Simple: Edgebreaker on a CornerTable
 Shape Modeling International Conference
, 2001
"... Edgebreaker is a simple technique for compressing 3D triangle meshes. We introduce here a new formulation, which leads to a simple implementation. We describe it in terms of a data structure, the Corner Table, which represents the connectivity of any manifold triangle mesh as two table of integ ..."
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Cited by 41 (15 self)
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Edgebreaker is a simple technique for compressing 3D triangle meshes. We introduce here a new formulation, which leads to a simple implementation. We describe it in terms of a data structure, the Corner Table, which represents the connectivity of any manifold triangle mesh as two table of integers. For meshes that are homeomorphic to a sphere, Edgebreaker encodes these two tables with less than 2 bits per triangle. It compresses vertex locations using a parallelogram predictor. Entropy encoding reduces this cost in practice to less than a bit per triangle when the mesh is large. The detailed compression and decompression algorithms fit on a page. Through minor modifications, the Edgebreaker algorithm has been adapted to manifold meshes with holes and handles, to nontriangle meshes, and to nonmanifold meshes. A CornerTable implementation of these extensions will be described elsewhere.
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.