Geometry Compression of 3D Mesh Utilising Robust Second Order Blind Identification Algorithm
University of Oradea, Department of Physics-Informatics-Chemistry
str. Universităţii nr. 1, zip code 410087 Oradea, Romania
University of Oradea, Department of Electronics
str. Universităţii nr. 1, zip code 410087 Oradea, Romania
Abstract: The 3D mesh geometry is spatially correlated on each direction in the Cartesian coordinate system, this redundancy leading to a huge VRML file. In order to decorrelate the geometry of 3D mesh, the linear prediction rule used by actual methods is substituted by a Blind Sources Separation technique. For this reason we propose to take the correlated geometry of 3D mesh as observations and decorrelated geometry as sources corresponding at largest energy. The global mixing matrix, achieved by the geometry division into blocks, represents the bitstream of compressed file. Its elements are quantized, binary approximated and encoded using arithmetic coding, providing effective compression. BSS technique proposed is entitled Robust Second Order Blind Identification.
Keywords: Robust Second Order Blind Identification, eigenvalues decomposition, Prediction, 3D mesh, compression.
Mircea Curilă is Associate Professor in Informatics, Head of Physics-Informatics-Chemistry Department, Faculty of Environmental Protection, University of Oradea, Romania. His fields of interest are in image enhancement, higher order statistics, image compression, blind sources separation, virtual reality and virtual environment
Sorin Curilă is Associate Professor in Electronics Department, Faculty of Electrical Engineering and Information Technology, University of Oradea, Romania. His fields of interest are in image representation, image enhancement, higher order statistics and image compression. He has published more than 55 technical papers in International, National journals and conferences
CITE THIS PAPER AS:
Mircea CURILĂ, Sorin CURILĂ, Geometry Compression of 3D Mesh Utilising Robust Second Order Blind Identification Algorithm, Studies in Informatics and Control, ISSN 1220-1766, vol. 17 (4), pp. 421-432, 2008.
The Virtual Reality Modeling Language (VRML) has become the most commonly used standard for representing such 3D models. A VRML file contains complex information in text format related either to the connectivity and the geometry of the model, or to the model properties. Basically, a 3D mesh is defined by a set of vertices and a set of faces. The vertex location is defined by its coordinates in the 3D Cartesian system. A face is defined as an ordered sequence of vertex indices. The connectivity represents the relationships between vertices, the geometry refers to the position of the vertices and the properties contain photometric information, including color, texture and normals.
The VRML files needs effective 3D compression techniques that would significantly reduce the transmission time, the used memory and local disk space. A very big community of researchers has tried to find different algorithms to manipulate the 3D data. One mentions here those whose results are remarkable and very close to aim of our work: J. Rossignak , G. Taubin  , M. Deering , F. Bossen , F. Lazarus , M. Chow, C. Gostman , C. J. Kuo , F. Preteux , D. Nuzillard , A. Gueziec , etc. The compression procedure involves three different coding steps for the connectivity, the geometry and the properties of the mesh. Our contribution is a method concerning the geometry coding.
Starting from the vertices coordinates decorrelation obtained after using a linear prediction law we have shown that the 3D mesh geometry is a linear combination by the decorrelated geometry vector’s components. This remark allows the applying of the Blind Sources Separation algorithms to the compression of mesh geometry of virtual reality.
Based on the experimental results we conclude that the best results for compression and reconstruction of 3D meshes are obtained when the correlated geometry is divided in two blocks (b=2), one separated three sources (M=3) from each block of correlated geometry, and one used a global reconstruction matrix with dimension equals N/2 x 3. The resulted error in mesh reconstruction is small. It is aproximativelly equal to the obtained error when the correlated geometry vector is not divided and one separated three sources. But the new dimension of reconstruction matrix provides good geometry compression.
The obtained results are comparable with those of actual compression methods of 3D meshes, BSS algorithms offering an alternative way.
- AMARI, S., J. F. CARDOSO, Blind Source separation – semiparametric statistical approach, IEEE Trans. Signal Processing, 45(11): 2692-2700.
- BAJAJ, C.L., V. PASCUCCI, G. ZHUANG, Single Resolution Compression of Arbitrary Triangular Meshes with Properties, Technical report, TICAM, The University of Texas at Austin, 1998.
- BELL, T., T. SEJNOWSKY, An information maximization approach to blind separation and blind deconvolution, Neural Computation, vol. 7, 1995, pp. 1129-1159.
- BELOUCHRANI, A., K. ABDEL-MERAIM, J.F. CARDOSO, E. MOULINES, A blind source separation technique using second-order statistics, IEEE Trans. Signal Processing, vol. 45, 1997, pp. 434-444.
- CHOW, M., Optimizel Geometry Compression for Real-time Rendering, In Proceedinngs of IEEE Visualization ’97, Phowenix AZ, 1997, pp. 347-354.
- CICHOCKI, A., S. AMARI, Adaptive Blind Signal and Image Processing. Learning Algorithms and Applications, John Wiley and Sons, Ltd Baffins Lane, Chichester West Sussex, PO19 1UD, 2002.
- CURILĂ, M., D. NUZILLARD, S. CURILĂ, Séparation Aveugle de Sources appliquée à la compression du maillage 3D, 19st GRETSI Symposium on Signal and Image Processing, Paris, France, 8-11 september, 2003.
- CURILĂ, M., S. CURILĂ, D. NUZILLARD, Decorrelation techniques for geometry coding of 3D mesh, Fourth International Symposium on Independent Component Analysis and Blind Signal Separation, Nara, Japan, Avril 1-4, 2003, pp. 885-890.
- CURILĂ, S., M. CURILĂ, T. ZAHARIA, G. MOZELLE, F. PRETEUX, A new prediction scheme for geometry coding of 3D meshes within the MPEG-4 framerwork, Nonliniear Image Processing X, Proceedings of SPIE, ’99, San Jose, California, January, pp. 240-250, 1999.
- DEERING, M., Geometric Compression, Computer Graphics (SIGGRAPH ’95 Proceedings), 1995, pp. 13-20.
- PRETEUX, F., T. ZAHARIA, M. CURIL?, S. CURIL?, G. MOZELLE, Geometry compression of 3D meshes: Results on Core Experiment M2, Report ISO/IEC JTC1/SC29/WG11, MPEG97/M4058, Atlantic City, October 1998.
- GUÉZIEC, A., G. TAUBIN, F. LAZARUS W. HORN, A Framework for Streaming Geometry in VRML, IEEE Computer Graphics and Applications. 19(2), march-April 1999, pp. 68-78.
- GUEZIEC, A., F. BOSSEN, G. TAUBIN, C. SILVA, Efficient Compression of Non-Manifold Polygonal Meshes, IEEE Visualization ’99, 1999.
- LI, J., C. J. KUO, Embedded Coding of Mesh Geometry, Research Report ISO/IEC JTC1/SC29/WG11, MPEG98 / M3325, Tokyo, Japan, March, 1998.
- MOFFAT, A., R. NEAL, I. WITTEN, Arithmetic Coding Revisited, In IEEE Data Compression Conference, Snowbirb, 16(3), Utah, 1995, pp. 256-294.
- NUZILLARD, D., J.-M. NUZILLARD, Second order blind source separation on the fourier space of data, To be published in: Signal Processing 2003.
- TAUBIN, G., J. ROSSIGNAC, Course on 3D Geometry Compression, Siggraph ‘2000, New Orleans, Louisiana, July 2000.
- TAUBIN, G., W.P. HORN, F. LAZARUS, and J. ROSSIGNAC, Geometric Coding and VRML, Proceedings of the IEEE. 86(6), June 1998, pp 1228-1243.
- TAUBIN, G., J. ROSSIGNAC, Geometric Compression through Topological Surgery, ACM Transaction on Graphics, April 1998, pp. 84-115.
- TAUBIN, G., 3D Geometry Compression and Progressive Transmission, Eurographics State of the Art Report, September 1999.
- TAUBIN G., and J. ROSSIGNAC, Course on 3D Geometry Compression, Siggraph’99, Los Angeles, CA, August 1999.
- TOUMA, C., C. GOTSMAN, Triangle mesh compression, In Graphics Interface Conference Proceegings, Vancouver, June, 1998, pp. 26-34.
- The Virtual Reality Modeling Language, ISO / IEC 14772 – 1, 1997, http://www.vrml.org/Specifications//VRML97.