The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.02 - February (2011 vol.17)
pp: 132-145
Iurie Chiosa , University of Siegen, Siegen
Andreas Kolb , University of Siegen, Siegen
ABSTRACT
The processing power of parallel coprocessors like the Graphics Processing Unit (GPU) is dramatically increasing. However, until now only a few approaches have been presented to utilize this kind of hardware for mesh clustering purposes. In this paper, we introduce a Multilevel clustering technique designed as a parallel algorithm and solely implemented on the GPU. Our formulation uses the spatial coherence present in the cluster optimization and hierarchical cluster merging to significantly reduce the number of comparisons in both parts. Our approach provides a fast, high-quality, and complete clustering analysis. Furthermore, based on the original concept, we present a generalization of the method to data clustering. All advantages of the mesh-based techniques smoothly carry over to the generalized clustering approach. Additionally, this approach solves the problem of the missing topological information inherent to general data clustering and leads to a Local Neighbors k-means algorithm. We evaluate both techniques by applying them to Centroidal Voronoi Diagram (CVD)-based clustering. Compared to classical approaches, our techniques generate results with at least the same clustering quality. Our technique proves to scale very well, currently being limited only by the available amount of graphics memory.
INDEX TERMS
Computer graphics, parallel processing, clustering methods, hierarchical methods, programmable graphics hardware.
CITATION
Iurie Chiosa, Andreas Kolb, "GPU-Based Multilevel Clustering", IEEE Transactions on Visualization & Computer Graphics, vol.17, no. 2, pp. 132-145, February 2011, doi:10.1109/TVCG.2010.55
REFERENCES
[1] D. Cohen-Steiner, P. Alliez, and M. Desbrun, "Variational Shape Approximation," Proc. ACM SIGGRAPH, pp. 905-914, 2004.
[2] M. Garland, A. Willmott, and P.S. Heckbert, "Hierarchical Face Clustering on Polygonal Surfaces," Proc. Symp. Interactive 3D graphics (I3D), pp. 49-58, 2001.
[3] I. Chiosa and A. Kolb, "Variational Multilevel Mesh Clustering," Proc. IEEE Int'l Conf. Shape Modeling and Applications (SMI), pp. 197-204, 2008.
[4] S. Valette and J.-M. Chassery, "Approximated Centroidal Voronoi Diagram for Uniform Polygonal Mesh Coarsening," Proc. Conf. Eurographics, vol. 23, no. 3, pp. 381-389, 2004.
[5] I. Chiosa, A. Kolb, N. Cuntz, and M. Lindner, "Parallel Mesh Clustering," Proc. Eurographics Symp. Parallel Graphics and Visualization (EGPGV), pp. 33-40, 2009.
[6] J. Wu and L. Kobbelt, "Structure Recovery via Hybrid Variational Surface Approximation," Proc. Conf. Eurographics, vol. 24, no. 3, pp. 277-284, 2005.
[7] D.-M. Yan, Y. Liu, and W. Wang, "Quadric Surface Extraction by Variational Shape Approximation," Proc. Int'l Conf. Geometric Modeling and Processing (GMP), pp. 73-86, 2006.
[8] D. Julius, V. Kraevoy, and A. Sheffer, "D-Charts: Quasi-Developable Mesh Segmentation," Proc. Conf. Eurographics, vol. 24, no. 3, pp. 581-590, 2005.
[9] M. Attene, B. Falcidieno, and M. Spagnuolo, "Hierarchical Mesh Segmentation Based on Fitting Primitives," The Visual Computer, vol. 22, no. 3, pp. 181-193, 2006.
[10] R. Xu and D.C. Wunsch, Clustering. Wiley IEEE Press, 2008.
[11] G. Gan, C. Ma, and J. Wu, Data Clustering: Theory, Algorithms, and Applications. ASA-SIAM, 2007.
[12] D. Pelleg and A. Moore, "X-Means: Extending k-Means with Efficient Estimation of the Number of Clusters," Proc. 17th Int'l Conf. Machine Learning, pp. 727-734, 2000.
[13] G. Hamerly and C. Elkan, "Alternatives to the k-Means Algorithm That Find Better Clusterings," Proc. 11th Int'l Conf. Information and Knowledge Management (CIKM '02), pp. 600-607, 2002.
[14] M. Steinbach, G. Karypis, and V. Kumar, "A Comparison of Document Clustering Techniques," Proc. KDD Workshop Text Mining, pp. 109-111, 2000.
[15] S.M. Savaresi and D.L. Boley, "A Comparative Analysis on the Bisecting k-Means and the Pddp Clustering Algorithms," Intelligent Data Analysis, vol. 8, no. 4, pp. 345-362, 2004.
[16] C.F. Olson, "Parallel Algorithms for Hierarchical Clustering," Parallel Computing, vol. 21, no. 8, pp. 1313-1325, 1995.
[17] M. Willebeek-LeMair and A.P. Reeves, "Region Growing on a Hypercube Multiprocessor," Proc. Third Conf. Hypercube Concurrent Computers and Applications, pp. 1033-1042, 1988.
[18] J.D. Hall and J.C. Hart, "GPU Acceleration of Iterative Clustering," Proc. ACM Workshop General Purpose Computing on Graphics Processors and SIGGRAPH 2004, Manuscript Accompanying Poster at $GP^2$ , 2004.
[19] A.K.T. Feng Cao and A. Zhou, "Scalable Clustering Using Graphics Processors," Lecture Notes in Computer Science, pp. 372-384, Springer, 2006.
[20] S.A. Shalom, M. Dash, and M. Tue, "Efficient k-Means Clustering Using Accelerated Graphics Processors," Proc. 10th Int'l Conf. Data Warehousing and Knowledge Discovery (DaWaK), pp. 166-175, 2008.
[21] V. Garcia, E. Debreuve, and M. Barlaud, "Fast k Nearest Neighbor Search Using GPU," Proc. CVPR Workshop Computer Vision on GPU, 2008.
[22] Q. Du, M. Gunzburger, L. Ju, and X. Wang, "Centroidal Voronoi Tessellation Algorithms for Image Compression, Segmentation, and Multichannel Restoration," J. Math. Imaging and Vision, vol. 24, no. 2, pp. 177-194, 2006.
[23] N. Cuntz, "gp3tools," http://www.cg.informatik.uni-siegen.de/Programming hase3d, 2010.
[24] M. Mäntylä, An Introduction to Solid Modeling. Computer Science Press, 1988.
[25] R. Mantiuk, G. Krawczyk, R. Mantiuk, and H.-P. Seidel, "High Dynamic Range Imaging Pipeline: Perception-Motivated Representation of Visual Content," Human Vision and Electronic Imaging XII, p. 649212, SPIE, 2007.
[26] Q. Du, V. Faber, and M. Gunzburger, "Centroidal Voronoi Tessellations: Applications and Algorithms," SIAM Rev., vol. 41, no. 4, pp. 637-676, 1999.
[27] D. Pelleg and A. Moore, "Auton Lab: K-Means and x-Means Implementation," http://www.cs.cmu.edu/~dpellegkmeans. html , 2010.
23 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool