The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.12 - Dec. (2012 vol.18)
pp: 2069-2077
K. C. Gurijala , Stony Brook Univ., Stony Brook, NY, USA
Lei Wang , Stony Brook Univ., Stony Brook, NY, USA
A. Kaufman , Stony Brook Univ., Stony Brook, NY, USA
ABSTRACT
We introduce a simple, yet powerful method called the Cumulative Heat Diffusion for shape-based volume analysis, while drastically reducing the computational cost compared to conventional heat diffusion. Unlike the conventional heat diffusion process, where the diffusion is carried out by considering each node separately as the source, we simultaneously consider all the voxels as sources and carry out the diffusion, hence the term cumulative heat diffusion. In addition, we introduce a new operator that is used in the evaluation of cumulative heat diffusion called the Volume Gradient Operator (VGO). VGO is a combination of the LBO and a data-driven operator which is a function of the half gradient. The half gradient is the absolute value of the difference between the voxel intensities. The VGO by its definition captures the local shape information and is used to assign the initial heat values. Furthermore, VGO is also used as the weighting parameter for the heat diffusion process. We demonstrate that our approach can robustly extract shape-based features and thus forms the basis for an improved classification and exploration of features based on shape.
INDEX TERMS
shape recognition, chemical engineering computing, computer graphics, diffusion, feature extraction, gradient methods, image classification, feature classification, cumulative heat diffusion, volume gradient operator, shape-based volume analysis, VGO, LBO, data-driven operator, half gradient, voxel intensity, local shape information, heat value, shape-based feature extraction, Heating, Shape analysis, Histograms, Diffusion processes, Equations, Volume measurement, transfer function, Heat diffusion, volume gradient operator, shape-based volume analysis, classification
CITATION
K. C. Gurijala, Lei Wang, A. Kaufman, "Cumulative Heat Diffusion Using Volume Gradient Operator for Volume Analysis", IEEE Transactions on Visualization & Computer Graphics, vol.18, no. 12, pp. 2069-2077, Dec. 2012, doi:10.1109/TVCG.2012.210
REFERENCES
[1] M. Belkin, J. Sun, and Y. Wang, Discrete laplace operator on meshed surfaces Proceedings of the Symposium on Computational Geometry, pages 278-287, 2008.
[2] S. Beucher and C. Lantuejoul, Use of watersheds in contour detection Proceedings of International Workshop on Image Processing: Real-time Edge and Motion Detection/Estimation, Sept. 1979.
[3] M. M, Bronstein and 1. Kokkinos. Scale-invariant heat kernel signatures for non-rigid shape recognition Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1704-1711, 2010.
[4] S. Bruckner and T. Möller., Isosurface similarity maps. Proceedings of Eurographics/IEEE-VGTC Symposium on Visualization 2010 (EuroVis 2010), 29(3): 773-782, June 2010.
[5] C. D. Correa and D. Silver., Dataset traversal with motion-controlled transfer functions Proceedings of IEEE Visualization, pages 359-366, Oct. 2005.
[6] J. Dodziuk, Finite-difference approach to the Hodge theory of harmonic forms American Journal of Mathematics, 98(1): 79-34, 1976.
[7] K. Gebal,J. A. Bærentzen, H. Aanæs, and R. Larsen, Shape analysis using the auto diffusion function Proceedings of the Eurographics Symposium on Geometry Processing, 28(5): 1405-34, 2009.
[8] M. Haidacher, S. Bruckner, and M. E Gröller., Volume analysis using multimodal surface similarity IEEE Transactions on Visualization and Computer Graphics, 17(12): 1969-1978, Oct. 2011.
[9] M. Hilaga, Y. Shinagawa, T. Kohmura,, and T. L. Kunii., Topology matching for fully automatic similarity estimation of 3D shapes. SIGGRAPH, pages 203-212, 2001.
[10] G. Kindlmann and J. W, Durkin. Semi-automatic generation of transfer functions for direct volume rendering Proceedings of the IEEE Symposium on Volume Visualization, pages 79-86, 1998.
[11] J. Kniss, G. Kindlmann, and C. Hansen, Multidimensional transfer functions for interactive volume rendering IEEE Transactions on Visualization and Computer Graphics, 8(3): 270-285, July 2002.
[12] A. Levin, D. Lischinski, and Y. Weiss, Colorization using optimization ACM Transactions on Graphics, 23(3): 689-694, Aug. 2004.
[13] B. Levy, Laplace-Beltrami eigenfunctions towards an algorithm that “un-derstands” geometry Proceedings of the IEEE International Conference on Shape Modeling and Applications, pages 13: 1-8, 2006.
[14] A. P. Mangan and R. T. Whitaker., Partitioning 3d surface meshes using watershed segmentation IEEE Transactions on Visualization and Computer Graphics, 5(4): 308-321, Oct. 1999.
[15] E. Mémoli., Spectral Gromov-Wasserstein distances for shape matching. Proc. Workshop on Non-Rigid Shape Analysis and Deformable Image Alignment, pages 256-263, October 2009.
[16] D. Mohr and G. Zachmann, Continuous edge gradient-based template matching for articulated objects Proceedings of the International Conference on Computer Vision Theory and Applications, pages 519-524, February 2009.
[17] M. Ovsjanikov, Q. Mérigot, F. Mémoli,, and L. J. Guibas., One point isometric matching with the heat kernel. Proceedings of the Eurographics Symposium on Geometry Processing, 29(5): 1555-34, 2010.
[18] U. Pinkall,S. D. Juni,, and K. Polthier., Computing discrete minimal surfaces and their conjugates. Experimental Mathematics, 2: 15-36, 1993.
[19] S. M. Pizer, G. Gerig, S. C. Joshi,, and S. R. Aylward., Multiscale medial shape-based analysis of image objects Proceedings of the IEEE, 91(10): 1670-1679, 2003.
[20] J.-S. Praßni, T. Ropinski, J. Mensmann,, and K. H., Hinrichs. Shape-based transfer functions for volume visualization. Proceedings of the IEEE Pacific Visualization Symposium, pages 9-16, Mar 2010.
[21] D. Raviv,M. M. Bronstein,A. M. Bronstein,, and R. Kimmel., Volumetric heat kernel signatures. Proceedings of the ACM Workshop on 3D Object Retrieval, pages 39-44, 2010.
[22] D. Reniers, A. Jalba, and A. Telea, Robust classification and analysis of anatomical surfaces using 3D skeletons Proceedings of the Eurographics Workshop on Visual Computing for Biomedicine, pages 61-68, 2008.
[23] M. E. Rettmann, X. Han, and J. L., Prince. Watersheds on the cortical surface for automated sulcal segmentation Proceedings of the IEEE Workshop on Mathematical Methods in Biomedical Image Analysis, pages 2027, 2000.
[24] M. Reuter, S. Biasotti, D. Giorgi, G. Patané, and M. Spagnuolo, Discrete Laplace-Beltrami operators for shape analysis and segmentation Proceedings of Computers & Graphics, 33: 381-390, Jun 2009.
[25] M. Reuter,E.-E. Wolter,, and N. Peinecke., Laplace-Beltrami spectra as “Shape-DNA” of surfaces and solids. Computer-Aided Design, 38(4): 342-366, Apr 2006.
[26] R. M, Rustamov. Laplace-Beltrami eigenfunctions for deformation invariant shape representation Proceedings of the Eurographics Symposium on Geometry Processing, pages 225-233, 2007.
[27] Y. Sato,C. E. Westin, A. Bhalerao, S. Nakajima, N. Shiraga, S. Tamura,, and R. Kikinis., Tissue classification based on 3D local intensity structure for volume rendering. IEEE Transactions on Visualization and Computer Graphics, 6(2): 160-34, 2000.
[28] D. Saupe and D. V. Vranic., 3D model retrieval with spherical harmonics and moments Proceedings of the Deutsche Arbeitsgemeinschaft für Mustererkennung Symposium on Pattern Recognition, pages 392-397, 2001.
[29] J. Sun, M. Ovsjanikov, and L. J. Guibas., A concise and provably informative multi-scale signature based on heat diffusion Proceedings of the Eurographics Symposium on Geometry Processing, 28(5): 1383-34, 2009.
[30] A. Vaxman,M. Ben-Chen,, and C. Gotsman., A multi-resolution approach to heat kernels on discrete surfaces. ACM Transactions on Graphics, 29:121: 1-121:10, July 2010.
[31] V. Zobel, J. Reininghaus, and 1. Hotz., Generalized heat kernel signatures. Journal of WSCG, International Conference on Computer Graphics, Visualization and Computer Vision, 19(3): 93-100, 2011.
13 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool