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Mumford and Shah Functional: VLSI Analysis and Implementation
March 2006 (vol. 28 no. 3)
pp. 487-494
This paper describes the analysis of the Mumford and Shah functional from the implementation point of view. Our goal is to show results in terms of complexity for real-time applications, such as motion estimation based on segmentation techniques, of the Mumford and Shah functional. Moreover, the sensitivity to finite precision representation is addressed, a fast VLSI architecture is described, and results obtained for its complete implementation on a 0.13 \mu\rm m standard cells technology are presented.

[1] D. Mumford and J. Shah, “Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems,” Comm. Pure Applied Math., vol. 42, pp. 577-685, 1989.
[2] F. Sroubek and J. Flusser, “Multichannel Blind Iterative Image Restoration,” IEEE Trans. Image Processing, vol. 12, no. 9, pp. 1094-1106, Sept. 2003.
[3] A. Brook, R. Kimmel, and N.A. Sochen, “Variational Restoration and Edge Detection for Color Images,” J. Math. Imaging and Vision, vol. 18, no. 3, pp. 247-268, 2003.
[4] D. Cremers and S. Soatto, “Motion Competition: A Variational Approach to Piecewise Parametric Motion Segmentation,” Int'l J. Computer Vision, vol. 62, no. 3, pp. 249-265, 2005.
[5] R. March, “Visual Reconstruction with Discontinuities Using Varaitional Methods,” Image and Vision Computing, vol. 10, pp. 30-38, 1992.
[6] G. Koepfler, C. Lopez, and J.M. Morel, “A Multiscale Algorithm for Image Segmentation by Variational Method,” SIAM J. Numerical Analysis, vol. 31, no. 1, pp. 282-299, Feb. 1994.
[7] D. Cremers, F. Tishhäuser, J. Weickert, and C. Shnörr, “Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford And Shah Functional,” Int'l J. Computer Vision, vol. 50, no. 3, pp. 295-313, 2002.
[8] T.P. Vogl, J.W. Mangis, A.K. Rigler, W.T. Zink, and D.L. Alkon, “Accelerating the Convergence of the Back-Propagation Method,” Biological Cybernetics, vol. 59, pp. 257-263, 1988.
[9] W. Vanzella, F.A. Pellegrino, and V. Torre, “Self-Adaptive Regularization,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 6, pp. 804-809, June 2004.
[10] F. Gibou, D. Levy, C. Cardenas, P. Liu, and A. Boyer, “Partial Differential Equation Based Segmentation for Radiotherapy Treatment Planning,” Math. Biosciences and Eng., vol. 2, pp. 209-226, 2005.
[11] Intel, http://www.intel.com/design/xeon/datashts 252135.htm, 2005.
[12] L. Ambrosio and V.M. Tortorelli, “Approximation of Functionals Depending on Jumps by Elliptic Functionals via $\Gamma{\hbox{-}}\rm Convergence$ ,” Comm. Pure Applied Math., vol. 43, pp. 999-1036, 1990.
[13] T.F. Chan and L.A. Vese, “Active Contours without Edges,” IEEE Trans. Image Processing, vol. 10, no. 2, pp. 266-277, Feb. 2001.
[14] M. Martina and G. Masera, “Mumford and Shah Functional: Finite Precision Analysis and Software Implementation,” Proc. IEEE Int'l Symp. Signal Processing and Information Technology, 2004.
[15] M.F. Adams, “A Distributed Memory Unstructured Gauss-Seidel Algorithm for Multigrid Smoothers,” ACM/IEEE Proc. SC2001: High Performance Networking and Computing, pp. 1-4, 2001.
[16] M.M. Strout, L. Carter, J. Ferrante, J. Freeman, and B. Kreaseck, “Combining Performance Aspects of Irregular Gauss-Seidel via Sparse Tiling,” Proc. 15th Workshop Languages and Compilers for Parallel Computing, pp. 1-4, 2002.
[17] F.Z. Hadjam, A. Rahmoun, and M. Benmohammed, “On Designing a Systolic Network for the Resolution of Linear Systems Using the Gauss-Seidel Method,” Proc. IEEE Int'l Conf. Computer Systems and Applications, pp. 283-286, 2001.
[18] J.A. Yang and Y. Choo, “Formal Derivation of an Efficient Parallel 2-D Gauss-Siedel Method,” Proc. Sixth Int'l Parallel Processing Symp., pp. 204-207, 1992.
[19] J.E. Robertson, “A New Class of Digital Division Methods,” IRE Trans. Electronic Computers, vol. 7, pp. 218-222, 1958.
[20] M. Martina, “Mumford and Shah C Model,” www.vlsilab.polito.itmartina, 2004.
[21] MegaWave2, http://www.cmla.ens-cachan.fr/cmla/megawave index.html, 2004.

Index Terms:
Index Terms- Image segmentation, Mumford and Shah, performance evaluation, VLSI implementation.
Citation:
Maurizio Martina, Guido Masera, "Mumford and Shah Functional: VLSI Analysis and Implementation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 3, pp. 487-494, March 2006, doi:10.1109/TPAMI.2006.59
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