cvpr cvpr2013 cvpr2013-171 cvpr2013-171-reference knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Lena Gorelick, Frank R. Schmidt, Yuri Boykov
Abstract: Trust region is a well-known general iterative approach to optimization which offers many advantages over standard gradient descent techniques. In particular, it allows more accurate nonlinear approximation models. In each iteration this approach computes a global optimum of a suitable approximation model within a fixed radius around the current solution, a.k.a. trust region. In general, this approach can be used only when some efficient constrained optimization algorithm is available for the selected nonlinear (more accurate) approximation model. In this paper we propose a Fast Trust Region (FTR) approach for optimization of segmentation energies with nonlinear regional terms, which are known to be challenging for existing algorithms. These energies include, but are not limited to, KL divergence and Bhattacharyya distance between the observed and the target appearance distributions, volume constraint on segment size, and shape prior constraint in a form of 퐿2 distance from target shape moments. Our method is 1-2 orders of magnitude faster than the existing state-of-the-art methods while converging to comparable or better solutions.
[1] I. Ben Ayed, H. Chen, K. Punithakumar, I. Ross, and S. Li.
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10] Graph cut segmentation with a global constraint: Recovering region distribution via a bound of the Bhattacharyya measure. In IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), June 2010. I. Ben Ayed, S. Li, A. Islam, G. Garvin, and R. Chhem. Area prior constrained level set evolution for medical image segmentation. In SPIE, Medical Imaging, March 2008. S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge Univ. Press, 2004. Y. Boykov and M.-P. Jolly. Interactive Graph Cuts for Optimal Boundary and Region Segmentation of Objects in ND Images. In IEEE Int. Conf. on Computer Vision (ICCV), 2001. Y. Boykov and V. Kolmogorov. An Experimental Comparison ofMin-Cut/Max-Flow Algorithms for Energy Minimization in Vision. IEEE Trans. on Pattern Analysis and Machine Intelligence (TPAMI), 29(9): 1124–1 137, 2004. Y. Boykov, V. Kolmogorov, D. Cremers, and A. Delong. An Integral Solution to Surface Evolution PDEs via Geo-Cuts. ECCV, LNCS 3953, 3:409–422, May 2006. D. Freedman and T. Zhang. Active contours for tracking distributions. IEEE Transactions on Image Processing, 13, April 2004. L. Gorelick, R. Schmidt, Y. Boykov, A. Delong, and A. Ward. Segmentation with Non-Linear Regional Constraint via Line-Search cuts. In European Conf. on Computer Vision (ECCV), October 2012. R. Hartley and A. Zisserman. Multiple View Geometry in Computer Vision. Cambridge University Press, 2003. J. Kim, V. Kolmogorov, and R. Zabih. Visual correspondence using energy minimization and mutual information. In Int.
[11]
[12]
[13]
[14]
[15]
[16]
[17] Conf. on Comp. Vision (ICCV), October 2003. M. Klodt and D. Cremers. A convex framework for image segmentation with moment constraints. In IEEE Int. Conf. on Computer Vision (ICCV), 2011. V. Kolmogorov, Y. Boykov, and C. Rother. Applications of Parametric Maxflow in Computer Vision. In IEEE Int. Conf. on Computer Vision (ICCV), November 2007. C. Rother, V. Kolmogorov, and A. Blake. GrabCut: Interactive Foreground Extraction using Iterated Graph Cuts. In ACM SIGGRAPH, 2004. C. Rother, V. Kolmogorov, T. Minka, and A. Blake. Cosegmentation of Image Pairs by Histogram Matching - Incorporating a Global Constraint into MRFs. In Computer Vision and Pattern Recognition (CVPR), June 2006. T. Werner. High-arity Interactions, Polyhedral Relaxations, and Cutting Plane Algorithm for Soft Constraint Optimisation (MAP-MRF). In IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), June 2008. O. J. Woodford, C. Rother, and V. Kolmogorov. A Global Perspective on MAP Inference for Low-Level Vision. In Int. Conf. on Computer Vision (ICCV), October 2009. Y. Yuan. A review of trust region algorithms for optimization. In Proceedings of the Fourth International Congress on Industrial & Applied Mathematics (ICIAM), 1999. 111777112199