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Remote sensing image object extraction using convex geometric active contour model

Published: 17 August 2013 Publication History

Abstract

The geometric active contour model is a popular method for computing the segmentation of an image into two phases, based on Mumford-Shah model. The main problem in image segmentation based this method may lead to non-convex minimization problems that it difficult to obtain a global solution. In this paper, we propose a convex relaxation of the popular K-means algorithm. Our approach is based on the vector-valued relaxation technique developed by Brown et al. (UCLA CAM Report 10-43, 2010) and Goldstein et al. (UCLA CAM Report 09-77, 2009). We applied the proposed framework to multi-object extraction problems on remote sensing images. We provide several experimental results to demonstrate that our convex model yields global solutions to the well known Mumford-Shah model.

References

[1]
D. Mumford and J. Shah. Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics, 42(5):577--685, 1989.
[2]
L. A. Vese and T. F. Chan. A multiphase level set framework for image segmentation using the mumford and shah model. International Journal of Computer Vision, 50:271--293, 2001.
[3]
L. Ambrosio and V. M. Tortorelli. Variational problems in SBV and image segmentation. Acta Applicandae Mathematicae, 17(1):1--40, 1989.
[4]
L. Ambrosio and V. M. Tortorelli. Approximation of functionals depending on jumps by elliptic functionals via Γ - convergence Comm. Pure Appl. Math., 43:999--1036, 1990.
[5]
E. Strekalovskiy, A. Chambolle, D. Cremers. A convex representation for the vectorial Mumford-Shah function, 2012 IEEE Conference on Computer Vision and Pattern Recognition, Vol.0(2012):1712--1719, 2012.
[6]
G. Albert, G. Bouchitte, and G. Dal Maso. The calibration method for the Mumford-Shah functional and freediscontinuity problems. Calc. Var. Partial Differential Equations, 16(3):299--333, 2003.
[7]
T. Chan, S. Esedoglu, and M. Nikolova. Algorithms for finding global minimizers of image segmentation and denoising models. SIAM Journal on Applied Mathematics, 66(5): 1632--1648, 2006.
[8]
T. Pock, D. Cremers, H. Bischof, and A. Chambolle. Global solutions of variational models with convex regularization. SIAM Journal on Imaging Sciences, 3(4): 1122--1145, 2010.
[9]
T. Pock, D. Cremers, H. Bischof, and A. Chambolle. An algorithm for minimizing the piecewise smooth Mumford-Shah functional. In ICCV, 2009.
[10]
H. Ishikawa. Exact optimization for Markov random fields with convex priors. IEEE Trans. Pattern Analysis and Machine Intelligence, 25(10): 1333--1336, 2003.
[11]
M. G. Mora. The calibration method for free-discontinuity problems on vector-valued maps. J. Convex Anal., 9(1): 1--29, 2002.
[12]
T. Goldstein, X. Bresson, and S. Osher. Global minimization of markov random fields with applications to optical flow. UCLA CAM Report 09-77, September, 2009.
[13]
H. Ishikawa. Exact optimization for markov random fields with convex priors. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(10): 1333--1336, 2003.
[14]
T. Pock, T. Schoenemann, G. Graber, H. Bischof, and D. Cremers. A convex formulation of continuous multi-label problems. In European Conference on Computer Vision (ECCV), Marseille, France, October 2008.
[15]
J. Lie, M. Lysaker, and X.-C.Tai. A variant of the level set method and applications to image segmentation. Mathematics of Computation, 75(255): 1155--1174, 2006.
[16]
Ethan S. Brown, Tony F. Chan, Xavier Bresson, A convex relaxation method for a class of vector-valued minimization problems with applications to Mumford-Shah segmentation, CAM report 10-43, 2010.

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  1. Remote sensing image object extraction using convex geometric active contour model

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    ICIMCS '13: Proceedings of the Fifth International Conference on Internet Multimedia Computing and Service
    August 2013
    419 pages
    ISBN:9781450322522
    DOI:10.1145/2499788
    • Conference Chair:
    • Tat-Seng Chua,
    • General Chairs:
    • Ke Lu,
    • Tao Mei,
    • Xindong Wu
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    • NSF of China: National Natural Science Foundation of China
    • University of Sciences & Technology, Hefei: University of Sciences & Technology, Hefei
    • Beijing ACM SIGMM Chapter

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    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 17 August 2013

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    Author Tags

    1. convex relaxation
    2. geometric active contour model
    3. object extraction
    4. remote sensing image

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    ICIMCS '13
    Sponsor:
    • NSF of China
    • University of Sciences & Technology, Hefei

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    ICIMCS '13 Paper Acceptance Rate 20 of 94 submissions, 21%;
    Overall Acceptance Rate 163 of 456 submissions, 36%

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