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A Direct Approach Toward Global Minimization for Multiphase Labeling and Segmentation Problems

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3 Author(s)
Ying Gu ; Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore ; Li-Lian Wang ; Xue-Cheng Tai

This paper intends to extend the minimization algorithm developed by Bae, Yuan and Tai [IJCV, 2011] in several directions. First, we propose a new primal-dual approach for global minimization of the continuous Potts model with applications to the piecewise constant Mumford-Shah model for multiphase image segmentation. Different from the existing methods, we work directly with the binary setting without using convex relaxation, which is thereby termed as a direct approach. Second, we provide the sufficient and necessary conditions to guarantee a global optimum. Moreover, we provide efficient algorithms based on a reduction in the intermediate unknowns from the augmented Lagrangian formulation. As a result, the underlying algorithms involve significantly fewer parameters and unknowns than the naive use of augmented Lagrangian-based methods; hence, they are fast and easy to implement. Furthermore, they can produce global optimums under mild conditions.

Published in:

IEEE Transactions on Image Processing  (Volume:21 ,  Issue: 5 )