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This paper is devoted to the optimization problem of continuous multi-partitioning, or multi-labeling, which is based on a convex relaxation of the continuous Potts model. In contrast to previous efforts, which are tackling the optimal labeling problem in a direct manner, we first propose a novel dual model and then build up a corresponding duality-based approach. By analyzing the dual formulation, sufficient conditions are derived which show that the relaxation is often exact, i.e. there exists optimal solutions that are also globally optimal to the original nonconvex Potts model. In order to deal with the nonsmooth dual problem, we develop a smoothing method based on the log-sum exponential function and indicate that such a smoothing approach leads to a novel smoothed primal-dual model and suggests labelings with maximum entropy. Such a smoothing method for the dual model also yields a new thresholding scheme to obtain approximate solutions. An expectation maximization like algorithm is proposed based on the smoothed formulation which is shown to be superior in efficiency compared to earlier approaches from continuous optimization. Numerical experiments also show that our method outperforms several competitive approaches in various aspects, such as lower energies and better visual quality. [ABSTRACT FROM AUTHOR]

In this paper, a class of deformable contour methods using a constrained optimization approach of minimizing a contour energy function satisfying an interior homogeneity constraint is proposed. The class is defined by any positive potential function describing the contour interior characterization. An evolutionary strategy is used to derive the algorithm. A similarity threshold Tv can be used to determine the interior size and shape of the contour. Sensitivity and significance of Tv and σ (a spreadness measure) are also discussed and shown. Experiments on noisy images and the convergence to a minimum energy gap contour are included. The developed method has been applied to a variety of medical images from CT abdominal section, MRI image slices of brain, brain tumor, a pig heart ultrasound image sequence to visual blood cell images. As the results show, the algorithm can be adapted to a broad range of medical images containing objects with vague, complex and/or irregular shape boundary, inhomogeneous and noisy interior, and contour with small gaps. [ABSTRACT FROM AUTHOR]