Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach

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 du...

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Vydané v:International journal of computer vision Ročník 92; číslo 1; s. 112 - 129
Hlavní autori: Bae, Egil, Yuan, Jing, Tai, Xue-Cheng
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Boston Springer US 01.03.2011
Springer
Springer Nature B.V
Predmet:
Algorithms
Applied sciences
Approximation
Artificial Intelligence
Computational efficiency
Computer Imaging
Computer Science
Computer science; control theory; systems
Convex analysis
Energy
Exact sciences and technology
Image Processing and Computer Vision
Labeling
Linear programming
Marking
Mathematical models
Maximization
Maximum entropy
Neighborhoods
Optimization
Pattern Recognition
Pattern Recognition and Graphics
Pattern recognition. Digital image processing. Computational geometry
Smoothing
Vision
Convex relaxation
Total variation
Image segmentation
Primal-dual methods
Smoothing methods
Image processing
Threshold detection
Competitiveness
Minimization
Method of maximum entropy
Potts model
Exponential function
Modeling
Optimization
Direct problem
Smoothing
Optimal solution
Primal dual method
Convex relaxation Image segmentation
Statistical mechanics
EM algorithm
Non convex analysis
Mathematical programming
ISSN:0920-5691, 1573-1405
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Shrnutí: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.
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ISSN:0920-5691
1573-1405
DOI:10.1007/s11263-010-0406-y