Segmentation is one of the fundamental tasks for image processing.
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DOMAIN DECOMPOSITION METHODS WITH GRAPH CUTS ALGORITHMS FOR IMAGE SEGMENTATION XUE-CHENG TAI∗ AND YUPING DUAN† Abstract. Recently, it is shown that graph cuts algorithms can be used to solve some variational image restoration problems, especially connected with noise removal and segmentation. For very large size problems, the cost for memory and computation increase dramatically. We propose a domain decomposition method with graph cuts algorithms. We show that the new approach is cost effective both for memory and computation. Experiments with large size 2D and 3D data are supplied to show the efficiency of the algorithms. Key words. multiphase Mumford-Shah, graph cuts, image segmentation, domain decomposition 1. Introduction. Segmentation is one of the fundamental tasks for image processing.
DOMAIN DECOMPOSITION METHODS WITH GRAPH CUTS
ALGORITHMS FOR IMAGE SEGMENTATION
XUE-CHENG TAI∗ AND YUPING DUAN†
Abstract. Recently, it is shown that graph cuts algorithms can be used to solve some variational
image restoration problems, especially connected with noise removal and segmentation. For very large
size problems, the cost for memory and computation increase dramatically. We propose a domain
decomposition method with graph cuts algorithms. We show that the new approach is cost effective
both for memory and computation. Experiments with large size 2D and 3D data are supplied to
show the efficiency of the algorithms.
Key words. multiphase Mumford-Shah, graph cuts, image segmentation, domain decomposition
1. Introduction. Segmentation is one of the fundamental tasks for image processing.
Mumford and Shah model [26] is an efficient tool for region based image
segmentation. This model is robust to noise and can segment objects without edges.
However, the minimization problem is difficult to solve numerically.
The level set method [11, 27] was first introduced to solve the Mumfod-Shah
functional by Chan and Vese in [7, 34]. In [24, 25, 30], some variants of the level set
method, so-called ”Piecewise Constant Level Set Method” (PCLSM), was introduced.
This method can identify several interfaces by one single level set function, which
makes it easier to solve the Mumford-Shah model.
Traditionally, methods based on gradient descent are often used for solving the
Mumford-Shah models, see [24, 25, 30]. These methods are normally slow and difficult
to find global minimizers. Recently, a lot of work have been done on applying graph
cuts algorithms for image segmentation [3, 4, 18, 12, 22]. It is more efficient for solving
this kind of minimization problem. The connection of graph cuts and variational
problems has been established in [2, 5, 10, 19]. For Mumford-Shah segmentation,
some work using graph cuts optimization for two-phase Mumford-Shah model has
been done in [9] and [13]. For multiphase problems, the method of [1, 10, 13, 23]
can be adapted to image segmentation. In this work, we shall follow the approach
given in [1]. In [1], the authors have extended the graph cuts idea of [10, 19, 20]
to the multiphases Mumford-Shah segmentation and it is more suitable for practical
applications. However, when the images become large and the number of phases
increases, both computational cost and memory usage are greatly increased. In this
work we try to find some remedies for these difficulties and show that we could get
some algorithms which has quite high efficiency as well as low memory usage. We
propose a method combining the domain decomposition method with graph cuts
algorithms.
The paper is organized as follows. Section 2, we review the PCLSM and its applications
to the Mumford-Shah model. Section 3, we review the graph cuts algorithm
of [1] to the multiphase Mumford-Shah model. In Section 4, we combine the domain
decomposition methods with this graph cuts idea to solve the Mumford-Shah model.
Some implementation detailed are supplied in Section 5. Finally, in Section 6, we
∗Division of Mathematical Science, School of Physical and Mathematical Sciences, Nanyang Technological
University, Singapore and Department of Mathematics, University of Bergen, Johannes
Brunsgate 12, N-5008 Bergen, Norway. tai@mi.uib.no
†Division of Mathematical Science, School of Physical and Mathematical Sciences, Nanyang Technological
University, Singapore. DUAN0010@ntu.edu.sg.
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