A Multilevel Thresholding Method Based on Multiobjective Optimization for Non-Supervised Image Segmentation

A Multilevel Thresholding Method Based on Multiobjective Optimization for Non-Supervised Image Segmentation

Leila Djerou (LESIA Laboratory, Universite Mohamed Khider de Biskra, Algeria), Naceur Khelil (Laboratory of Applied Mathematics, Universite Mohamed Khider de Biskra, Algeria), Nour El Houda Dehimi (L.B.M. University, Algeria) and Mohamed Batouche (University Mentouri–Constantine, Algeria)
DOI: 10.4018/978-1-4666-1830-5.ch011
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Abstract

The aim of this work is to provide a comprehensive review of multiobjective optimization in the image segmentation problem based on image thresholding. The authors show that the inclusion of several criteria in the thresholding segmentation process helps to overcome the weaknesses of these criteria when used separately. In this context, they give a recent literature review, and present a new multi-level image thresholding technique, called Automatic Threshold, based on Multiobjective Optimization (ATMO). That combines the flexibility of multiobjective fitness functions with the power of a Binary Particle Swarm Optimization algorithm (BPSO), for searching the “optimum” number of the thresholds and simultaneously the optimal thresholds of three criteria: the between-class variances criterion, the minimum error criterion and the entropy criterion. Some examples of test images are presented to compare with this segmentation method, based on the multiobjective optimization approach with Otsu’s, Kapur’s, and Kittler’s methods. Experimental results show that the thresholding method based on multiobjective optimization is more efficient than the classical Otsu’s, Kapur’s, and Kittler’s methods.
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Introduction

Image segmentation is a low level image processing task that aims at partitioning an image into regions in order that each region groups contiguous pixels sharing similar attributes (intensity, color, etc.). It is a very important process because it is the first step of the image understanding process, and all others steps, such as feature extraction, classification and recognition, depend heavily on its results.

Image segmentation has been the subject of intensive research; the number of published works treating this problem is difficult to value. It is a consequence of several factors:

  • The diversity of images and the increase of their use.

  • The evolution of computation machines that allows the exploration of news approaches and techniques and also it facilitates the evaluation of empiric results.

  • The complexity of the segmentation problem; the uniqueness of segmentation of an image doesn't exist in most cases; a good method of segmentation is therefore, the one that will permit to arrive to a better interpretation of the image segmentation.

A wide variety of image segmentation techniques have been reported in the literature. A good review of these methods can be found in (Pal, 1993). In general, these techniques can be categorized into thresholding, edge-based, region growing and clustering techniques.

Image thresholding is an important technique for image processing and pattern recognition that can be classified as bi-level thresholding and multilevel thresholding. Bi-level thresholding classifies the pixels of an image into two classes, one including those pixels with gray levels above a certain threshold, the other including the rest. Multilevel thresholding divides the pixels into several classes. The pixels belonging to the same class have gray levels within a specific range defined by several thresholds.

Edge-based segmentation algorithms are the most common methods for identifying meaningful image discontinuities. The gray-level discontinuity focuses on abrupt changes in gray level, color or texture. The edge information is very useful for segmentation since it can be used to obtain other image properties such as area and shape.

In region growing techniques, the regions start from a set of seed points. From these points, the regions grow by appending to each seed those neighbouring pixels that have similar properties. The selection of the seed points and of similarity criteria depends on the problem under consideration and the type of image data that is available depends on the problem.

Clustering in image segmentation is defined as the process of identifying groups of similar image primitives. These image primitives can be pixels, regions, line elements and so on, depending on the problem encountered. This is accomplished by a predefined list of quality criteria such as spatial coherence and feature homogeneity.

In spite of the abundance of works in this domain, the problem of image segmentation remains the subject of several research efforts, which have shown that the segmentation techniques based on the combination of some criteria give a good segmentation result and increase the ability to apply the same technique to a wide variety of images. They have also shown that combining criteria helps to overcome the weaknesses of these criteria when used separately. A new trend of problem formulation for image segmentation is to use multiobjective optimization approach in its decision making process.

Multiobjective optimization (MO) (also known as multicriterion) extends the optimization theory by permitting several design objectives to be optimized simultaneously (Nakib and al.,2007). A MO problem is solved in a way similar to the conventional single-objective (SO) problem. The goal is to find a set of values for the design variables that simultaneously optimizes several objectives (or cost) functions. In general, the solution obtained through a separate optimization of each objective (i.e. SO optimization) does not represent a feasible solution of the multiobjective problem.

The use of MO approaches has been found in image segmentation methods with clustering (Handl and Knowles, 2007), (Matake and al., 2007), (Saha and Bandyopadhyay,2008), histogram thresholding methods. There is also an attempt of using multiobjective approach for evaluation of image segmentation methods (Saha and Bandyopadhyay, 2010), (Bong and Mandava, 2010).

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