Thresholding Selection Based on Fuzzy Entropy and Bee Colony Algorithm for Image Segmentation

1. Introduction

Image segmentation is an important task where pixels with similar features (such as gray, color, texture, and shape) are classified into semantic objects or homogeneous regions. It serves as a key in image understand and pattern recognition and is a fundamental step toward high-level vision, which is significant for object recognition, image retrieval, video tracking, semantic analysis and other applications. In recent years, a large of segmentation methods have been developed, among all the existing segmentation techniques, thresholding technique is one of the most popular due to its simplicity and accuracy. The threshold processing plays an important role in the image segmentation (Sezgin & Sankur, 2004). In classical threshold segmentation (Sahoo, Soltani, Wong, et al., 1988; Pal & Pal, 1993; Sezgin & Sankur, 2004; Otsu, 1979), an image is usually segmented and classified to object and background according to threshold selection. The threshold segmentation is not suitable definitely when an image is complex. There have been some approaches based on threshold segmentation which give the optimum threshold, such as Otsu algorithm (Unnikrishnan, Pantofaru, & Hebert, 2007; Enyedi, Konyha, & Fazekas, 2005; Bilger, Kupferschlager, Muller-Schauenburg, et al., 2001; Otsu, 1979). One-dimensional Otsu algorithm can obtain better segmentation results, but it can’t reflect the space-related information among the image pixels, it is difficult to obtain satisfactory segmentation results when the image has noise. To solve this problem, Liu (Liu & Li, 1993) proposed the two-dimensional histogram which is composed of the pixel gray-level distribution and neighborhood average gray-level distribution. Hou (Hou, Hu, & Nowinski, 2006) presented that the threshold obtained by otsu’method tends to get closer to the cluster with a larger variance or a larger quantity of pixels in an image. Hou also proposed a minimum class variance thresholding method which decides the optimal threshold based on the smallest variance of pixels within a class. There is some uncertainty when the image quality is not so good. The nature of this ambiguity in an image therefore arises from the uncertainty present. In order to decide whether a pixel can classify as a white or black, it is proposed to suggest a quantitative measure for fuzziness present in an image (Huang & Wang, 1995).

Entropy plays a significant role in image processing. The principle of entropy is to use uncertainty as a measure to describe the information contained in a source. Fuzzy entropy does not have the same meaning to information entropy, but rather provides a flexible description of the histogram. It is generally accepted that the histograms of most images follow multimodal distribution. There is many methods about entropy in image segmentation (Pal & Pal, 1989; Kapur, Sahoo, & Wong, 1985; Cheng, Chen, & Jiang, 2000). Pal (Pal & Pal, 1991) proposed an approach to measure the degree of resemblance between the template and the gray-scale image. The classification status of the edge pixels in the template is modified in a way to maximize the Gray-scale Image Entropy. Cheng et al. (Cheng, Chen, & Jiang, 2000) presented a threshold approach by performing fuzzy partition on a two-dimensional histogram, which is based on the fuzzy relation and the maximum fuzzy entropy principle. Zhao et al. (Zhao, Fu, & Yan, 2001) designed a three-level threshold method for image segmentation. Fuzzy entropy through probability analysis, fuzzy partition and entropy theory is defined. Shelokar (Shelokar, Jayaraman, & Kulkarni, 2004) considered the fuzzy memberships as an indication, showing how strongly a gray value belongs to the background or to the foreground. There is obviously no guarantee of regular and simple conditions when segmenting natural images containing multiple objects with great variance of contents. A large number of previous works focused on segmenting images with distinct foreground will probably not be able to correctly detect objects from such images.