A Hierarchical Multilevel Image Thresholding Method Based on the Maximum Fuzzy Entropy Principle

A Hierarchical Multilevel Image Thresholding Method Based on the Maximum Fuzzy Entropy Principle

Pearl P. Guan (City University of Hong Kong, Hong Kong) and Hong Yan (City University of Hong Kong, Hong Kong & University of Sydney, Australia)
DOI: 10.4018/978-1-4666-2518-1.ch010


Image thresholding and edge detection are crucial in image processing and understanding. In this chapter, the authors propose a hierarchical multilevel image thresholding method for edge information extraction based on the maximum fuzzy entropy principle. In order to realize multilevel thresholding, a tree structure is used to express the histogram of an image. In each level of the tree structure, the image is segmented by three-level thresholding based on the maximum fuzzy entropy principle. In theory, the histogram hierarchy can be combined arbitrarily with multilevel thresholding. The proposed method is proven by experimentation to retain more edge information than existing methods employing several grayscale images. Furthermore, the authors extend the multilevel thresholding algorithm for color images in the application of content-based image retrieval, combining with edge direction histograms. Compared to using the original images, experimental results show that the thresholding images outperform in achieving higher average precision and recall.
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2. Background

There is extensive literature on image thresholding and content-based image retrieval. Considering the purpose of this chapter, we introduce the image thresholding techniques according to different classifications. The literature review mainly concentrates on the last category although some related papers are given to illustrate the classification. As for content-based image retrieval, the literature is described according to various kinds of feature representations, such as color, shape, etc.

Key Terms in this Chapter

Histogram Hierarchy: It is used in the proposed method to improve the efficiency of searching the optimal thresholds. The basic concept is to first segment the original gray image to three gray level images, then treat the dark part, the medium part and the bright part as three new input images , , and with the same gray information. Finally, choose one or more images from , , and and perform the above segmentation process recursively until the pre-specified number of segments is reached.

Maximum Fuzzy Entropy Principle: For a digitized image with ( ) gray levels, if are selected as the R threshold values, then is a probability partition of with the following probabilistic distribution , . Select the optimal R threshold values to make the entropy function for multilevel thresholding be maximal.

Edge Direction Histogram: It is used to describe the distribution of the edge points in each direction. Usually, it is calculated by counting the number of the pixels in each user-defined direction.

Contend-Based Image Retrieval (CBIR): It is also known as query by image content (QBIR), and its purpose is to find the images most similar to the query image in large database using image features, such as colors, shapes, textures or other feature representations of an image.

Edge Similarity Coefficient: It is defined by making use of the Euclidean distance of the edge points from two edge maps. Since the relative edge information is limited in a small region, it is more reasonable to average the Euclidean distances of the edge points in a small window of the two edge map.

Edge Information: It is a fundamental feature in image processing and can be obtained by applying an edge operator. It aims at identifying pixels in a digital image at which the image brightness changes sharply, which indicates the boundaries of objects.

Multilevel Thresholding: It aims to segment complex images to several gray levels. It determines the optimal thresholds by optimizing a certain objective function.

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