Performance analysis for a class of iterative image thresholding algorithms

A performance analysis procedure that analyses the properties of a class of iterative image thresholding algorithms is described. The image under consideration is modeled as consisting of two maximum-entropy primary images, each of which has a quasi-Gaussian probability density function. Three iterative thresholding algorithms identified to share a common iteration architecture are employed for thresholding 4595 synthetic images and 24 practical images. The average performance characteristics including accuracy, stability, speed and consistency are analysed and compared among the algorithms. Both analysis and practical thresholding results are presented. Copyright ~ 1996 Pattern Recognition Society. Published by Elsevier Science Ltd. Iterative algorithm Image thresholding Performance analysis Image segmentation Maximum entropy easily extended to multiple-class thresholding. Besides speed and simplicity consideration, other objectives have also been incorporated into thresholding design. Example objectives include cross-entropy minimization,(l) between class variance maximization,(6) total segmentation error minimization,(7) a posteriori entropy maximization,(8) likelihood function maximization,(9) etc. For analysis and performance comparison purposes, various thresholding algorithms have been grouped under a common framework, such as global threshold,(lO) maximum likelihood parameter estimation(ll) and histogram-based global thresholding.(12) In this paper we will identify a common iteration architecture for a group of iterative thresholding algorithms and then evaluate their performance. An iterative thresholding algorithm, while in general being able to achieve better result when compared with its single-run counterpart,(9) has been reported to suffer from various pitfalls, such as nonconvergence, multiple convergence points and converging to a nonsensical thresholding value.(7) Furthermore, due to the probabilistic nature of the iteration process, it is difficult to compare different iterative thresholding algorithms on a fair basis. In this paper a systematic performance analysis procedure is proposed to alleviate these pitfalls. In Section 2 the maximum-entropy image model is briefly described and three iterative thresholding algorithms are reviewed ~nder the same architectural and notational framewo~k. In Section 3 the proposed performance analysis procedure is described in detail. In Section 4 the analysis of the average performance of each of the three iterative algorithms is described and th~ results are summarized and discussed. In Section 5 aconclus~on is given. 1. INTRODUCnON An image is a collection of picture elements (pixels) representing some scene of interest for an observer. In practice, many images are a representation of scenes consisting of different constituent parts. These constituent parts are to be identified by an image understanding or pattern recognition system. For this purpose, image segmentation is performed to transform the raw gray-scale image to a form more suitable for pattern recognition processing by template matching, correlation or moment-based methods.(l) Applications of image segmentation in areas such as medical imaging, machine parts inspection,(2) objects location and identification (3) have been reported. Segmentation is a pixel classification process whereby each pixel of an image is classified into one of several classes. In general, each pixel will be considered separately for classification, but in practice this approach is seldom adopted when speed of operation is the prime consideration. Instead, a group of pixels possessing some identical feature will be segmented into the same class. The most widely utilized pixel features have been the gray level of the pixels as well as the related statistics such as the mean and the standard deviation. For real-time applications and simple implementation, thresholding has been the most popular image segmentation technique and has been reviewed quite extensively:4.S) In the thresholding approach a threshold value t is selected and then all pixels having gray-level values greater than t will be classified into one class, while the rest of the pixels will be classified into another. The idea of two-class thresholding can be * Author for correspondence.