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A Fast Algorithm for Multilevel Thresholding

**Ping-Sung Liao, Tse-Sheng Chen ^{*} and Pau-Choo Chung^{+}**

ChengShiu Institute of Technology

Kaohsiung, 833 Taiwan

National Cheng Kung University

Tainan, 701 Taiwan

Department of Electrical Engineering

National Cheng Kung University

Tainan, 701 Taiwan

Otsu reference proposed a criterion for maximizing the between-class variance of pixel intensity to perform picture thresholding. However, Otsu¡¦s method for image segmentation is very time-consuming because of the inefficient formulation of the between-class variance. In this paper, a faster version of Otsu¡¦s method is proposed for improving the efficiency of computation for the optimal thresholds of an image. First, a criterion for maximizing a modified between-class variance that is equivalent to the criterion of maximizing the usual between-class variance is proposed for image segmentation. Next, in accordance with the new criterion, a recursive algorithm is designed to efficiently find the optimal threshold. This procedure yields the same set of thresholds as the original method. In addition, the modified between-class variance can be pre-computed and stored in a look-up table. Our analysis of the new criterion clearly shows that it takes less computation to compute both the cumulative probability (zeroth order moment) and the mean (first order moment) of a class, and that determining the modified between-class variance by accessing a look-up table is quicker than that by performing mathematical arithmetic operations. For example, the experimental results of a five-level threshold selection show that our proposed method can reduce down the processing time from more than one hour by the conventional Otsu¡¦s method to less than 107 seconds.

Keywords: Otsu¡¦s thresholding, image segmentation, picture thresholding, multilevel thresholding, recursive algorithm

Retrieve PDF document (**200109_01.pdf**)

Received May 5, 1999; revised August 24, 1999; accepted December 30, 1999.

Communicated by Wen-Hsiang Tsai.