A Fast Algorithm for Multilevel Thresholding
JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 17, 713-727 (2001)
A Fast Algorithm for Multilevel Thresholding
PING-SUNG LIAO, TSE-SHENG CHEN* AND PAU-CHOO CHUNG+
Department of Electrical Engineering ChengShiu Institute of Technology Kaohsiung, 833 Taiwan * Department of Engineering Science 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
A Fast Algorithm for Multilevel Thresholding
PING-SUNG LIAO, TSE-SHENG CHEN* AND PAU-CHOO CHUNG+
Department of Electrical Engineering ChengShiu Institute of Technology Kaohsiung, 833 Taiwan * Department of Engineering Science 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