Fast recursive segmentation algorithm based on Kapur´s entropy

Thresholding is an important operation in image analysis which is used in many applications. One of the most efficient techniques for image segmentation is the entropy-based thresholding technique. A popular entropy-based thresholding method is the Kapur thresholding method. In this method, the criterion to select a suitable threshold is the maximization of the Kapur´s entropies based on gray-level histogram. Kapur´s original method is very time-consuming due to the inefficient formulation of the Kapur entropy and the exhaustive search in multilevel thresholding. In order to reduce the computational time of the entropy function, a fast recurring thresholding algorithm based on two look-up tables and new form of Kapur entropy is proposed. Our analysis of the new algorithm clearly shows that it takes less computation to compute both the probability distribution of gray levels and the Kapur entropy, and that determining the Kapur entropy by accessing a look-up table based on new form of entropy is quicker then that based on performing arithmetic operations. This algorithm yields the same set of thresholds as the original Kapur method. For example, the experimental result of a five-level threshold selection in LENA image shows that the proposed algorithm can reduce the processing time from more than two hours by the conventional Kapur method to less then 170 seconds.