Hierarchical fast two-dimensional entropic thresholding algorithm using a histogram pyramid

Chein-I Chang, MEMBER SPIE University of Maryland Baltimore County Department of Computer Science and Electrical Engineering Baltimore, Maryland 21228-5398 E-mail: [email protected] Abstract. Entropic thresholding provides an alternative view to the design rationale of conventional thresholding. Abutaleb proposed a second-order entropic thresholding approach to improve Pun’s first-order entropic thresholding by introducing a 2-D gray-level histogram to take into account the spatial correlation. Abutaleb’s (1989) method was further modified by Brink (1992). However, a major drawback of AbutalebBrink’s method is very high computational cost. Recently, Chen et al. (1994) developed a fast efficient 2-D algorithm that reduces computational complexity from O(L4) to O(L8/3), where L is the total number of gray levels. A hierarchical fast 2-D entropic thresholding algorithm using a gray-level histogram pyramid is presented that can be viewed as a generalization of Chen et al.’s algorithm. The new algorithm consists of a 2-D gray-level histogram pyramid build-up procedure expanding Abutaleb’s 2-D gray-level histogram to a histogram pyramid, and a thresholding process applying a modified version of Chen et al.’s algorithm to the histogram pyramid layer by layer from top to bottom. As a result, the computational complexity of Chen et al.’s algorithm can be further reduced to the optimal complexity, O(L2). The experiments show that the computer time of the new algorithm is only one tenth of that required for Chen et al.’s algorithm, which is a significant saving. © 1996 Society of Photo-Optical Instrumentation Engineers.