Fast recursive algorithms for two-dimensional thresholding

Two-Dimensional (2D) thresholding behaves well in segmenting images of low siginal-to-noise ratio. But the computation complexity of the conventional 2D entropic algorithm is bounded by O(L-4). In this paper, firstly, a fast recursive 2D entropic thresholding algorithm is proposed. By rewriting the formula for calculation of entropy in recurrence form, a lengthy calculation is saved. Analysis shows that the computation complexity of 2D entropic thresholding is reduced to O(L-2). The fast recursive algorithm is also used successfully in 2D Otsu thresholding method. Experimental results show that the processing time of each image is reduced from more than 2 h to less than 10 s. The required memory space is also greatly reduced. (C) 1997 Pattern Recognition Society. Published by Elsevier Science Ltd.