A fast recursive algorithm for two-dimensional thresholding

Two-dimensional (2D) thresholding behaves well in segmenting images of low signal-to-noise ratio. But the computational complexity of the conventional 2D entropic algorithm is bounded by O(L⁴). Firstly, a fast recursive 2D entropic thresholding algorithm is proposed. By rewriting the formula for calculation of the entropy in a recurrence form, a great deal of calculation is saved. Analysis shows that the computational complexity of 2D entropic thresholding is reduced to O(L²). The fast recursive algorithm is also used successfully in the 2D Otsu (1979) method. Experimental results show that the processing time of each image is reduced from more than 2 h to less than 10 sec. The required memory space is also greatly reduced