Fast recursive mathematical morphological transforms

Since many mathematical morphology operations are recursive transforms of dilation and erosion, this paper proposes fast recursive transforms to reduce computational complexity. The basic idea of the method is to compute the temporary results within a series of adaptive windows and the computing is performed on specific pixels. Each step of the recursive process consists of two parts: 1) computation is limited to the specific pixels (foreground or background pixels) within a window; 2) update the window adoptively and delete those varied pixels. Extensive results show that the time complexity of the method is proportional to the number of the specific pixels.