Morphological 1D gray-scale structural function decomposition
Wei Gong, Qingyun Shi · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1994
Decomposability of convex grayscale structural functions on 1D digital space Z will be discussed. Based on this, we will consider how to decompose 1D digital structural functions, especially those functions taking integer values, into bipoint functions or into locally defined functions (i.e. functions with small sized support domains). It will be shown that any real valued convex function on Z must be able to be decomposed and some efficient decomposing algorithms will be offered. For integral valued convex function on Z, although most of them may be indecomposable, we will show that after changing them a little an (approximate) decomposition can be found efficiently. A simple technique will be presented to remove the distortion of morphological transformation caused by using this approximate decomposition. Finally, a brief discussion will be given to decomposition of nonconvex structural function.