Fast Implementation of Gray-scale Morphological Matching Measurement

This paper describes a fast algorithm for gray-scale image matching. This algorithm is based on the opening operation of mathematical morphology and presents a concept of morphological size in theory. By operating the morphological size of the discrepancy function between two gray-scale images, their matching degree can be measured well. By analyzing the sufficient condition to the result of that gray-scale image opened by 3-D sphere is non-empty in 3-D digital space, we adopted a technique of threshold decomposition to transform morphological operations from gray-scale to binary, which resolved the problems of difficult construction to 3-D structuring element and complex operations. A fast method of interval approximation was proposed to calculate the gray-scale morphological size quickly. Binary morphological operations use flat structuring elements and it is essentially boolean operations. Thus, this fast algorithm can be applied on the hardware platform well.