A Design Method for Morphological Filters with Approximations of Min/Max Operators
Makoto Nakashizuka · Institutional Repositories DataBase (IRDB) · 2009
Abstract—This paper presents a novel design method for the structuring elements of morphological filters. The morphological filters, which have been applied to low-level image processing tasks, are implemented with max and min functions. Due to the non-differentiability of the max and min functions, it is difficult to apply any gradient-based optimization technique to design of the morphological filters. In this paper, we introduce approximating functions of the max and min functions to approximate the mor-phological filters. Since the proposed approximating functions are differentiable, the outputs of the approximated morphological filters are also differentiable. The gradient based optimization technique can be easily applied to the proposed approximated morphological filters. We approximate the dilation and opening filters with the approximated max and min functions, and design the quasi-optimum structuring elements for the both filters. In experiments, we demonstrate several design examples and applications to image denoising. I.