Advanced morphological distances based on dilation and erosion

Abstract

© 2019 IOS Press. Distances based on morphological operations have shown good performance in a number of applications. Still, the existing erosion and dilation distance for gray scale images can not be computed in all situations. Furthermore, it is possible that dissimilarity between objects which are compared grows strongly, but the value of a mentioned distance does not change. We present a proposition with the necessary and sufficient conditions for computing these morphological distances and discuss drawbacks that they possess. In addition, we propose novel morphological distances, which can be computed in all situations and provide results with desirable properties. The applicability of novel morphological distances is presented in illustrative examples, including their applicability to real data.