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Advanced Morphological Distances Based on Dilation and Erosion

Dražić Slobodan

Fundamenta Informaticae

2019

Vol. 164, nr 1

17--39

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.

Positive definite functions and dual pairs of locally convex spaces

Alpay D., Gabriyelyan S.

Opuscula Mathematica

2018

Vol. 38, no. 4

463--482

Using pairs of locally convex topological vector spaces in duality and topologies defined by directed families of sets bounded with respect to the duality, we prove general factorization theorems and general dilation theorems for operator-valued positive definite functions.