A simple expression for the map of Asplund's distances with the multiplicative Logarithmic Image Processing (LIP) law

TL;DR

This paper presents a straightforward formula for computing Asplund's distance map using the multiplicative Logarithmic Image Processing law, leveraging morphological operations to simplify the process.

Contribution

It introduces a simple expression for Asplund's distances based on morphological dilation and erosion under the multiplicative LIP law, simplifying previous methods.

Findings

Provides a concise formula for Asplund's distance map

Utilizes morphological gradient with additive structuring function

Simplifies computation under the multiplicative LIP law

Abstract

We introduce a simple expression for the map of Asplund's distances with the multiplicative Logarithmic Image Processing (LIP) law. It is a difference between a morphological dilation and a morphological erosion with an additive structuring function which corresponds to a morphological gradient.