Logarithmic Mathematical Morphology: theory and applications

TL;DR

This paper introduces Logarithmic Mathematical Morphology (LMM), a new framework that adapts morphological operators to lighting variations in images by using a logarithmic additive law, enhancing robustness in grey-level analysis.

Contribution

The paper proposes LMM, a novel morphological framework based on logarithmic laws, addressing lighting variations in grey-level image analysis, which was not possible with traditional additive methods.

Findings

LMM operators are robust to lighting changes.

LMM improves grey-level image analysis accuracy.

The framework is grounded in physical lighting models.

Abstract

In Mathematical Morphology for grey-level functions, an image is analysed by another image named the structuring function. This structuring function is translated over the image domain and summed to the image. However, in an image presenting lighting variations, the amplitude of the structuring function should vary according to the image intensity. Such a property is not verified in Mathematical Morphology for grey level functions, when the structuring function is summed to the image with the usual additive law. In order to address this issue, a new framework is defined with an additive law for which the amplitude of the structuring function varies according to the image amplitude. This additive law is chosen within the Logarithmic Image Processing framework and models the lighting variations with a physical cause such as a change of light intensity. The new framework is named Logarithmic Mathematical Morphology (LMM) and allows the definition of operators which are robust to such lighting variations.