Logarithmic mathematical morphology: a new framework adaptive to illumination changes

TL;DR

This paper introduces a new mathematical morphology framework based on logarithmic image processing, designed to adapt to illumination changes and improve pattern recognition in low-contrast images.

Contribution

It defines new logarithmic MM operators using the LIP model, enhancing robustness to illumination variations compared to classical methods.

Findings

Logarithmic-MM outperforms classical MM on low-contrast images.

The framework is consistent with human vision and physical acquisition models.

Mathematical relations between classical and logarithmic operators are established.

Abstract

A new set of mathematical morphology (MM) operators adaptive to illumination changes caused by variation of exposure time or light intensity is defined thanks to the Logarithmic Image Processing (LIP) model. This model based on the physics of acquisition is consistent with human vision. The fundamental operators, the logarithmic-dilation and the logarithmic-erosion, are defined with the LIP-addition of a structuring function. The combination of these two adjunct operators gives morphological filters, namely the logarithmic-opening and closing, useful for pattern recognition. The mathematical relation existing between ``classical'' dilation and erosion and their logarithmic-versions is established facilitating their implementation. Results on simulated and real images show that logarithmic-MM is more efficient on low-contrasted information than ``classical'' MM.