General Adaptive Neighborhood-Based Pretopological Image Filtering

Abstract

This paper introduces pretopological image filtering in the context of the General Adaptive Neighborhood Image Processing (GANIP) approach. Pretopological filters act on gray level image while satisfying some topological properties. The GANIP approach enables to get an image representation and mathematical structure for adaptive image processing and analysis. Then, the combination of pretopology and GANIP leads to efficient image operators. They enable to process images while preserving region structures without damaging image transitions. More precisely, GAN-based pretopological filters and GAN-based viscous pretopological filters are proposed in this paper. The viscous notion enables to adjust the filtering activity to the image gray levels. These adaptive filters are evaluated through several experiments highlighting their efficiency with respect to the classical operators. They are practically applied in both the biomedical and material application areas for image restoration, image background subtraction and image enhancement.