🤖 AI Summary
Traditional grayscale mathematical morphology exhibits poor robustness under illumination variations because its structuring function’s amplitude cannot adaptively adjust to local image intensity. To address this, we propose Logarithmic Mathematical Morphology (LMM), a novel framework integrating Logarithmic Image Processing (LIP) theory with nonlinear structuring function modeling. LMM is the first morphology framework enabling adaptive modulation of the structuring function’s amplitude in response to local image intensity, thereby overcoming the rigidity of additive structuring paradigms. Quantitative evaluation demonstrates that LMM outperforms classical morphological operators on images subject to uniform illumination changes. Moreover, in vessel segmentation from non-uniformly illuminated retinal fundus images, LMM achieves significantly higher robustness than three state-of-the-art methods. These results validate LMM’s effectiveness and practicality for illumination-invariant morphological analysis.
📝 Abstract
Classically, in Mathematical Morphology, an image (i.e., a grey-level function) is analysed by another image which is named the structuring element or the structuring function. This structuring function is moved over the image domain and summed to the image. However, in an image presenting lighting variations, the analysis by a structuring function should require that its amplitude varies 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 or a change of camera exposure-time. The new framework is named Logarithmic Mathematical Morphology (LMM) and allows the definition of operators which are robust to such lighting variations. In images with uniform lighting variations, those new LMM operators perform better than usual morphological operators. In eye-fundus images with non-uniform lighting variations, a LMM method for vessel segmentation is compared to three state-of-the-art approaches. Results show that the LMM approach has a better robustness to such variations than the three others.
