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Logarithmic Mathematical Morphology: Theory and applications

arXiv 2309.02007 ↗First posted 5 Sep 2023eess.IV cs.CV cs.NAcited by 0

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Abstract (arXiv)

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, when the structuring function is added to this image, the amplitude of this translated 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. This issue has been addressed by defining a framework that uses an additive law, for which the amplitude of the structuring function added to the image varies according to the amplitude of the image itself. 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 framework is named Logarithmic Mathematical Morphology (LMM) and allows the definition of operators which are robust to such lighting variations.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 9 of its 62 references that are in the map. First posted on arXiv 5 Sep 2023.

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References · 9

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  2. 2021RV-GAN: Segmenting Retinal Vascular Structure in Fundus Photographs using a Novel Multi-scale Generative Adversarial Networkcited by 24
  3. 2021Study Group Learning: Improving Retinal Vessel Segmentation Trained with Noisy Labelscited by 20
  4. 2017Double-sided probing by map of Asplund's distances using Logarithmic Image Processing in the framework of Mathematical Morphologycited by 2
  5. 2018Logarithmic mathematical morphology: a new framework adaptive to illumination changescited by 2
  6. 2019Region homogeneity in the Logarithmic Image Processing framework: application to region growing algorithmscited by 1
  7. 2019A Link Between the Multiplicative and Additive Functional Asplund's Metricscited by 1
  8. 2020Retinal vessel segmentation by probing adaptive to lighting variationscited by 1
  9. 2022Logarithmic Morphological Neural Nets robust to lighting variationscited by 1

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