Logarithmic Mathematical Morphology: theory and applications
This work addresses lighting variation issues in image processing for applications like computer vision, though it appears incremental as it builds on existing Logarithmic Image Processing.
The paper tackles the problem of lighting variations in grey-level image analysis by introducing Logarithmic Mathematical Morphology (LMM), a new framework that uses a logarithmic additive law to make structuring functions vary with image intensity, resulting in operators robust to such variations.
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.