Gray-Level LIP Model. Notations, Recalls, and First Applications

Logarithmic Mathematical Morphology: A New Framework Adaptive to Illumination Changes

“…In LMM, the k th minimum logarithmic filter ζ △ + b,k : F M → F M and the k th maximum logarithmic filter ϑ △ + b,k can also be defined by using the k th minimum ∧ k and the k th maximum ∨ k in ( 8) and (7), respectively. The k th minimum and maximum logarithmic filters ζ △ + b,k and ϑ △ + b,k are also related to the k th minimum and maximum filters ζ b,k and ϑ b,k by replacing the erosions, ε b and ε △ + b , and dilations, δ b and δ △ + b , by their corresponding rank filters in (13) and (12).…”

“…(2) Secondly, adding a structuring function to an image without taking into account the image intensity into the amplitude of the structuring function is not physically justified. As in human vision, the eye response to light intensity variations is known to be logarithmic [9], [10], [11], [12], [13], it follows that in images the contrast variations are also logarithmic and the darkest variations are more attenuated than the brightest ones [14], [15]. The amplitude of the structuring function must therefore depend on the image intensity, i.e.…”

Double-Sided Probing by Map of Asplund’s Distances Using Logarithmic Image Processing in the Framework of Mathematical Morphology

“…The LIP model, created by Jourlin et al [15,17,16,10], is a mathematical framework for image processing based on the physical law of transmittance. It is per-fectly suited to process images acquired with transmitted light (when the object is located between the source and the sensor) but also with reflected light, due to the consistency of the model with human vision [6].…”