THE LOGARITHMIC IMAGE-PROCESSING MODEL - CONNECTIONS WITH HUMAN BRIGHTNESS PERCEPTION AND CONTRAST ESTIMATORS

The logarithmic image processing (LIP) model is a mathematical framewo rk based on abstract linear mathematics which provides a set of specif ic algebraic and functional operations that can be applied to the proc essing of intensity images valued in a bounded range. The LIP model ha s been proved to be physically justified in the setting of transmitted light and to be consistent with several laws and characteristics of t he human visual system. Successful application examples have also been reported in several image processing areas, e.g., image enhancement, image restoration, three-dimensional image reconstruction, edge detect ion and image segmentation. The aim of this article is to show that th e LIP model is a tractable mathematical framework for image processing which is consistent with several laws and characteristics of human br ightness perception. This is a survey article in the sense that it pre sents (almost) previously published results in a revised, refined and self-contained form. First, an introduction to the LIP model is expose d. Emphasis will be especially placed on the initial motivation and go al, and on the scope of the model. Then, an introductory summary of ma thematical fundamentals of the LTP model is detailed. Next, the articl e aims at surveying the connections of the LIP model with several laws and characteristics of human brightness perception, namely the bright ness scale inversion, saturation characteristic, Weber's and Fechner's laws, and the psychophysical contrast notion. Finally, it is shown th at the LIP model is a powerful and tractable framework for handling th e contrast notion. This is done through a survey of several LIP-model- based contrast estimators associated with special subparts (point, pai r of points, boundary, region) of intensity images, that are justified both from a physical and mathematical point of view.