The logarithmic image processing model: Connections with human brightness perception and contrast estimators

The logarithmic image processing (LIP) model is a mathematical framework based on abstract linear mathematics which provides a set of specific algebraic and functional operations that can be applied to the processing of intensity images valued in a bounded range. The LIP model has been proved to be physically justified in the setting of transmitted light and to be consistent with several laws and characteristics of the 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 detection and image segmentation. The aim of this article is to show that the LIP model is a tractable mathematical framework for image processing which is consistent with several laws and characteristics of human brightness perception. This is a survey article in the sense that it presents (almost) previously published results in a revised, refined and self-contained form. First, an introduction to the LIP model is exposed. Emphasis will be especially placed on the initial motivation and goal, and on the scope of the model. Then, an introductory summary of mathematical fundamentals of the LTP model is detailed. Next, the article aims at surveying the connections of the LIP model with several laws and characteristics of human brightness perception, namely the brightness scale inversion, saturation characteristic, Weber's and Fechner's laws, and the psychophysical contrast notion. Finally, it is shown that the LIP model is a powerful and tractable framework for handling the contrast notion. This is done through a survey of several LIP-model-based contrast estimators associated with special subparts (point, pair of points, boundary, region) of intensity images, that are justified both from a physical and mathematical point of view.