PIECEWISE LINEAR APPROXIMATION OF LOGARITHMIC IMAGE PROCESSING MODELS FOR DYNAMIC RANGE ENHANCEMENT
Corneliu Florea, Constantin Vertan · 2009
Modelele logaritmice de prelucrare a imaginilor ofera un cadru potrivit pentru vizualizarea si imbunataţirea unei game variate de imagini digitale. Desi iniţial aceste modele au fost dezvoltate pentru sisteme in care fenomenele fizice de baza sunt multiplicative, incadrarea ulterioara in structuri algebrice a permis diversificarea aplicaţiilor. In consecinţa, ne putem pune problema construcţiei matematice a unor modele neliniare care sa ofere un cadru practic pentru aplicaţii specifice din domeniul prelucrarii de imagini. In aceasta lucrare vom deriva un set de condiţii suficiente pentru elaborarea unor asemenea modele care sa aiba o structura algebrica de spaţiu vectorial. Pe baza acestora vom construi modele noi, liniare pe porţiuni, care, in plus, sa reduca efortul computaţional necesar implementarii directe a modelelor neliniare. In final, vom demonstra utilitatea practica a formalismului matematic dezvoltat prin descrirea unei aplicaţii simple de crestere a gamei dinamice a imaginilor achiziţionate cu camere fotografice digitale. It has been proven that Logarithmic Image Processing (LIP) models provide a suitable framework for visualizing and enhancing digital images acquired by various sources. The underlying initial reason for derivation of such models has been the necessity to deal with multiplicative phenomena. Later, it has been proven that LIP models have a precise mathematical structure and, hence, are suitable for various image processing applications, not necessarily of multiplicative nature. In this paper, we investigate, from a mathematical point of view, the set of sufficient conditions to derive such a non-linear image processing model that complies with the algebraic structure of a vector space. Given this set of conditions, we build new models, that are piecewise linear and reduce the intense computational effort required by the classical models. Finally, we prove the usability of the developed theory by proposing a simple and practical application of digital still camera dynamic range enhancement.