Logarithmic Image Processing for Color Images

Abstract

The LIP (Logarithmic Image Processing) framework is classically devoted to grayscale images. The aim of the present study is to extend this framework to color images. This new model is noted LIPC for LIP Color. It does not consist in applying the LIP Model to each channel R, G, B of a color image. We define the transmittance of color images in order to give a physical justification, on which will be based the definition of logarithmic operators like addition, subtraction and scalar multiplication, respectively noted in the LIPC : c , c and c . As for the classical LIP Model, the laws c and c define a vector space structure on the space of images which enables us to present notions requiring such a structure. For example, we define a color logarithmic interpolation by associating to a pair (F, G) of images the interval [F, G], set of barycenters of F and G. A new notion of color contrast is defined, which satisfies sub-additivity and homogeneity for scalar multiplication. This notion is proved to be efficient for edge detection. We note that the vector space structure opens the way to a lot of developments concerning the definition of metrics, norms, scalar products...and to transfer to LIPC gauges theory, duality theory... In this initial paper, we preferred insist on applications of the LIPC. For example, color prediction is presented and discussed as well as stabilization of images by dynamic range centring and enhancement of under-lighted images. Concerning the implementation of the LIPC operators and algorithms, informations are given on their execution time.

Asplünd's metric defined in the logarithmic image processing (LIP) framework for colour and multivariate images

“…The LIP framework has been originally defined by Jourlin et al in [1,2,3]. It consists in performing operations between images such as addition, subtraction or multiplication by a scalar with a result staying in the bounded domain of the images, for example [0...255] for grey-scale images on 8 bits.…”

A Novel Method for the Recognition of Air Visibility Level Based on the Optimal Binary Tree Support Vector Machine

“…The definition of contrast in each field is different. The LIP model proposed by Jourlin and Pinoli [20] defines the semi-closed operation on the real interval [0, M). In this model, the contrast of two adjacent pixels (x 1 , y 1 ) and (x 2 , y 2 ) is defined by:…”

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

“…There exists a colour version of the LIP model [12]. The LIP framework has been successfully applied to numerous problems for industry, medical applications, digital photography, etc.…”