Image Dynamic Range Enhancement in the Context of Logarithmic Models

Images of a scene observed under a variable illumination or with a variable optical aperture are not identical. Does a privileged representant exist? In which mathematical context? How to obtain it? The authors answer to such questions in the context of logarithmic models for images. After a short presentation of the model, the paper presents two image transforms: one performs an optimal enhancement of the dynamic range, and the other does the same for the mean dynamic range. Experimental results are shown.

The Affine Transforms for Image Enhancement in the Context of Logarithmic Models

The logarithmic model offers new tools for image processing. An efficient method for image enhancement is to use an affine transformation with the logarithmic operations: addition and scalar multiplication. We define some criteria for automatically determining the parameters of the processing and this is done via mean and variance computed by logarithmic operations.

A Mathematical Model for Logarithmic Image Processing

In this paper, we propose a new mathematical model for image processing. It is a logarithmical one. We consider the bounded interval (-1, 1) as the set of gray levels. Firstly, we define two operations: addition <+> and real scalar multiplication <x>. With these operations, the set of gray levels becomes a real vector space. Then, defining the scalar product (.|.) and the norm || . ||, we obtain an Euclidean space of the gray levels. Secondly, we extend these operations and functions for color images. We finally show the effect of various simple operations on an image.

Color Image Enhancement In the Framework of Logarithmic Models

In this paper, we propose a mathematical model for color image processing. It is a logarithmical one. We consider the cube (-1,1)x(-1,1)x(-1,1) as the set of values for the color space. We define two operations: addition <+> and real scalar multiplication <x>. With these operations the space of colors becomes a real vector space. Then, defining the scalar product (.|.) and the norm || . ||, we obtain a (logarithmic) Euclidean space. We show how we can use this model for color image enhancement and we present some experimental results.