A Mathematical Model for Logarithmic Image Processing
This work presents a new mathematical framework for image processing, but it appears incremental as it builds on existing logarithmic concepts without clear application to a specific problem.
The authors introduced a mathematical model for image processing based on logarithmic operations, defining a vector space for gray levels and extending it to color images, and demonstrated the effects of simple operations on images.
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.