Medical image enhancement using logarithmic image processing

The logarithmic image processing theory is a mathematical framework that provides a set of specific algebraic and functional operations and structures that are well adapted to the representation and processing of nonlinear images, and more generally of non-linear signals, valued in a bounded intensity range. The purpose of this paper is to introduce a new mathematical LIP model focused on theoretical and practical aspects concerning the enhancement of the transmitted medical images and the physical absorption/transmission laws expressed within LIP mathematical framework. First of all the bounded interval (-1,1) is considered as the set of gray levels and we define two operations: addition left angle bracket+right angle bracket and real scalar multiplication left angle bracketXright angle bracket. With these operations, the set of gray levels becomes a real vector space. Then, defining the scalar product (.vertical bar.) and the norm parallel to.parallel to, we obtain an Euclidean space of the gray levels. Secondly, we extend these operations and functions for color images. Finally, the experimental results, shown as enhanced medical images, reveal that this method has wide potential areas of impact which may include: Digital Xray, Digital Mammography, Computer Tomography Scans, Nuclear Magnetic Resonance Imagery and Telemedicine Applications.