The Symmetric Generalized LIP Model and Its Application in Dynamic Range Enhancement

Abstract

The theory and applications of the logarithmic image processing (LIP) have been studied by many researchers. In this work, we develop a symmetric generalized LIP (SGLIP) model. The development is based on a comparative study of recent theoretical development which include the original LIP model, the generalized LIP model (GLIP), the symmetric LIP (SLIP) model, and the log-ratio model. The study is conducted under the framework of a generalized linear system which is formally defined in this paper from a vector space perspective. Using the main idea of the log-ratio model, we review an alternative link between the LIP and the SLIP model. This leads naturally to the combination of the idea of the SLIP model with the GLIP model to develop the SGLIP model. We demonstrate that (1) the SLIP model is a special case of the SGLIP model; (2) the SGLIP model has desirable properties overcoming problems associated with the LIP model and GLIP model; and (3) the SGLIP model provides new insights into the generating function and the gray tone function which are essential concepts in the LIP model. We also demonstrate an application of the SGLIP model in enhancing the dynamic range of images.