A GENERAL COMPARATIVE-STUDY OF THE MULTIPLICATIVE HOMOMORPHIC, LOG-RATIO AND LOGARITHMIC IMAGE-PROCESSING APPROACHES

This article presents a comparative study of the multiplicative homomo rphic image processing (MHIP), the log-ratio image processing (LRIP) a nd the logarithmic image processing (LIP). These three image processin g approaches are based on abstract linear mathematics and provide spec ific operations and structures that have opened up new pathways to the development of image processing techniques. The MHIP approach was des igned for the processing of multiplied images, the LRIP approach was i ntroduced to overcome the out-of-range problem associated with many im age processing techniques, while the LIP approach was developed for th e processing of images valued in a bounded intensity range. First, it is claimed that an image processing framework must be physically relev ant, mathematically consistent, computationally tractable and practica lly fruitful. It is also pointed out that the classical linear image p rocessing (CLIP) is not adapted to non-linear and/or bounded range ima ges or imaging systems, such as transmitted light images, practical di gital images or the human brightness perception system. Then, the impo rtance and usefulness of several mathematical fields, such as abstract linear algebra and abstract analysis, for image representation and pr ocessing within such image settings are discussed. Third, the MHIP, LR IP and LIP approaches are presented, focusing on their distinctive ide as, structures and properties for image representation and processing, rather than an in-depth review. Next, a study of the relationships an d differences between their image representations and basic algebraic operations is detailed. Finally, a general comparative discussion is d eveloped, showing the main physical, mathematical, computational and p ractical characteristics of these three abstract-linear-mathematics-ba sed image processing approaches, and summarizing their respective adva ntages and disadvantages. It is concluded and highlighted through real application examples in both image enhancement and edge detection are as that the LIP approach surpasses the two other approaches, although, from a strictly practical point of view, a detailed quantitative comp arative study on real applications is now necessary. (C) 1997 Elsevier Science B.V.