Logarithmic Image Processing - The mathematical and physical framework for the representation and processing of transmitted images

An introductory account of the logarithmic image processing, theoretical and practical aspects focusing on the transmitted image settings is reviewed. Several LIP basic, less basic, and advanced image-processing techniques have been introduced, justified, and applied on real and various situations. LIP framework is consistent with the transmitted image-formation settings. Indeed, it fully expresses the image-formation process of these images, in the sense that LIP addition expresses the transmittance superposition law. Moreover, the intensity range constraints are involved, since gray-tone functions are valued in a bounded gray-tone range. LIP framework consists in a positive ordered functional vector-cone structure, where the modulus notion plays a key role, since it gives a mathematical meaning to the physical magnitude and allows several main LIP functional operations to be positively valued in the bounded gray-tone range. LIP framework provides a set of operations that overcome the out-of-range problem intrinsically or by using the modulus notion.