A model for logarithmic image processing

Up to now, image processing and image analysis techniques have borrowed their basic tools from functional analysis: Fourier filtering, differential and integral calculus, and so on. These tools, however, only realize their efficiency when they are put into a well‐defined algebraic frame, most of the time of a vectorial nature. Unfortunately, the class of functions modelling ‘images’, commonly referred to as ‘grey tone functions’ does not necessarily present this very type of structure. We present here an operation for the ‘addition’ of two images, with a physical justification in the context of transmitted light. Such an addition permits the construction of the family of ‘positive homothetics' of the grey tone function at hand. The vectorial context sought is well defined: The class of images associated with the class of their grey tone functions naturally becomes the positive cone of an ordered real vector space.