Comparametric equation

Abstract: It is argued that, hidden within the flow of signals from typical cameras, through image processing, to display media, is a homomorphic filter. While homomorphic filtering is often desirable, there are some occasions where it is not. Thus, cancellation of this implicit homomorphic filter is proposed, through the introduction of an antihomomorphic filter. This concept gives rise to the principle of quantigraphic image processing, wherein it is argued that most cameras can be modeled as an array of idealized light meters each linearly responsive to a semi-monotonic function of the quantity of light received, integrated over a fixed spectral response profile. This quantity depends only on the spectral response of the sensor elements in the camera. A particular class of functional equations, called comparametric equations, is introduced as a basis for quantigraphic image processing. These are fundamental to the analysis and processing of multiple images differing only in exposure. The "gamma correction" of an image is presented as a simple example of a comparametric equation, for which it is shown that the underlying quantigraphic function does not pass through the origin. Thus, it is argued that exposure adjustment by gamma correction is inherently flawed, and alternatives are provided. These alternatives, when applied to a plurality of images that differ only in exposure, give rise to a new kind of processing in the "amplitude domain". The theoretical framework presented in this paper is applicable to the processing of images from nearly all types of modern cameras. This paper is a much revised draft of a 1992 peer-reviewed but unpublished report by the author, entitled "Lightspace and the Wyckoff principle".