Comparametric equations with practical applications in quantigraphic image processing

Abstract

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 is neither radiometric nor photometric, but, rather, 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. Comparametric equations are fundamental to the analysis and processing of multiple images differing only in exposure. The well-known "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. For this reason 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" (as opposed to the time domain or the frequency domain). While the theoretical framework presented in this paper originated within the field of wearable cybernetics (wearable photographic apparatus) in the 1970s and early 1980s, it is applicable to the processing of images from nearly all types of modern cameras, wearable or otherwise. This paper is a much revised draft of a 1992 peer-reviewed but unpublished report by the author, entitled "Lightspace and the Wyckoff principle."

Comparametric image compositing: Computationally efficient high dynamic range imaging

“…, N}, and each image has exposure k i . The subscript indicates it is the i-th in a Wyckoff set [3], i.e. a set of images differing only in exposure, and by convention k i < k i+1 ∀ i < N. The notation f −1 means the mathematical inverse of f if it has only one argument, and otherwise means a joint estimator 2 of photoquantity, q.…”

Estimating Radiometric Response Functions from Image Noise Variance

“…Grossberg and Nayar apply principal component analysis (PCA) to a database of real-world response functions (DoRF) and show that the space of response functions can be represented by a small number of basis functions [5]. Mann [6] uses the comparametric equation that defines the relationship between two images taken with different exposure times.…”

“…(6). Because the i-th moment of image noise N i can be computed as the sum of the readout and shot noise as (12).…”

Background estimation under rapid gain change in thermal imagery

“…Mann [6] introduces the idea of a comparametric plot of f (kq) with respect to f (q), using pairs of corresponding pixel values observed from images taken at different exposure settings. Fitting a parametric model to the observed correspondences yields a comparametric function that relates pixel intensities before and after a change in exposure.…”