Canonical images
Abstract
Most forms of optical image formation involve the use of an optical system to form a real image on an array of sensing elements. The output from the sensing elements is a sampled image. Mathematically, this process is described by convolution of the point spread function of the system (including the sensing elements) and the projection of objects in the image plane. In general, this process cannot be done mathematically in closed form for arbitrary images. Sampling and image processing algorithms are often assessed with respect to their performance on sampled images that are accepted standards. By applying known degradations such as noise and blur to a standard image, operating on the degraded image with a prospective algorithm, and comparing the result with the original uncorrupted image, an image processing algorithm or sampling scheme can be assessed. A weakness of this approach is the fact that the accepted standard is just that: an accepted standard. The image contains within itself uncertainties associated with the original image acquisition process. These uncertainties place bounds on the utility of the image. In this research we introduce the concept of canonical images. Canonical images are closed form, mathematically computable images that retain the essentials of the linear shift invariant image formation process. We derive one form of a canonical image, show its properties, and show how complex images can be generated using superposition. We also demonstrate how arbitrary images can be decomposed into canonical images that approximate them. We discuss applications for canonical images that include modeling and simulation, sensor testing, perception testing, and algorithm development.
Publication Title
Proceedings of SPIE - The International Society for Optical Engineering
Recommended Citation
Jacobs, E., & Bahhur, B. (2019). Canonical images. Proceedings of SPIE - The International Society for Optical Engineering https://doi.org/10.1117/12.2518912
