Correction of geometric perceptual distortions in pictures

Abstract

We suggest an approach for correcting several types of perceived geometric distortions in computer-generated and photographic images. The approach is based on a mathematical formalization of desirable properties of pictures. We provide a review of perception of pictures and identify perceptually important geometric properties of images. From a small set of simple assumptions we obtain perceptually preferable projections of three-dimensional space into the plane and show that these projections can be decomposed into a perspective or parallel projection followed by a planar transformation. The decomposition is easily implemented and provides a convenient framework for further analysis of the image mapping. We prove that two perceptually important properties are incompatible and cannot be satisfied simultaneously. It is impossible to construct a projection such that the images of all lines are straight and the images of all spheres are exact circles. Perceptually preferable tradeoffs between these two types of distortions can depend on the content of the picture. We construct parametric families of projections with parameters representing the relative importance of the perceptual characteristics. By adjusting the settings of the parameters we can minimize the overall distortion of the picture. It turns out that a simple family of transformations produces results that are sufficiently close to optimal. We implement the proposed transformations and apply them to computer-generated and photographic perspective projection images. Our transformations can considerably reduce distortion in wide-angle motion pictures and computer-generated animations.