### 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.

From a small set of simple assumptions we obtain perceptually preferable
viewing transformations and show that these transformations 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
viewing transformation 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 transformations 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.