Abstract

A scheme suitable for image representation in vision is elaborated using a 2-D extension of Bastiaan's work (1980). Investigation of image structure in Gabor space shows that important characteristics of vision are inherent in the scheme, lending itself to image representation by machines. With logarithmic scaling (octave relationship) along the frequency axis, it is shown that certain visual invariances are characteristic of image representation in a combined frequency position space. It appears as though the representation in the combined space captures attractive properties previously shown exclusively for either the position or frequency space. An interesting issue relating to paving of the combined space is concerned with the number of required elementary functions (or channels in vision). It is shown that a trade-off exists between the number of frequency components employed per position and the number of such clusters (sampling rate) utilized along the spatial coordinate. This observation settles arguments against the channel approach in vision, since it shows that a small number of frequency channels can suffice (provided there are enough spatial sampling points). Whereas the analytic solution requires the elaboration of auxiliary functions, it is unlikely that cortical representation employs such operation. We therefore also consider image representation by a set of almost orthogonal functions.

© 1985 Optical Society of America