Rodriguez A, Granger R (2017). The differential geometry of perceptual similarity.

Rodriguez A, Granger R

Abstract

We propose a novel theoretical framework for understanding the underlying principles of perceptual similarity.

The work is based on differential geometry and graph theory. The framework enables the re-interpretation of a host of findings in perception, ranging from visual compression to Tversky’s demonstration of triangle inequality violations. The detailed work described here focuses just on visual compression. Using the new framework we demonstrate a novel analysis of the JPEG compression method, and outperformance of it, with no statistics or training, but solely arising from the new understanding that the framework confers. The JPEG algorithm uses the Discrete Cosine Transform (DCT) basis which has been proposed as an optimal entropy encoding basis. However, none of the proposed DCT bases used by JPEG take into account the perceptual capacities of the observer. If these are measured, or defined a priori, they may be used to produce an entropy basis that minimizes the errors registered by a particular observer under particular conditions, and thus identifying an encoding optimized with respect to that observer.