Abstract

The scale invariant property of an ensemble of natural im- ages is examined which motivates a new early visual representation termed the higher order pyramid. The representation is a non-linear gen- eralization of the Laplacian pyramid and is tuned to the type of scale invariance exhibited by natural imagery as opposed to other scale invari- ant images such as 1/f correlated noise and the step edge. The trans- formation of an image to a higher order pyramid is simple to compute and straightforward to invert. Because the representation is invertible it is shown that the higher order pyramid can be truncated and quan- tized with little loss of visual quality. Images coded in this representation have much less redundancy than the raw image pixels and decorrelating transformations such as the Laplacian pyramid. This is demonstrated by showing statistical independence between pairs of coefficients. Because the representation is tuned to the ensemble redundancies the coefficients of the higher order pyramid are more efficient at capturing the variation within the ensemble which leads too improved matching results. This is demonstrated on two recognition tasks, face recognition with illumina- tion changes and ob ject recognition which viewpoint changes.