Higher order image pyramids: an early visual representation

The scale invariant property of an ensemble of natural images is examined, which motivates a new early visual representation termed the higher order pyramid. The representation is a non-linear generalization of the Laplacian pyramid, tuned to the type of scale invariance exhibited by natural imagery as opposed to other scale invariant images such as 1/f correlated noise and the step edge. The transformation 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 quantized 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. The representation is tuned to the ensemble redundancies, and hence the coefficients of the higher order pyramid are more efficient at capturing the variation within the ensemble which leads to improved matching results. This is demonstrated on several recognition tasks: object recognition with viewpoint changes, object recognition with scale changes, and face recognition with illumination changes.