Traditional linear multiscale representations of discretized images describe an image as a sum of translated and scaled copies of a set of basis functions. The steerable pyramid is an example of such a representation where the basis functions used are derivative operators, and the subbands are then gradients of progressively blurred copies of the original image.

In this talk, I present a nonlinear representation based on the steerable pyramid where only the orientation of the gradient is kept, and all of the magnitude information is discarded. The representation is thus entirely based on measurements of local geometry of the image. Surprisingly, I am able to recover the original image from only the orientation information.  I will describe the basic iterative reconstruction algorithm and some tricks to speed up its convergence. At the end I will discuss some ongoing issues in using this novel representation as a tool for image processing.