On the Computation of the Discrete Log-Polar Transform

This paper reports algorithms for computing the log-polar transform (LPT) of a digital image using optimal parameters for use in an active vision system. The LPT is a space-variant mapping similar in form to the human retina, with a central high-resolution fovea and a periphery of radially decreasing resolution. In the past, only cursory attention has been given to the selection of transform parameters. This is likely because the exact values of the parameters are of little significance when the images are defined on the Euclidean plane. However, in the practical transformation of digital images, the parameters have a much greater significance. For example, a correct choice will assure that the fovea can cover all the pixels in the input image that are mapped to one pixel at the extreme periphery of the output. Then any pixel-sized feature in the periphery can be imaged at full resolution with a single camera motion. The paper reports the derivation of the optimal parameters, gives practical algorithms for computing the log-polar transform of a digital image and demonstrates how non-optimal parameters affect the transformation.