Design strategies for direct multi-scale and multi-orientation feature extraction in the log-polar domain

Despite the well known advantages that a space-variant representation of the visual signal offers, the required adaptation of the algorithms developed in the Cartesian domain, before applying them in the log-polar space, has limited a wide use of such representation in visual processing applications. In this paper, we present a set of original rules for designing a discrete log-polar mapping that allows a direct application in the log-polar domain of the algorithms, based on spatial multi-scale and multi-orientation filtering, originally developed for the Cartesian domain. The advantage of the approach is to gain, without modifications, an effective space-variance and data reduction. Such design strategies are based on a quantitative analysis of the relationships between the spatial filtering and the space-variant representation. We assess the devised rules by using a distributed approach based on a bank of band-pass filters to compute reliable disparity maps, by providing quantitative measures of the computational load and of the accuracy of the computed visual features.