Reciprocal-Wedge Transform for Space-Variant Sensing

The Reciprocal-Wedge Transform (RWT) is presented as an alternative to the log-polar transform which has been a popular model for space-variant sensing in computer vision. The log-polar transform provides efficient data reduction. It simplifies the centric rotational and scaling image transformations. However, it adversely complicates the linear features and translational transformations. The RWT facilitates an anisotropic variable resolution. Unlike the log-polar, its variable resolution is predominantly in one dimension. Consequently, the RWT preserves linearity of lines and translations in the original image. In this paper, a concise matrix representation of the RWT is presented. Its properties in geometrical transformations and data reduction are described. A projective model for the transform and a potential hardware RWT camera design are also illustrated. As examples of initial applications, the RWT is used for finding road directions in navigation, and for recovering depth in motion stereo. Two types of motion stereo are presented, namely the longitudinal and lateral motion stereo. In all cases, the RWT images offer much reduced and adequate data owing to the variable resolution. In road navigation, perspective distortion of the road image is readily corrected by the variable resolution of the RWT. In cases of the motion stereo, the correspondence problem in the RWT domain is reduced to a simpler problem of extracting collinear points in the epipolar plane. Preliminary experimental results from test images of road-vehicle navigation and moving objects on a miniature assembly line are demonstrated.