Construction and detection of straight lines, distances, and circles in log-polar images

This paper investigates, how two fundamental measurement operations in Euclidean space, namely the construction of a straight line of given orientation angle and the measurement of distances along this line, are mapped to the non-Euclidean log-polar image plane. It is shown, how these two operations can be efficiently implemented for discrete log-polar images. The measurement operations are used to perform line and circle detection in log-polar sampled images, a task, which can only be solved with the usual methods known from Cartesian images, if the two operations are available: chains of edgels are extracted from an image, then lines and circles are found through geometric constructions and testing of geometric relations. Experiments with both synthetic and real images are presented, and the detection results are quantitatively evaluated.