Geometry and construction of straight lines in log-polar images

This paper investigates, how straight lines are mapped to the non-Euclidean log-polar image plane and how their properties in log-polar coordinates can be used to perform two fundamental measurement operations: the construction of straight lines of given orientation angle and the measurement of distances along these lines. It is shown, how the two operations can be efficiently implemented for discrete log-polar images. The usefulness of the developed theory is demonstrated by applying it to different image processing tasks. As a first example, it is used for line and circle detection in log-polar sampled images. As a second example, it is used to construct epipolar lines and perform disparity estimation in log-polar images. Experiments with both synthetic and real images are presented, and the feature detection results are quantitatively evaluated.