Fourier parameterization provide uniform bounded Hough Space

Abstract

The Hough transform is a popular technique for feature detection and object recognition. In its original formulation for lines, the slope parameter is unbounded. Moreover, a rotation of the image will cause uneven representation accuracy of the slope. In a classic paper, Duda and Hart solved these problems by introducing a modified ρ-Θ parameterization, which has since become very popular in the computer vision community for parameterizing lines. Unfortunately, no equivalent parameterization exists for curves. This has led to ad hoc choice of parameterizations for circles, ellipses, conic sections etc. In this paper, we propose the novel use of Fourier descriptor as parameterized curve equation in a Hough transform. We show that using this Fourier parameterization, all parameters are bounded and the representation have uniform accuracy for all parameters.