Complex-Valued Hough Transforms for Circles

TL;DR

This paper introduces a complex-valued approach to the Hough transform for circle detection, utilizing complex votes to improve robustness and accuracy over traditional methods, demonstrated through experiments on synthetic and real data.

Contribution

It proposes a novel complex-valued voting scheme in the Hough transform that enhances robustness and accuracy in circle detection tasks.

Findings

Complex votes enable cancellation effects improving detection robustness.

Magnitude squared of complex votes correlates with shape likelihood.

Experimental results show superior performance over classic algorithms.

Abstract

This paper advocates the use of complex variables to represent votes in the Hough transform for circle detection. Replacing the positive numbers classically used in the parameter space of the Hough transforms by complex numbers allows cancellation effects when adding up the votes. Cancellation and the computation of shape likelihood via a complex number's magnitude square lead to more robust solutions than the "classic" algorithms, as shown by computational experiments on synthetic and real datasets.