Complex-Valued Hough Transforms for Circles
This work addresses circle detection in computer vision, offering an incremental improvement over classic methods.
The paper tackles the problem of circle detection in images by proposing a complex-valued Hough transform, where votes are represented as complex numbers to enable cancellation effects, resulting in more robust solutions as demonstrated in computational experiments on synthetic and real datasets.
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.