Geometry of the Hough transforms with applications to synthetic data
This work addresses a specific bottleneck in image recognition algorithms for detecting curves, offering incremental improvements in efficiency and robustness.
The authors tackled the problem of optimizing the Hough transform for curve detection in images by providing a bound on the number of transforms needed, based on geometric arguments, and demonstrated robustness on noisy synthetic datasets, with an algebraic approach yielding a better theoretical bound in exact cases.
In the framework of the Hough transform technique to detect curves in images, we provide a bound for the number of Hough transforms to be considered for a successful optimization of the accumulator function in the recognition algorithm. Such a bound is consequence of geometrical arguments. We also show the robustness of the results when applied to synthetic datasets strongly perturbed by noise. An algebraic approach, discussed in the appendix, leads to a better bound of theoretical interest in the exact case.