  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.
