Detecting parameteric curves using the straight line Hough transform

A novel approach for the detection of parametric curves using the straight-line Hough transform is presented. The transform function of a curve can be expressed as the sum of two terms, namely, the intrinsic term and the translation term. This representation allows a natural decomposition of the high-dimensional parameter space into three subspaces: the intrinsic curve parameters, translation, and rotation. By eliminating either the translation term or the intrinsic term, one can easily determine the parameters of the remaining term. The complexity of this method depends mainly on the angular resolution, which is relatively independent of the arc length of the curve. The computational complexity of this approach compares favorably with that of other approaches based on the Hough transform.