Improving parameter space decomposition for the generalised Hough transform

The generalised Hough transform extracts arbitrary objects by using a non-analytic model shape representation obtained from gradient direction information. The main drawback of this technique is the excessive computational burden because of the four-dimensional parameter space required when orientation and scale are unknown. We present a novel representation of a model shape defined by the geometric relationship given by the position of a collection of edge points. This representation avoids errors due to unreliable gradient direction information and is used to reduce the computational requirements by decomposing the four-dimensional parameter space into two two-dimensional sub-spaces. Experimental results show the efficacy of the new technique for extracting shapes from synthetic and real images.