Hough Array Processing via Fast Multi-Scale Clustering

The major emphasis in fast Hough transform algorithms has been placed on the transformation involved. Little attention has been paid to fast processing of a Hough array without requiring one to specify a threshold value to determine candidate parameters in the Hough array. This paper gives a comprehensive discussion of Hough array processing as a part of Hough transform, and presents a time efficient clustering algorithm, called Fast Multi-Scale Clustering, to obtain the number of and hence to select the locations of candidate parameters in a Hough array in a threshold independent manner. It is shown that the complexity of this algorithm is O (ndr) where n is the number of non-zero cells in the Hough array, d is the number of cells used in the discretization of the corresponding parameter space, and r is the dimensionality of the Hough array. Two examples of line and circle detection are provided to illustrate the steps involved in deploying this Hough array processing approach.