Connective hough transform

Abstract

A method to extend the Hough transform (HT) to detect connectivity by ordered accumulation is reported. The method is applied to the dynamic combinatorial HT [6]. A focus of attention mechanism is also reported. Our connective HT with focus of attention reduces the computational complexity of the DCHT and increases the S/N ratio of the peak in its accumulator. It may be regarded as a principled method for curve tracing. A general method to improve the computational efficiency of the DCHT by probabilistic selection of interesting fixation points is also introduced. Results using simulated and real data are reported. The connectivity problemA common problem to all Hough transform (HT) [4] is the 'connectivity problem'. It arises because the accumulator counts only give the number of points that share the same parameters. These points may not be connected with each other. Hence the number of points is not necessarily a good measure for the strength of the pattern. In the case of straight line detection, Duda and Hart [3] remarked as early as 1972 that "... the (Hough) technique finds collinear points without regard to contiguity. Thus the position of a best-fit line can be distorted by the presence of unrelated figure points in another part of the picture. A related problem is that of meaningless groups of collinear points being detected".Though this is a fundamental problem, it has not received much attention in the past. We are only aware of one effort in solving this problem. Motivated by practical application in integrated circuits, Shu, Li, Mancuso and Sun [10] replaced the counters by bit maps. Instead of accumulating, the appropriate bits in the bit map are set to '1'. After the accumulation is complete, each bit map is searched for sequences of '1' s. Unfortunately, this method amounts to no more than a brute force search. Also, for an TV x N input image, the memory required is increased by }o N N , making this practical only for small images.In the rest of this paper, we shall report a new method, known as Connective Hough Transform (CHT), to add connectivity by ordered accumulation 'supported by a Croucher Foundation fellowship. I thank Jim Stone and David Young for meticulous proofreading, Alistair Bray for supplying the real image, and the referees for thoughtful comments.