The Performance of the Generalised Hough Transform: Concavities, Ambiguities and Positional Accuracy

This paper studies the use of the generalised Hough transform to locate objects possessing concavities. Hhen locating objects with internal symmetries, ambiguities can arise which nay not be resolvable in the presence of occlusions. On the other hand concavities can help to lake object location more accurate. The boundary orientation distribution can be used to analyse the situation: it shows that enhanced accuracy of location along one axis may result in reduced accuracy in a perpendicular direction. Finally, accuracy of location is independent of the position of the object localisation point. This paper starts with the observation that a problem arises when the GHT is used to detect objects possessing concavities. In principle this can lead to ambiguities in the location of such objects, and it was felt necessary to investigate the problem closely in order to find how its effects could be minimised. In section II we briefly describe the operation of the GHT. Then in section III we consider the problem posed by concavities, following this in section IV by a discussion of the effects of symmetries. In sections V and VI we investigate how the accuracy with which an object can be located is affected by its shape and by errors in the estimation of edge orientation. Although the Hough transform was originally devised for the detection of straight lines as long ago as 1962 (Hough 1962), it only came into wide use in the image processing community after it was 're-discovered' by Rosenfeld in 1969 and further developed by Duda and Hart in 1972. Subsequent work applied the technique to the detection of circles, at the same time making it more efficient by showing how locally available edge orientation information could be used to cut down the number of votes accumulated in parameter space (ICimme et al 1975). Later, the technique was applied to other specific types of curve such as ellipses and parabolas before Ballard finally generalised it so that it could be applied to the detection of arbitrary shapes (Ballard 1981). The resulting 'generalised Hough transform' (GHT) retained the facility for making use of local edge orientation information, and is thus a highly efficient procedure. More recently, Davies has found that one advantage of using the GHT rather than the basic Hough transform to detect straight edges is that this enables objects such as squares and rectangles to be detected directly-i.e. without further high-level …