The Generalized Hough Transform on Mesh-Connected Computers

Abstract This work analyzes the computational complexity of the Generalized Hough Transform (GHT) on a mesh-connected (MCC) and introduces practical algorithms for bidimensional shape recognition useful in real situations, and not just in asymptotic cases. This paper shows how to map such a transform onto a massive parallel computer that consists of a mesh of 4-connected processing elements (PEs). While a class of algorithms relying on general purpose data movements techniques has time complexity O ( Rn log n ) on an n × n MCC under the SIMD bit model, R being the number of points used to describe the shape, an important criterion implicitly embedded in the transform is not reflected in such implementations: namely, the locality of the transform with respect to the input image. Indeed, most shapes are bound by a circle having a radius d usually much smaller than the linear dimension of the mesh. This paper shows how an efficient implementation of the GHT can be obtained using this geometric constraint. Two classes of algorithms are introduced; both exhibit an asymptotic complexity O ( Rd 2 log n ) which is a function of the region enclosing the sought for shape. The derivation of exact time costs both for the standard implementations and for the new ones establishes the break-even point for any problem size. The proposed algorithms outperform the standard ones in all practical situations.