Designing efficient hough transform by noise-level shaping

A large number of techniques have been proposed for acceleration of the Hough Transform, because the transformation is computationally very expensive in general. It is known that the sampling interval in parameter space is strongly related to the computation cost. The precision of the transformation and the processing speed are in a trade-off relationship. No fair comparison of the processing speed between various methods was performed in all previous works, because no criterion had been given for the sampling interval of parameter, and because the precision of parameter was not equal between methods. At the beginning of our research, we derive the relationship between the sampling interval and the precision of parameter. Then we derive a framework for comparing computation cost under equal condition for precision of parameter, regarding the total number of sampling points of a parameter as the computation cost. We define the transformation error in the Hough Transform, and the error is regarded as transformation noise. In this paper we also propose a design method called "Noise-level Shaping," by which we can set the transformation noise to an arbitrarily level. The level of the noise is varied according to the value of a parameter. Noise-level Shaping makes it possible for us to find the efficient parameterization and to find the efficient sampling interval in a specific application of the Hough Transform.