Reduction of computational complexity of Hough transforms using a convolution approach

The Hough transform finds wide application in machine and robot vision. The family of Hough transforms allows a variety of geometric objects to be located and described in an image. However, the classical Hough transform is computationally complex when targeting complex objects. This renders the Hough transform unsuitable for many real-time applications. We present a new algorithm for calculating the circle Hough transform by recasting it as a convolution. This new approach allows the transform to be calculated using the fast Fourier transform, yielding an algorithm with lower computational complexity than the traditional approach. Although the convolution approach is applicable to the same range of different targets as the traditional Hough transform, we limit ourselves to a consideration of the circle Hough transform in this treatment.