The generalized Radon transform: Sampling, accuracy and memory considerations

The generalized Radon (or Hough) transform is a well-known tool for detecting parameterized shapes in an image. The Radon transform is a mapping between the image space and a parameter space. The coordinates of a point in the latter correspond to the parameters of a shape in the image. The amplitude at that point corresponds to the amount of evidence for that shape. In this paper we discuss three important aspects of the Radon transform. The first aspect is discretization. Using concepts from sampling theory we derive a set of sampling criteria for the generalized Radon transform. The second aspect is accuracy. For the specific case of the Radon transform for spheres, we examine how well the location of the maxima matches the true parameters. We derive a correction term to reduce the bias in the estimated radii. The third aspect concerns a projection-based algorithm to reduce memory requirements.