Bias and Noise in the Hough Transform I: Theory
Christopher M. Brown · UR Research (University of Rochester)
The main results of this work are the following. 1. An approach to Hough Transforms (HT) based on a linear imaging model. The HT produces a peak in accumulator (parameter) space corresponding to likely parameters of an interesting phenomenon in the image. It also produces background off-peak sidelobes, which are important because they can add significant variance and background bias to the accumulator space and make peak-finding a local and difficult process. 2. Definitions of bias and noise in the HT. 3. Analytical techniques for reasoning about sidelobe shapes, and some descriptions of sidelobes in practically important parameter spaces under continuous, noise-free conditions. 4. The CHough method, which can eliminate sidelobe bias and decrease sidelobe variance. The peak height is then an unbiased estimator for the amount of evidence consistent with the peak parameter vector, and simple global techniques (such as global thresholding) will find peaks. Compared to traditional HT, CHough seems to have much better sidelobe bias properties, significantly better sidelobe variance properties, equal or worse quantization noise properties, and equal or better resistance to "noise" features in the image.