Detection of Lines with Wiggles using the Radon Transform

The discrete Radon transform is a useful tool in image processing for detection of lines (or in general curves) in digital images. One of the key properties of the discrete Radon transform is that a line in an image is transformed into a peak in the parameter domain, where the position of the peak corresponds to the line parameters. What often is needed, is to determine whether a Radon transform based curve detection algorithm will work in presence of noise. Lately analytical expressions for the probability of detecting a curve in presence of additive noise has been analyzed, and in this paper another kind of noise is analyzed theoretically, namely that the lines in the images might not be perfectly linear but include some random misalignment, here called wiggles.