A probabilistic approach to the Hough Transform

The mathematical principles come from the "Maximum Likelihood Method" [2, 3], used in probability theory for the determination of distribution parameters from experimental data. The Maximum Likelihood analysis leads to the definition of the Probabilistic Hough Transform, which is a likelihood function. If certain assumptions are made about the error characteristics, the PHT is very close to conventional Hough Transforms. If, in a particular application, these assumptions are a reasonable approximation, good results are usually obtained using standard Hough methods. However, where these assumptions are far from the truth, the Hough Transform will not work well, and steps should be taken to improve the model of input feature errors, such as filtering the Hough space, or incrementing an extended region instead of just the voting space. As a last resort, the full PHT can be computed, but this is much more computationally expensive than conventional Hough methods.