Towards Automated Filtering of the Medial Axis Using the Scale Axis Transform

This paper analyzes the problem of determining the optimal scaling to prune the medial axis of spurious branches with the use of the Scale Axis Transform (SAT) in R-2. This optimal scaling is found by minimizing the Frechet distance between the boundary of the true shape and the boundary of the SAT-filtered version of the shape perturbed by noise. To compute the minimum, the noisy shape is filtered using a variety of scalings s > 1 of the SAT algorithm. The optimal scaling is then related to the level of noise used to perturb the true shape. The minimization problem is repeated for various shapes and different noise levels. In applications such as image recognition and registration, the medial axis is very relevant. However, it is highly susceptible to noise along the boundary. The results presented here offer crucial information to automate the de-noising process, by providing a link between the level of noise and the optimal SAT scaling factor.