Detection of linear and circular shapes in image analysis

A two-step algorithm is proposed for estimating linear and circular shapes in noisy images. Initially and based on a previously proposed method, the pixels which are close to the edges of the shape are detected. These edges are assumed to be coming from a mixture of (linear or circular) regression functions and the parameters of these functions are estimated. An example with a triangle demonstrates the immense advantage of using an outlier robust estimator for the edge points. A second example deals with a problem from biology where the detection of circular shapes of fungi colonies is of interest.