Array Processing and Fast Optimization Algorithms for Distorted Circular Contour Retrieval

A specific formalism for virtual signal generation permits to transpose an image processing problem to an array processing problem. The existing method for straight-line characterization relies on the estimation of orientations and offsets of expected lines. This estimation is performed thanks to a subspace-based algorithm called subspace-based line detection (SLIDE). In this paper, we propose to retrieve circular and nearly circular contours in images. We estimate the radius of circles and we extend the estimation of circles to the retrieval of circular-like distorted contours. For this purpose we develop a new model for virtual signal generation; we simulate a circular antenna, so that a high-resolution method can be employed for radius estimation. An optimization method permits to extend circle fitting to the segmentation of objects which have any shape. We evaluate the performances of the proposed methods, on hand-made and real-world images, and we compare them with generalized Hough transform (GHT) and gradient vector flow (GVF).