Strongly concave star-shaped contour characterization by algebra tools

In this paper, we discuss the problem of recovering a star-shaped contour with the assumption that the contour coordinates can be decomposed into damped sinusoids. We propose a signal generation method derived from the array processing paradigm, which yields the center and radius of a circle fitting the contour. Starting from an initialization circle, we propose to estimate the oscillations of the expected contour around this circle with a method which copes with noise and strong concavities. We adopt a signal characterization method which provides the parameters of damped sinusoids. In addition, we propose a refinement step based on an optimization method which improves the adequation of the collected signals to the proposed model. The novel proposed method is compared with an approach based on signal generation and gradient optimization method, and with GVF method. The experiments show that the proposed method offers a significant improvement in terms of pixel bias and computational load, in particular when strongly concave contours in noisy images are considered. Moreover, the computational load of the proposed method is independent from the contour concavity and the noise level.

► The retrieval of strongly concave contours in a noisy environment is considered.
► A strongly concave contour is modeled as the superposition of damped sinusoids.
► A signal generation method turns the processed 2-D image into a 1-D signal.
► A damped sinusoid characterization method characterizes entirely the contour.
► Our method is robust to concavity and noise compared with Gradient and GVF.