Ellipse Recovery From Blurred Binary Images.

In this paper, we address the problem of ellipse recovery from blurred shape images. A shape image is a binary-valued (0/1) image in continuous-domain that represents one or multiple shapes. In general, the shapes can also be overlapping. We assume to observe the shape image through finitely many blurred samples, where the 2D blurring kernel is assumed to be known. The samples might also be noisy. Our goal is to detect and locate ellipses within the shape image. Our approach is based on representing an ellipse as the zero-level-set of a bivariate polynomial of degree 2. Indeed, similar to the theory of finite rate of innovation (FRI), we establish a set of linear equations (annihilation filter) between the image moments and the coefficients of the bivariate polynomial. For a single ellipse, we show that the image can be perfectly recovered from only 6 image moments (improving the bound in [Fatemi et al., 2016]). For multiple ellipses, instead of searching for a polynomial of higher degree, we locally search for single ellipses and apply a pooling technique to detect the ellipse. As we always search for a polynomial of degree 2, this approach is more robust against additive noise compared to the strategy of searching for a polynomial of higher degree (detecting multiple ellipses at the same time). Besides, this approach has the advantage of detecting ellipses even when they intersect and some parts of the boundaries are lost. Simulation results using both synthetic and real world images (red blood cells) confirm superiority of the performance of the proposed method against the existing techniques.