Elliptical Shape Recovery From Blurred Pixels Using Deep Learning

In this paper, we study the problem of ellipse recovery from blurred shape images. A shape image is a continuous-domain black and white (binary-valued) image in which the points of the same color form a shape. We assume to have a digitized version of the shape image which is a sampled and blurred version of the image using a $2$D kernel (the point spread function); the resulting pixels may also be corrupted by additive noise. Our goal in this work is to recover the original continuous-domain image based on the available pixels when the shape image is an ellipse. Our approach is to represent an ellipse as the zero-level-set of a bivariate polynomial of degree $2$ and estimate the involved $6$ polynomial coefficients based on a deep neural network. Our model is trained end to end on a wide range of blurring setups with varying noise levels. Besides, the network is trained to recover the ellipse even when the available noisy pixels cover only a part of the ellipse. Simulation results validate the performance of the proposed method and indicate its superiority compared to the state of art methods.