Image Edges Resolved Well When Using an Overcomplete Piecewise-Polynomial Model

Used in the paper is an overcomplete piecewise-polynomial image model incorporating sparsity. The paper shows that using such a model, the edges in the image can be resolved robustly with respect to noise. Two variants of the proposed approach are both shown to be superior to the use of the classic edge detecting kernels. The proposed method is in turn also suitable for image segmentation.