Image edges resolved well when using an overcomplete piecewise-polynomial model

TL;DR

This paper introduces an overcomplete piecewise-polynomial model with sparsity for robust edge detection in images, outperforming classic kernels and also enabling effective image segmentation.

Contribution

The paper presents a novel overcomplete piecewise-polynomial model that improves edge resolution and robustness to noise, with two variants outperforming traditional methods.

Findings

Edges are resolved more accurately with the proposed model.

The approach demonstrates robustness against noise.

The method is effective for image segmentation.

Abstract

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.