Title

Characterization and analysis of edges using the continuous shearlet transform

Abstract

This paper shows that the continuous shearlet transform, a novel directional multiscale transform recently introduced by the authors and their collaborators, provides a precise geometrical characterization for the boundary curves of very general planar regions. This study is motivated by imaging applications, where such boundary curves represent edges of images. The shearlet approach is able to characterize both locations and orientations of the edge points, including corner points and junctions, where the edge curves exhibit abrupt changes in tangent or curvature. Our results encompass and greatly extend previous results based on the shearlet and curvelet transforms which were limited to very special cases such as polygons and smooth boundary curves with nonvanishing curvature.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1137/080741537

Keywords

Analysis of singularities, Continuous wavelets, Curvelets, Directional wavelets, Edge detection, Shearlets, Wavelets

Publication Date

1-1-2009

Journal Title

SIAM Journal on Imaging Sciences

Share

COinS