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
Rights Information
© 2009 Society for Industrial and Applied Mathematics (SIAM)
Keywords
Analysis of singularities, Continuous wavelets, Curvelets, Directional wavelets, Edge detection, Shearlets, Wavelets
Publication Date
1-1-2009
Recommended Citation
Guo, Kanghui, and Demetrio Labate. "Characterization and analysis of edges using the continuous shearlet transform." SIAM journal on Imaging Sciences 2, no. 3 (2009): 959-986.
Journal Title
SIAM Journal on Imaging Sciences
