Journal
SIAM JOURNAL ON IMAGING SCIENCES
Volume 2, Issue 3, Pages 959-986Publisher
SIAM PUBLICATIONS
DOI: 10.1137/080741537
Keywords
analysis of singularities; continuous wavelets; curvelets; directional wavelets; edge detection; shearlets; wavelets
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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.
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