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Detection of boundary curves on the piecewise smooth boundary surface of three dimensional solids.
- Source :
-
Applied & Computational Harmonic Analysis . Jan2016, Vol. 40 Issue 1, p137-171. 35p. - Publication Year :
- 2016
-
Abstract
- Suppose that Ω is a three-dimensional solid with boundary surface S = S 1 ∪ ⋯ ∪ S q , where each S r is a smooth surface with boundary curve Γ r . Multiscale directional representation systems (e.g., shearlets) are able to capture the essential geometry of Ω by precisely identifying the boundary set N = { ( p , n r ( p ) ) : p ∈ S r , r = 1 , … , q } , where n r ( p ) denotes the normal vector to the surface S r at p . This property has resulted in the successful application of multiscale directional methods in a variety of image processing problems, since edges and boundary sets are usually the most informative features in many types of multidimensional data. However, existing methods are ill-suited to capture those edge-type singularities in the three-dimensional setting resulting from the intersection of piecewise smooth boundary surfaces. In this paper, we introduce a new multiscale directional system based on a modification of the shearlet framework and prove that the associated continuous transform has the ability to precisely identify both the location and orientation of the boundary curves Γ r from the solid Ω . This paper extends a number of results appeared in the literature in recent years to the challenging problem of extracting curvilinear singularities in three-dimensional objects and is motivated by image analysis problems arising from areas including biomedical and seismic imaging and astronomy. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10635203
- Volume :
- 40
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Applied & Computational Harmonic Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 111442308
- Full Text :
- https://doi.org/10.1016/j.acha.2015.01.004