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Separation of Edges in X‐Ray Images by Microlocal Analysis
Author(s) -
Storath Martin
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110420
Subject(s) - intersection (aeronautics) , submanifold , orientation (vector space) , gravitational singularity , mathematics , image (mathematics) , microlocal analysis , enhanced data rates for gsm evolution , boundary (topology) , geometry , singularity , mathematical analysis , computer science , computer vision , engineering , aerospace engineering , operator theory , fourier integral operator
In many x‐ray images, we find crossing structures, for example the rib bones of a thorax image. Hence, many edges in such images intersect with other edges. We propose a new algorithm, which simultaneously detects and separates such crossing edges. We prove the functionality of the algorithm under the geometric assumption that the edges possess different orientations at the points of intersection. To this end, we model edges as singularities of distributions with a submanifold structure and define the edge orientation to be the orientation of the corresponding singularity in the sense of microlocal analysis. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)