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A Faster, Unbiased Path Opening by Upper Skeletonization and Weighted Adjacency Graphs
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.ORCID iD: 0000-0002-0612-558X
Flagship Biosci Inc, Westminster, CO 80021 USA.
2016 (English)In: IEEE Transactions on Image Processing, ISSN 1057-7149, E-ISSN 1941-0042, Vol. 25, no 12, 5589-5600 p.Article in journal (Refereed) Published
Abstract [en]

The path opening is a filter that preserves bright regions in the image in which a path of a certain length L fits. A path is a (not necessarily straight) line defined by a specific adjacency relation. The most efficient implementation known scales as O(min(L, d, Q)N) with the length of the path, L, the maximum possible path length, d, the number of graylevels, Q, and the image size, N. An approximation exists (parsimonious path opening) that has an execution time independent of path length. This is achieved by preselecting paths, and applying 1D openings along these paths. However, the preselected paths can miss important structures, as described by its authors. Here, we propose a different approximation, in which we preselect paths using a grayvalue skeleton. The skeleton follows all ridges in the image, meaning that no important line structures will be missed. An H-minima transform simplifies the image to reduce the number of branches in the skeleton. A graph-based version of the traditional path opening operates only on the pixels in the skeleton, yielding speedups up to one order of magnitude, depending on image size and filter parameters. The edges of the graph are weighted in order to minimize bias. Experiments show that the proposed algorithm scales linearly with image size, and that it is often slightly faster for longer paths than for shorter paths. The algorithm also yields the most accurate results- as compared with a number of path opening variants-when measuring length distributions.

Place, publisher, year, edition, pages
2016. Vol. 25, no 12, 5589-5600 p.
Keyword [en]
graph theory, image filtering, transforms, 1D openings, H-minima transform, filter parameters, graph edges, grayvalue skeleton, image analysis, image filtering, image size, unbiased path opening, upper skeletonization, weighted adjacency graphs, Approximation algorithms, Gray-scale, Image edge detection, Length measurement, Periodic structures, Skeleton, Transforms, Path opening, granulometry, image analysis, length distribution, line segment, mathematical morphology, unbiased
National Category
Other Computer and Information Science
Research subject
Computerized Image Processing
Identifiers
URN: urn:nbn:se:uu:diva-309087DOI: 10.1109/TIP.2016.2609805ISI: 000388205100007OAI: oai:DiVA.org:uu-309087DiVA: diva2:1051614
Funder
Swedish Research Council, 2014-5983
Available from: 2016-12-02 Created: 2016-12-02 Last updated: 2016-12-22Bibliographically approved

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Asplund, Teo
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Division of Visual Information and InteractionComputerized Image Analysis and Human-Computer Interaction
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