Cubical cohomology ring of 3D photographs
نویسندگان
چکیده
Cohomology groups and the cohomology ring of threedimensional (3D) objects are topological invariants that characterize holes and their relations. Cohomology ring has been traditionally computed on simplicial complexes. Nevertheless, cubical complexes deal directly with the voxels in 3D images, no additional triangulation is necessary. This could facilitate efficient algorithms for the computation of topological invariants in the image context. In this article, we present a constructive process, made up by several algorithms, to compute the cohomology ring of 3D binary-valued digital photographs represented by cubical complexes. Starting from a cubical complex Q that represents such a 3D picture whose foreground has one connected component, we first compute the homological information on the boundary of the object, @Q, by an incremental technique; using a face reduction algorithm, we then compute it on the whole object; finally, applying explicit formulas for cubical complexes (without making use of any additional triangulation), the cohomology ring is computed from such information. VC 2011 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 21, 76–85, 2011; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/ima.20271
منابع مشابه
Cubical Cohomology Ring of 3D Pictures
Cohomology and cohomology ring of three-dimensional (3D) objects are topological invariants that characterize holes and their relations. Cohomology ring has been traditionally computed on simplicial complexes. Nevertheless, cubical complexes deal directly with the voxels in 3D images, no additional triangulation is necessary, facilitating efficient algorithms for the computation of topological ...
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عنوان ژورنال:
- Int. J. Imaging Systems and Technology
دوره 21 شماره
صفحات -
تاریخ انتشار 2011