Shape Reconstruction from Unorganized Cross-sections

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dc.contributor.authorBoissonnat, Jean-Danielen_US
dc.contributor.authorMemari, Pooranen_US
dc.contributor.editorAlexander Belyaev and Michael Garlanden_US
dc.date.accessioned2014-01-29T09:43:08Z
dc.date.available2014-01-29T09:43:08Z
dc.date.issued2007en_US
dc.description.abstractIn this paper, we consider the problem of reconstructing a shape from unorganized cross-sections. The main motivation for this problem comes from medical imaging applications where cross-sections of human organs are obtained by means of a free hand ultrasound apparatus. The position and orientation of the cutting planes may be freely chosen which makes the problem substantially more difficult than in the case of parallel cross-sections, for which a rich literature exists. The input data consist of the cutting planes and (an approximation of) their intersection with the object. Our approach consists of two main steps. First, we compute the arrangement of the cutting planes. Then, in each cell of the arrangement, we reconstruct an approximation of the object from its intersection with the boundary of the cell. Lastly, we glue the various pieces together. The method makes use of the Delaunay triangulation and generalizes the reconstruction method of Boissonnat and Geiger [BG93] for the case of parallel planes. The analysis provides a neat characterization of the topological properties of the result and, in particular, shows an interesting application of Moebius diagrams to compute the locus of the branching points. We have implemented our algorithm in C++, using the [CGAL] library. Experimental results show that the algorithm performs well and can handle complicated branching configurations.en_US
dc.description.seriesinformationGeometry Processingen_US
dc.identifier.isbn978-3-905673-46-3en_US
dc.identifier.issn1727-8384en_US
dc.identifier.urihttps://doi.org/10.2312/SGP/SGP07/089-098en_US
dc.publisherThe Eurographics Associationen_US
dc.subjectCategories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling.en_US
dc.titleShape Reconstruction from Unorganized Cross-sectionsen_US
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SGP07: Eurographics Symposium on Geometry Processing