Piecewise-linear interpolation between polygonal slices

Gill Barequet*, Micha Sharir

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In this paper we present a new technique for piecewise-linear surface reconstruction from a series of parallel polygonal cross-sections. This is an important problem in medical imaging, surface reconstruction from topographic data, and other applications. We reduce the problem, as in most previous works, to a series of problems of piecewise-linear interpolation between each pair of successive slices. Our algorithm uses a partial curve matching technique for matching parts of the contours, an optimal triangulation of 3-D polygons for resolving the unmatched parts, and a minimum spanning tree heuristic for interpolating between non simply connected regions. Unlike previous attempts at solving this problem, our algorithm seems to handle successfully any kind of data. It allows multiple contours in each slice, with any hierarchy of contour nesting, and avoids the introduction of counter-intuitive bridges between contours, proposed in some earlier papers to handle interpolation between multiply connected regions. Experimental results on various complex examples, involving actual medical imaging data, are presented, and show the good and robust performance of our algorithm.

Original languageEnglish
Title of host publicationProceedings of the Annual Symposium on Computational Geometry
PublisherAssociation for Computing Machinery (ACM)
Number of pages10
ISBN (Print)0897916484, 9780897916486
StatePublished - 1994
EventProceedings of the 10th Annual Symposium on Computational Geometry - Stony Brook, NY, USA
Duration: 6 Jun 19948 Jun 1994

Publication series

NameProceedings of the Annual Symposium on Computational Geometry


ConferenceProceedings of the 10th Annual Symposium on Computational Geometry
CityStony Brook, NY, USA


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