TY - GEN

T1 - Piecewise-linear interpolation between polygonal slices

AU - Barequet, Gill

AU - Sharir, Micha

N1 - Funding Information:
* Work on this paper by the second author has been supported by National Science Foundation Grant CCR-91-22103, and by grants from the U.S.–Israeli Binational Science Foundation, the Fund for Basic Research administered by the Israeli Academy of Sciences, and the G.I.F., the German-Israeli Foundation for Scientific Research and Development.

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0028092564&partnerID=8YFLogxK

U2 - 10.1145/177424.177562

DO - 10.1145/177424.177562

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AN - SCOPUS:0028092564

SN - 0897916484

SN - 9780897916486

T3 - Proceedings of the Annual Symposium on Computational Geometry

SP - 93

EP - 102

BT - Proceedings of the Annual Symposium on Computational Geometry

PB - Association for Computing Machinery (ACM)

T2 - Proceedings of the 10th Annual Symposium on Computational Geometry

Y2 - 6 June 1994 through 8 June 1994

ER -