Contour interpolation by straight skeletons

Authors:
Gill Barequet;Michael T. Goodrich;Aya Levi-Steiner;Dvir Steiner
Affiliations:
Department of Computer Science, The Technion--Israel Institute of Technology, Haifa 32000, Israel;Department of Information and Computer Science, Unirversity of Colifornia, Irvine, CA;Department of Mathematics, The Technion--Israel Institute of Technology, Haifa 32000, Israel;Department of Mechanical Engineering, The Technion--Israel Institute of Technology, Haifa 32000, Israel
Venue:
Graphical Models
Year:
2004

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Abstract

In this paper we present an efficient method for interpolating a piecewise-linear surface between two parallel slices, each consisting of an arbitrary number of (possibly nested) polygons that define 'material' and 'non-material' regions. This problem has applications to medical imaging, geographic information systems, etc. Our method is fully automatic and is guaranteed to produce non-self-intersecting surfaces in all cases regardless of the number of contours in each slice, their complexity and geometry, and the depth of their hierarchy of nesting. The method is based on computing cells in the overlay of the slices that form the symmetric difference between them. Then, the straight skeletons of the selected cells guide the triangulation of each face of the skeletons. Finally, the resulting triangles are lifted up in space to form an interpolating surface. We provide some experimental results on various complex examples to show the good and robust performance of our algorithm.