Reconstructing polygons from x-rays |
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Authors: | Henk Meijer Steven S Skiena |
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Institution: | (1) Department of Computer and Information Science, Queen's University, K7L 3N6 Kingston, Ontario, Canada;(2) Department of Computer Science, State University of New York, 11794-4400 Stony Brook, NJ, U.S.A. |
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Abstract: | We present strategies for interactively reconstructing polygons from carefully chosen x-ray probes, generalizing previous results for convex polygons to a significantly larger class of objects. In particular, we show that n+h+2 parallel x-ray probes are sufficient to determine an n-gon P with h vertices on its convex hull, provided no three vertices of P are collinear. If given an upper bound n on the number of vertices of P, then 2n +2 parallel probes or 3n origin probes suffice. Further, we show that lg n–2 probes are necessary. Finally, we present verification strategies for arbitrary polygons. Interactive probing strategies have the potential to minimize radiation exposure in medical imaging. |
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Keywords: | 51M20 52C05 51N20 |
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