On the Camera Placement Problem

Authors:
Rudolf Fleischer;Yihui Wang
Affiliations:
Department of Computer Science and Engineering, IIPL, Fudan University, Shanghai, China;Department of Computer Science and Engineering, IIPL, Fudan University, Shanghai, China
Venue:
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Year:
2009

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Abstract

We introduce a new probing problem: what is the minimum number of cameras at fixed positions necessary and sufficient to reconstruct any strictly convex polygon contained in a disk of radius 1 if cameras only see the silhouette of the polygon? The optimal number only depends on the largest angle 驴 of the polygon. If no two camera tangents overlap, $\lceil \frac{3\pi}{\pi-\alpha} \rceil$ cameras are necessary and sufficient. Otherwise, approximately $\lceil \frac{4\pi}{\pi-\alpha} \rceil$ cameras are sufficient. Reconstruction only takes time linear in the number of cameras. We also give results for the 3D case.