Reconstructing a convex polygon from binary perspective projections

摘要

The data obtained from a binary perspective projection of a convex planar set is equivalent to the data obtained by tactile measurements using a certain kind of geometric probe composed of two line probes rotating about a common axis point. The reconstruction of a convex polygon (with V vertices) using this type of data is considered and a measurement strategy which guarantees a unique reconstruction following no more than 3V − 3 measurements is proposed. It is also shown that no strategy can achieve complete reconstruction using less than 3V − 3 measurements. Duality implies that the same reconstruction performance is achieved when probing with a composite finger probe.