Efficient determination of shape from multiple images containing partial information

We consider the problem of reconstructing the shape of an object from multiple images related by translations, when only small portions of the object can be observed in each image. Lindenbaum and Bruckstein (1988) have considered this problem in the specific case where the translating object is seen by small sensors, for application to the understanding of insect vision. Their solution is limited by the fact that its run time is exponential in the number of images and sensors. We show that the problem can be solved in time that is polynomial in the number of sensors, but is in fact NP complete when the number of images is unbounded. We therefore consider the special case of convex objects, which we can solve efficiently even when many images are used.

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