A homotopy for solving general polynomial systems that respects m-homogenous structures
Applied Mathematics and Computation
Coefficient-parameter polynomial continuation
Applied Mathematics and Computation
Finding all isolated solutions to polynomial systems using HOMPACK
ACM Transactions on Mathematical Software (TOMS)
Motion Estimation with More than Two Frames
IEEE Transactions on Pattern Analysis and Machine Intelligence
Motion from point matches: multiple of solutions
International Journal of Computer Vision
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Much of the literature in dynamic computer vision deals with the determination of 3-D motion and structure ofrigid objects from their perspective 2-D projection onto a camera plane taken at several instants of time. Many of the applications, on the other hand, have to do with motion ofnonrigid bodies. Modeling of nonrigid behavior of an object can be done in a number of ways. In this paper, we consider the case of uniform expansion (or contraction) of a body around an unknown point. Volumes of objects are assumed to be increasing or decreasing at either a constant exponential or a linear rate. In addition the body undergoes rotation and translation. We show that 3-D motion cannot be recovered using only three snapshots from a single camera, no matter how many point correspondences are permitted. In four snapshots, however, using only three point correspondences, a unique solution to motion, position, and rate and center of expansion can be obtained. With these four views of three points there is zero probability that such a uniformly expanded body can be mistaken for a rigid object, so a simple nonrigid interpretation of motion such as uniform expansion is reasonable. Several relevant examples are worked out in detail. .