The recovery of non-rigid motion from stereo images

The problem of recovering the three-dimensional motion of a non-rigid object from a sequence of stereo images is discussed. The object undergoes uniform expansion and three-dimensional shearing about an unknown point in space, in addition to being subjected to rigid motion. Feature correspondence over multiple frames is assumed. The problem of recovering the three-dimensional motion uniquely is reduced to the (unique) solution of a set of homogeneous polynomial equations using algebraic geometry, the commutative algebra software package, MACAULAY, and the Fortran polynomial continuation program POLSYS. It is shown that, with four points correspondence, only two (stereo) snapshots are needed to determine the motion uniquely