Recovering motion from range image sequences

In this paper, a new formulation and method is presented to directly recover 3D short term motion from range image sequences. In the case of a rigid-body motion, the formulation relates through a set of linear equations the six motion parameters to the first spatial-temporal derivatives and coordinates of a point. A weighted least square method is used to find the solution of this equation set. In case of locally rigid motion, the six rigid motion parameters of each point are estimated from the first and second spatial-temporal derivatives. For each point, a set of 10 linear equations with six unknowns is again solved by the least square method. The special case of local translation with small rotation gives a very elegant closed-form solution and an explicit geometric explanation. We also shown that the formulation can be easily generalized to any arbitrary motion. The proposed formulation has theoretical elegance since it only involves solving a set of linear equations. Results on both synthetic and real data are given.