Estimation of 3-D motion and structure based on a temporally-oriented approach with the method of regression

It is argued that the 3-D velocity of a single point up to a scalar factor can be recovered from its 2-D trajectory under the perspective projection. The authors then extend this idea to the recovery of 3-D motion of rigid objects. In both cases measurements are collected through temporal axis first. The analysis is based on the assumption that the 3-D motion of object is smooth so that its 3-D velocity can be approximated as a truncated Taylor series of the predetermined degree. Regression relations between unknown motion parameters and measurements for a single point and rigid body are derived. The method of maximum likelihood is used to estimate the motion. The uniqueness of determining the 3-D motion of the single point is discussed. Experimental results obtained from simulated data and real images are given to illustrate the robustness of this approach