Detecting 3D flow

An algorithm for computing 3D motion (velocity field and motion parameters) from a sequence of range images is presented. The algorithm is based on a new integral 3D rigid motion invariant feature which can be computed locally at every point of the moving surface. This feature is the trace of a 3×3 matrix (referred to as “feature matrix” in the paper) which is closely related to the moment of inertia tenser in physics. This trace of the “feature matrix” at any point provides a quantitative measure of the local shape of the surface around that point. Since the trace feature is rigid motion invariant, it remains conserved along the trajectory of every moving point. Based on that, a 3D flow constraint equation is formulated at every point on the surface, which can be solved for the velocity at the point using optical flow techniques. Since the proposed feature is integral in nature, it is robust in terms of noise and discontinuity in the moving surface. Theoretical analysis is provided to justify these claims. Experimental results are also provided to justify the efficacy of the method