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Incremental recovery of 3-D rigid and nonrigid structure from image sequences: An approach based on smoothness of motion

If an object is a rigid body, it is possible to estimate its three-dimensional structure and motion mathematically from motion information. However, the assumption that objects are rigid bodies includes a disadvantage that it is not stable against noise and that the circumstance of application is restricted. 
 
 
 
When considering application to natural images or modeling of vision, a general-purpose method for estimating three-dimensional structure and motion which allows discrepancy from rigid bodies is desired. Thus, in this paper, an algorithm is presented for estimating three-dimensional structure and motion incrementally from a long image sequence using the condition for “smoothness of motion” instead of the rigid body assumption. That is, as a constraint, a physical property is used whereby an object generally performs a smooth motion due to inertia and elasticity. Formulating this condition, i.e., smoothness of motion as a stabilizing function for regularization, the three-dimensional information is estimated incrementally so that it is suitable to an input image and motion is smooth. By considering smoothness of motion, three-dimensional information of each frame can be stored incrementally, and thus a flexible algorithm that is robust and also applies to the motion of a nonrigid body is obtained. Furthermore, by presenting the results when applying this method to the motion of rigid and nonrigid bodies, the robustness of this method against noise and flexibility is shown which also applies to nonrigid bodies.