Variational Smooth Motion Design using Machine Vision Registration

We discuss the following important problem which arises in computer vision and computer animation: Given are N positions or keyframes ( ) ∑ i t of a moving body ∑⊂ 3 R at time instances i t . Compute a smooth motion ( ) ∑ t which interpolates or approximates the given positions ( ) ∑ i t , such that chosen feature points of the moving system run on smooth paths. We present an algorithm that can be considered as a transfer principle from curve design algorithms to motion design. The algorithm relies on known curve design algorithms, and on registration techniques from Computer Vision. We prove that the motion generated in this way is of the same smoothness as the curve design algorithm employed. The potential applications include keyframe interpolation in Computer Graphics, motion planning in Robotics and smooth camera motion in Vision systems.