Captured motion is considered as a set of time-dependent parameter curves that are altered. The original curve is scaled, time-stretched or added with another displacement curve. In every case the motion details (e.g. high frequencies), which are responsible for "aliveness" of captured motion are preserved in the original motion curve. Displacement and scaling curves and time-stretching is defined friendly by altered a few keyframes in the original motion and interpolated by a spline. Fairly wide variety of useful motion modifications can be achieved so, however a possible violation of constraints implicit in motion is not considered.

Several techniques of signal processing are applied to motion as a signal. Multiresolution filtering – decomposing the signal to several frequency bands filtered separately. Adjusting low, middle or high frequencies different effects are obtained. Interpolation – blending of several motions with different weight to one result. The most interesting there is an automatic time-alignment and non-linear stretching of motions similar to image registration called "dynamic timewarping". Finally a waveshaping technique and motion displacement are presented.

Path of an existing (captured) motion is altered. The path is extracted from the original motion of the root automatically, smoothed by filtering and interactively edited to satisfy user demands. Character pose in each frame is expressed relative to the path then, in local coordinate frame moving along the original path. The motion details are decoupled from then the motion path so. The motion along the new path is generated then by transforming details by moving coordinate frame of the new path. Finally, violated constraints are re-established by modifying the motion, not the path.
This technique is useful for adjusting basic motions stored in a motion library.

Fundamental paper about motion retargeting. The proposed method retargets a motion as a whole in spacetime, not in individual frames independently. The motion is rescaled to a new character first, necessary constraints (defined by an animator, e.g. on end-effectors interacting with environment) are re-established then by numerical optimization minimizing the changes of the original motion. The size of target character can even vary within the motion, but the structure must be always identical to original character.
The global nature of the approach results in hundreds or thousands of constraints for numerical solver even for simple figures and motions a few seconds long. Retargeting requires still several seconds in that case, but it can be a real drawback for more complex figures or longer motions. A pose of the target in a particular frame actually doesn't depend on the whole motion; rather on a certain interval of time before and after the frame, maybe with decreasing weight with the distance in a time sense. The method of sliding window could be used.

A complete approach to realtime (or online) computer puppetry. Computer puppetry is realtime retargeting of captured motion to a virtual character. Since proportions of the virtual character may be different from the real actor's, the joint angles and end-effector positions cannot be preserved both. An importance based approach determines how much the joint angles should be preserved and how much the end effector positions. Importance of an end effector is based on its distance to the nearest object (useful for grasping). A simple analytic solution of inverse kinematics is developed for the realtime purpose, working on human-like characters.

A tutorial about Kalman filter. Kalman filter is used to online filter noisy data of a dynamical process in time. It is based on predictor-corrector principle – new state of the process is predicted from the actual state and corrected by a measurement of the new (noisy) state. Varying filter constants affects influence of the prediction and influence of the measured noisy data to the resultant new state. Very clearly written, with illustrative examples, still not absolutely clear to me.

Retargeting of motion to a different character. A correspondence between performer and (possibly topologically different) target skeleton is specified manually. An intermediate skeleton with target topology but performer pose is constructed. Copying only the local values (differences to a rest pose) of joint rotation matrices in the intermediate skeleton to local values of the target character allows the target to have a different rest pose. That (and the topological difference) is the purpose of the intermediate skeleton. The retargeted motion can be adjusted then by IK due to manually given constraints and their duration (eased-in and eased-out).

Automatic identification of spacetime constraints in a motion interacting with its environment. A constraint for an end-effector is set in each frame where acceleration of the end-effector is crossing zero and the end-effector is close to an object or a body part. The constraints are re-established by inverse kinematics and interpolation when the motion is applied to a different sized actor. Hence a correct interaction with environment is achieved for the motion mapped to an actors with any proportions.

Using time × frequency representation of a signal (similar to wavelets) it is possible to warp the signal (i.e. to expand its duration) while its frequency characteristics are preserved. Cyclification of a signal is the just the signal warped to a desired duration. Autocorrelation is used to find a period (the lowest frequency) of the signal.