This paper discusses the use of registration curves (a "automaticall constructed data structure that encapsulates relationships involving the timing, local coordinate frame, and constraint stats of an arbitrary number of input motion") to "expand the range of motions that can be successfully blended without requiring manual intervention").

The paper consists of 2 major contributions, the discussion of how to construct registration curves, and a blending algorithm that uses registration curves to achieve better results.

Overview of registration curves.

 *  motions are assumed to be constrained in some manner - for example footplants
 *  "our strategy is thus to still combine frames via averaging , but to automatically extact information from the input motions to help decide which frames to combine, how to position and orient them prior to averaging, and what constraints should exist on the result."  This information is used to create a registration curve consisting of a "timewarp curve, a coordinate alignment curve, and a set of constraint matches".
  * timing - create a timewarp curve "such that the corresponding frames are all logically related"
  *  Coordinate frame alignment - align the local coordinate frame of the motions - this allows motions with different paths to be blended 
  *  constraint matches 

Creating registration curves

 *  construction of timewarp curves - use dynamic timewarping - based on dynamic programming techniques - "find a minimal-cost connecting path" with the following properties - continuity, causality (don't reverse directions), slope limit(only a certain number of consecutive vertical steps may be taken)
 *  creating timewarp curves for more than 2 motions is similar but scales exponentially, but instead multiple timewarp curves that each relate pairs of motions can be combined.
 *  construction of the alignment curve - fit a 3d quadratic curve to the 2d rigid transformation that "aligns the second frame with the first"
 *  identification of constraint matches - map duration of constraints via timewarp curve - each constraint match "must contain exactly one constraint from each motion" and each constraint match "must be connected in the sense that the union of all the constraint intervals must form a single continuous interval" - matches are found by processing constraints sequentially, checking in each iteration "whether unprocessed constraints of each motion are connected" - if not the constraint match is discared and processed to the next iteration.

Using registration curves in blending

 -  each frame involves - determining position on timewarp curve - position and orient frames - combine frames based on blending weights and determine constraints on resulting frame


 questions I had regarding this paper

 I think that I understand this paper thoroughly now.