Motion Editing ( Geometric and Constraint-Based Methods )

1. Motion Editing(Geometric and Constraint-Based Methods) Jehee Lee

2. Animation from Motion Capture • Motion capture provides a large collection of realistic motion data • What can we do with this data set ? • Applications • Animation authoring: Film, music video, TV ad., … • Interactive characters: Video games, VR, … • Live performance: Computer puppetry

3. The Art of Animation Motion Editing Toolbox Custom Animation Motion Database Preprocess Controllable Characters On-line Controller Motion Sensor Data High-Level User Interfaces Mapping Live Performance Computer Puppetry

4. The Art of Animation Motion Database Motion Sensor Data Motion Editing Toolbox Preprocess Custom Animation Animation Authoring • Animators select motion segments from the database • Motion segments will be modified, blended, and stitched • Animators need a variety of motion editing tools !

5. Motion Retargetting [Gleicher 98]

6. Motion Database Motion Sensor Data Controllable Characters Preprocess On-line Controller High-Level User Interfaces Interactive Characters • Users interact (or control) with computer-generated characters through high-level user interfaces • System selects appropriate motions from the database • User interfaces and control algorithms are required

7. Sketch Interface

8. Computer Puppetry • Motion sensor data is mapped to an animated character in realtime • No database is required

9. Motion Representation • Configuration of an articulated figure • Linear components: • Angular components: Theposition of the root segment Theorientation of the root segment Theorientations of body segmentsw.r.t. their parents (joint angles)

10. Simple Operations • Translation • Rotation

11. Simple Operations • Exercise joints • Motion displacements • independent translation and rotation

12. Motion Displacement • Rigid Transformation at the root segment

13. Motion Displacement • Rigid Transformation at the root segment

14. Simple Operations • Valid operations • Invalid operations

15. Simple Operations • Time warping • Properties

16. Transition Graph TurnL TurnR Right foot forward Start Stand Stop Loop

17. Transition Graph

18. Connecting Motion Segments • Alignment and warping First Motion Second Motion Rotate and translate the second motion to align two motions Warp the motions at the boundary so that they can be connected smoothly

19. Alignment • The end of one motion A should be aligned to the beginning of the next motion B • The root location of the end of A: • The root location of the beginning of B: • Apply to motion B, that is

20. Alignment Using In-Plane Transformation • Rigid transformation restricted within a plane • Rotation about the vertical axis, followed by • Translation along two horizontal axes • How can we find in-plane rotation from arbitrary rotation ? • Euler angles • Discard rotation about x- and z-axes

21. Optimal In-Plane Transformation • Closest point from a geodesic curve to a point • The geodesic curve represents a set of orientation that can be reached by rotating about the vertical axis

22. Optimal In-Plane Transformation

23. Point Cloud Matching

24. Warping • Deform a motion smoothly so that it is seamlessly connected its previous motion • A scalar transition function s(t) Second Motion First Motion d

25. Motion Database • Reusability and flexibility • Motion capture is not cheap ! • Motion capture data doesn’t always reflect our intention • There is no live performer who can move like an ant or Godzilla Godzilla (1998) Antz (1998)

26. Motion Database • Reusability and flexibility • Motion capture is not cheap ! • Motion capture data doesn’t always reflect our intention • We are not always able to construct an appropriate physical environment in a mocap studio

27. Motion Database • Reusability and flexibility • Motion capture is not cheap ! • Motion capture data doesn’t always reflect our intention • There is no live performer who can move like an ant or Godzilla • We are not always able to construct an appropriate physical environment in a mocap studio • We sometimes want to reuse existing data rather than capturing new motion whenever needed • Video games, interactive characters

28. Adaptation/Retargetting/Editing • Reusing motion is challenging, because the motion was acquired • For a specific character • Within a specific environment • In a specific style and mood

29. Constraint-Based Approaches • Constraints specify • Features to be retained • New features to be accomplished • Find a new motion • Satisfy given constraints • While preserving the characteristics of the original motion as much as possible • The core of constraint-based approaches can be formulated as an optimization problem

30. Constraints • Preserve important features of the original motion • Contact with environments (foothold positions) • Balance (dynamic constraints) • Subtle details (frequency bands) • Accomplish new features for the target motion • Interactive manipulation • New characters/environment • New style/mood (How do you define?)

31. Constraint-Based Approaches

32. Inter- and Intra-Frame Coherency Within each frame • Enforce constraints • By inverse kinematics Inter-frame coherence • Avoid discontinuity • By using smooth splines

33. Motion and Constraints How would we warp the motion to meet the constraints ? Original Motion

34. Motion and Constraints Original Motion Bad warping

35. Displacement Mapping • Motion warping[Popovic & Witkin 95] • Motion displacement mapping[Bruderlin & Williams 95] OriginalMotion Displacement Map Target Motion

36. Displacement Mapping Original Motion Displacement map

37. Non-Uniform Spline Interpolation • How would you create a smooth curve (displacement map) that interpolates given joint displacements ? • Spline interpolation • You already know how to do it ! • Constraints are distributed non-uniformly • Variational constraints (constraints that stand over a time period) are discretized as a sequence of constraints • Small details are added for constrained intervals • Details (high frequency) of the original motion could be destroyed • IK solution is not always coherent • Small change of start poses and constraints doesn’t necessarily yeild small change of output poses

38. Least-Squares Curve Fitting • We would like to discard outliers • Approximation rather than interpolation • We don’t want to add unnecessary high-frequency • Uniform splines • IK solving and curve fitting should be applied alternatively for several times • The linear system could be partially over-specified and partially under-specified

39. Non-Linear Optimization • Formulation [Gleicher 98] • Curve approximation and IK can be combined into a single large non-linear optimization problem • Objective function: minimize distortion • Parameters • All joint angles at all time instances (It is a huge problem !) • Joint angles are often represented by B-splines • in order to reduce the number of parameters • in order to maintain inter-frame coherency

40. Adaptive Refinement • Shape freedom vs. Smoothness • Hard to determine the density of knots • Multi-level (hierarchical) B-splines • Adaptive refinement of knot sequences • Sum of uniform B-splines with different knot spacings • Coarse-to-fine hierarchy

41. Hierarchical Displacement Mapping

42. Algorithm

43. Examples • Adaptation to New Environments

44. Examples • Adaptation to New Characters

45. Examples • Character Morphing

46. Adapting Motion for Humanoids • Different structures and DOFs [Pollard 2002]

48. Adapting Motion for Humanoids • Different structures and DOFs • Adaptation algorithm is similar to IK with multiple goals • Gimble lock avoidance • Teapot demo by Pollard (2002) • Jello demo by Choi (2004)

49. Adapting Motion for Humanoids • Different structures and DOFs • Adaptation algorithm is similar to IK with multiple goals • Gimble lock avoidance • Joint limit • Inequality constraints • Similar to collision avoidance

50. Inequality Constraints Upper bound Lower bound