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

4. 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 ! Motion Database Preprocess Motion Editing Toolbox Motion Sensor Data Custom Animation The Art of Animation

5. Motion Retargetting [Gleicher 98]

6. 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 Motion Database Preprocess On-line Controller Motion Sensor Data Controllable Characters High-Level User Interfaces

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: The position of the root segment The orientations of body segments w.r.t. their parents (joint angles) The orientation of the root segment

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 Stand Right foot forward Start Stop TurnR TurnL 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) First Motion Second 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 Antz (1998) Godzilla (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 Original Motion How would we warp the motion to meet the constraints ?

34. Motion and Constraints Original Motion Bad warping

35. Displacement Mapping Motion warping [Popovic & Witkin 95] Motion displacement mapping [Bruderlin & Williams 95] Displacement Map Original Motion 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)Teapot demo –Jello demo by Choi (2004)Jello demo

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

51. Inequality Constraints Upper bound Lower bound

52. Inequality Constraints Upper bound Lower bound Hierarchical displacement mapping can be used

53. Inequality Constraints Upper bound Lower bound Much better in terms of motion quality

54. Adapting Motion for Humanoids Different structures and DOFs Joint limit Dynamic limit –Velocity, torque, balance, …

55. Physically Based Motion Transform by Popovic (1999) Normal run: run-norm.movrun-norm.mov Stiff leg: run-stiff.movrun-stiff.mov Low gravity: run-moon.movrun-moon.mov High gravity: run-neptune.movrun-neptune.mov

56. Motorized Marionette by Yamane (2003) Marionette 6 motors for hands and 2 motors for legs Limited kinematic range Limited dynamic capability Avoid undesired swing Cockrobin Alaska

57. Summary Motion data processing –Reusability and flexibility –Efficient and correct –A Toolbox of motion editing tools Motion adaptation/retargeting/editing –Displacement mapping It is just spline interpolation/approximation It can be formulated as a non-linear optimization problem –Hierarchical displacement mapping Adaptive refinement is desired