1. Automatic Joint Parameter Estimation from Magnetic Motion Capture Data James F. O’Brien, Robert E. Bodenheimer, Gabriel J. Brostow, Jessica K. Hodgins Presented by Jeff Stricker

2. Why is Motion Capture Good? Human and human-like characters Retains subtle elements of a performer’s style Powerful solution when animations must be generated quickly –Immersive virtual environments “because you squished a jellyfish and took out the magic juice”

3. Why is Motion Capture Bad? Optical and magnetic systems suffer from sensor noise Sensors require careful calibration Precise measurements of limb lengths –Taken by hand in a reference pose –Tedious –Prone to error –Often impractical “this has been my life’s passion for the past day”

4. Purpose of Algorithm Address the problems associated with calibration by automatically computing joint locations Perks –No external measurement –No constraints on sensor placement –No posing in particular configurations Requirement –Data must exercise all DOF of joints for an unambiguous answer “minification is used to create a minified version”

5. Method Comparison Some methods –Joint location determined from weighted average of points –Concerned with detailed model from data points Use multiple markers for redundancy –Instantaneous joint center from single instant of motion This method –Does not require manual processing of data –More concerned with creating animation –Not an IK technique since dimensions of skeleton aren’t known Could be considered a preliminary step to IK computation –Joints are reasonable approximation over entire sequence of motion “unfortunately the world isn’t all rendered bunnies”

6. Method Definitions System of m rigid bodies T i  j is the transformation from ith body’s coordinate system to the coordinate system of the jth body (i, j  [0…m-1]) Index  [0…m-1] used to indicate world coordinate such that T i  is the global transformation from the ith body’s coordinate system to the world coordinate system “put that on a stack, and it’ll get popped off on tuesday”

7. Method and Linear Algebra Transformation T consists of t and R where t is a translational component and R is the rotational component From i coordinate system to j –x j = R i  j (x i )+ t i  j Compute T j  i given T i  j –R j  i = (R j  i ) -1 –t i  j = (R j  i ) -1 (-t j  i ) T k i  j refers to value of T i  j at frame k “i am bezier!”

8. Method Definitions P(x) gives parent of x –  with P(  ) =  is root object Inboard means towards root Outboard means away from root All bodies have at most one inboard joint but may have multiple outboard joints c i refers to location of joint i in body i’s coordinate system l i refers to location of joint i in body P(i)’s coordinate system “combing a hairy ball is like this problem”

9. Method Re-express x P(i) = R k i  P(i) (x i - c i ) + l i = R k i  P(i) x i - R k i  P(i) c i + l i Simplify, convert to global transformations (using T i  ) and simplify again to get R k i  c i + t k i   R k P(i)  l i + t k P(i)  Makes sense—location of joint in outboard coordinate system and location of the joint in the inboard coordinate system should transform to the same place in the world coordinate system “even if we can’t do artistic things, we can write algorithms to replace them”

10. Method Rewrite with matrices and do some magic Uh? –We found a linear system of equations that can be used to solve the joint location parameters c i and l i “disney is one of the world’s most capitalist countries”

11. Method Problems –Q has more rows than columns (system is over- constrained) –Input motions do not span the space of rotations (system is under-constrained) Solution –Solve for a lease squares solution Small problems with single-axis joints –Solution (joint center) is arbitrary point on axis –Avoid this by exercising full range of motion and all DOF of joints “i guess someone decided whales would be more appropriate drafting tools than ducks”

12. Determining the Body Hierarchy Finding optimal hierarchy = finding a minimum spanning tree –Body = node –Joint = edge –Fit error (  i ) = edge weight Select root node  Minimize  i for all joints in the hierarchy Residual errors cause joints to move apart during playback –Use inferred join locations and create an articulated model with kinematic joint constraints “i just want to see jesus, i don’t need to see 3d jesus”

13. Results Simulated human figure –Correct hierarchy, errors less than 10 -6 m Wooden mechanical figure with five ball-and- socket joints –6 trials (last one markers were moved) –Maximum error was 1.1cm –Correct hierarchy in every case People –“Exercise” set –“Walk” set “i want to be a cowboy, i want to be a render wrangler”

14. Results Male –Max error 4.1 cm –Average less than 1 cm (upper arms 1.4cm and 2.2cm for left and right arms) Female –Max error 2.4 cm –Average greater than 1 cm Problems –Upper leg child of other upper leg instead of pelvis Speed on SGI O2 with 195MHz R10k –< 4 seconds for 45 seconds of motion capture when hierarchy specified –< 14 seconds when hierarchy was not specified “you've got to find a way to bang on it until it's square again”

15. Conclusions Results are good, given resolution of sensors Provides a fast way to accomplish calibration for magnetic motion capture systems Applications where explicit calibration is infeasible –“Exercise” could be a pre-show portion of location-based entertainment experience “did anyone catch dawson’s creek last night?”

16. Questions? “just bring it”