# NEW CLOSED FORM SOLUTIONS FOR SKELETAL EXTRACTION FROM MOTION CAPTURE

### Sudhanshhu Semwal, Jonathan Kip Knight

#### 2009

#### Abstract

We present a fast closed form solution for estimating the exact joint locations inside the human body from motion capture data. The new closed-form solution is more robust and faster. For example, the formulae are as much as about 100 times faster than the traditional non-linear Maximum Likelihood Estimator and about 9 times faster than linear least squares methods. The methods are proven to be statistically efficient when measurement error is smaller than the joint-marker distance. Unbiased Generalized Delogne-Kása (UGDK), multiple radii solution, and incremental GDK are important contributions of our research providing closed form fast solutions for skeleton extraction from motion capture data. Skeletal animation sequences are generated using the CMU and Eric Camper’s motion capture database.

#### References

- Aguiar, D., Theobalt, C., Seidal,H., Automatic learning of articulated Skeletons from 3D marker Trajectories, in International Symposium, ISVC 2006, part I, SpringerVeralag, Lecture Notes in Computer Science, vol. 4291, pp. 485-494 (2006).
- O'Brien, J. F., Bodenheimer Jr R. E. ., Brostow G. J., and Hodgins J. K.. Automatic Joint Parameter Estimation from Magnetic Motion Capture Data, pages 53-60, Montreal, Quebec, Canada, May 15-17 2000. Graphics Interface.
- Burr, M., Cheng, A., Coleman, R., and Souvaine, D., Transformations and Algorithms for Least Sum of Squares Hypersphere Fitting. 16th Canadian Conference on Computational Geometry, 2004, pp 104-107.
- Corral, C., Lindquist, C., On implementing Kása's circle fit procedure. IEEE Transactions on Instrumentation and Measurement, 47(3):789-795, June 1998.
- Delogne, P.,Computer Optimization of Deschamps Method and Error Cancellation in Reflectometry. In Proceedings of the IMEKO Symposium on Microwave Measurements, Budapest, Hungary, May 1972, pp. 117-129.
- Gander, W., Golub, G., Strebel, R., Least-Squares Fitting of Circles and Ellipses. BIT Numerical Mathematics 34, Springer 1994, pp 558-578.
- Herda, L., Fua, P., Plankers, R., Boulic, R., D. Thalmann, D., Skeleton-based motion capture for robust reconstruction of Human Motion, Computer Animation (book), Philadelphia, PA, pp.77-May (2000).
- Kása, I., A circle fitting procedure and its error analysis. IEEE Transactions on Instrumentation and Measurement, 25:8-14, March 1976.
- Kirk, A. G., O'Brien, J., Forsyth, D.A. Skeletal parameter estimation from optical motion capture data. In IEEE Conf. on Computer Vision and Pattern Recognition (CVPR). IEEE, 2005.
- Knight, J., Semwal, S., Fast Skeleton estimation from motion captured using Genralized Delogne-Kasa method, In 15th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, Plzen, WSCG Conference Proceedings, pp. 225-232, ISBN 978-80-86943-98-5, Feb 2007.
- Knight, J., Rotation Points from Motion Capture Data using a closed form solution, PhD thesis, University of Colorado at Colorado Springs, Advisor Professor Semwal, SK., pp. 1-152 (2008).
- Lukács, G., Marshall, A., Martin, R., Geometric LeastSquares Fitting of Spheres, Cylinders, Cones, and Tori RECCAD Deliverable Documents 2 and 3 Copernicus Project No. 1068 Reports on basic geometry and geometric model creation, etc. Edited by Dr. R. R. Martin and Dr. T. Varady Report GML 1997/5, Computer and Automation Institute, Hungarian Academy of Sciences, Budapest, 1997.
- Pratt, V., Direct least-squares fitting of algebraic surfaces. Computer Graphics, 21(4):145-152, July 1987.
- Press, W., Teukolsky, T., Vetterling, W., Flannery, B., Numerical Recipes in C: The Art of Scientific Computing. 2nd.ed., Cambridge University Press: 1992.
- Robinson, S.Fitting Spheres by the Method of Least Squares, In Communications of the ACM, Volume 4, No. 11; November 1967, p. 491.
- Shakarji, C., Least-Squares Fitting Algorithms of the NIST Algorithm Testing System, J. of Research of the National Institute of Standards and Technology: 103, No. 6 (1998): 633.
- Strandlie, A., Wroldsen, J., Frühwirth, R., and Lillekjendlie, B.,Track Fitting on the Riemann Sphere. International Conference on Computing in High Energy and Nuclear Physics, Padova, Italy; February, 2000.
- Thomas S., Chan, Y., Cramer-Rao Lower Bounds for Estimation of a Circular Arc Center and Its' Radius. CVGIP: Graphics Model and Image Processing, Vol. 57, No. 6, pages 527-532, 1995.
- Witte, L.. Least Squares Fitting of a Great Circle Through Points on a Sphere. Communications of the ACM, Volume 3, No. 11, November 1960, pp. 611-613.
- Zelniker E., Clarkson, I., A Statistical Analysis LeastSquares Circle-Centre Estimation. In IEEE International Symposium on Signal Processing and Information Technology, December 2003, Darmstadt, Germany, pp 114-117.
- Zelniker, E., Clarkson, I., A Generalisation of the Delogne-Kása Method for Fitting Hyperspheres. Thirty-Eighth Asiomar Conference on Signals, Systems and Computers. Pacific Grove, California, November 2004.

#### Paper Citation

#### in Harvard Style

Semwal S. and Knight J. (2009). **NEW CLOSED FORM SOLUTIONS FOR SKELETAL EXTRACTION FROM MOTION CAPTURE** . In *Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2009)* ISBN 978-989-8111-67-8, pages 249-256. DOI: 10.5220/0001799702490256

#### in Bibtex Style

@conference{grapp09,

author={Sudhanshhu Semwal and Jonathan Kip Knight},

title={NEW CLOSED FORM SOLUTIONS FOR SKELETAL EXTRACTION FROM MOTION CAPTURE},

booktitle={Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2009)},

year={2009},

pages={249-256},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001799702490256},

isbn={978-989-8111-67-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2009)

TI - NEW CLOSED FORM SOLUTIONS FOR SKELETAL EXTRACTION FROM MOTION CAPTURE

SN - 978-989-8111-67-8

AU - Semwal S.

AU - Knight J.

PY - 2009

SP - 249

EP - 256

DO - 10.5220/0001799702490256