Robust affine regression.

For non-commercial uses, please email me and I will send you the code free of charge.

For commercial uses, please contact me regarding licensing.

Password protected tar file (0.75MB)


This tar file contains experimental C-code, and examples, for computing multiple affine motions using robust estimation.

The motion within an image region is modeled using an affine transformation. Affine motion parameters are estimated using a coarse-to-fine gradient-based method. The approach is implemented using a robust M-estimation technique to make the computation insensitive to outliers which result from multiple motions. The approach estimates a dominant motion in the scene and detects points which are not moving consistently with the dominant motion. Additional motions are optionally estimated using these outliers.

This is a very basic starter package. The basic code has been extended in many ways for other problems but this basic package will give you an idea about how robust regression is applied to motion estimation.

The main paper describing this is:

Black, M. J. and Anandan, P., The robust estimation of multiple motions: Parametric and piecewise-smooth flow fields, Computer Vision and Image Understanding, CVIU, 63(1), pp. 75-104, Jan. 1996. (abstract)

All the papers below also use some variant of this basic technique:

Jepson A. and Black, M., Mixture models for optical flow computation, in Partitioning Data Sets, DIMACS Workshop, April 1993 Eds. Ingemar Cox, Pierre Hansen, and Bela Julesz, AMS Pub., Providence, RI., pp. 271-286; also, Tech. Report, Res. in Biol. and Comp. Vision, Dept. of Comp. Sci., Univ. of Toronto, RBCV-TR-93-44, 1993.

Ju, S. X., Black, M. J., and Yacoob, Y., Cardboard people: A parameterized model of articulated motion, 2nd Int. Conf. on Automatic Face- and Gesture-Recognition, Killington, Vermont, Oct 1996, pp.38-44.

Ju, S., Black, M. J., and Jepson, A. D., Skin and Bones: Multi-layer, locally affine, optical flow and regularization with transparency, IEEE Conf. on Computer Vision and Pattern Recognition, CVPR'96, San Francisco, CA, June 1996, pp. 307-314.

Black, M. J. and Jepson, A., EigenTracking: Robust matching and tracking of articulated objects using a view-based representation, to appear, International Journal of Computer Vision, also Xerox PARC, Technical Report P95-000515, Feb. 1996.

Black, M. J. and Rosenholtz, R. Robust estimation of multiple surface shapes from occluded textures, International Symposium on Computer Vision, Miami, FL, Nov. 1995, pp. 485-490.

Black, M. J. and Yacoob, Y. Tracking and recognizing rigid and non-rigid facial motions using local parametric models of image motion, Fifth International Conf. on Computer Vision, ICCV'95, Boston, MA, June 1995, pp 374-381.

Black, M. J. and Jepson, A., Estimating multiple independent motions in segmented images using parametric models with local deformations, Workshop on Non-rigid and Articulate Motion, Austin, Texas, Nov. 1994, pp. 220-227.