Visual Tracking via Particle Filtering on the Affine Group



We deal with the problem of estimating the affine motion change of the object image region. The affine transformation matrix can be considered as one of matrix Lie groups, the affine group. Unlike the conventional affine motion tracker relying on the local parameterization of the affine matrix, we develop a geometric affine motion tracker based on particle filtering on Lie groups. The state space is the affine group itself, and the state equation is derived from the SDE on the affine group.


The formulation of geometric particle filtering on general matrix Lie groups including SO(3) and SE(3) can be found in our 2007 Robotica paper. The superiority of our geometric affine motion tracker to the conventional tracker is demonstrated conceptually and experimentally in our 2010 IJRR paper. In our recent CVPR 2009 paper, we have shown that how the optimal importance functions can be employed within our visual tracking framework via particle filtering on the affine group.


Note that the MATLAB code and video data for our CVPR 2009 paper can be downloaded here. There are two main m-files in the below zip file. The first (Tracking_compare.m) is for comparison with the Rosss tracker using the state transition density as the importance function (Experiment 1) and the second (Optimal_affine_tracking_PCA.m) is for demonstrating the idea of using the optimal importance function (Experiment 2).


Related Publications      



J. Kwon, K.M. Lee, and F.C. Park, Visual tracking via geometric particle filtering on the affine group with optimal importance functions, in Proc. IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2009), Miami, USA, 2009. (Oral presentation) [pdf] [video] [slides] [code] [data]


J. Kwon and F.C. Park, Visual tracking via particle filtering on the affine group, The International Journal of Robotics Research, vol. 29, no. 2-3, pp. 198-217, 2010. (Special issue on robot vision) [pdf]


J. Kwon, M. Choi, C. Chun, and F.C. Park, Particle filtering on the Euclidean group: framework and applications, Robotica, vol. 25, no. 6, pp. 725-737, 2007. (Special issue on geometry in robotics) [pdf]


Last updated on Mar. 1, 2010