Linear combination representation for outlier detection in motion tracking

In this paper we show that Ullman and Basri´s linear combination (LC) representation, which was originally proposed for alignment-based object recognition, can be used for outlier detection in motion tracking with an affine camera. For this task LC can be realized either on image frames or feature trajectories, and therefore two methods are developed which we call linear combination of frames and linear combination of trajectories. For robust estimation of the linear combination coefficients, the support vector regression (SVR) algorithm is used and compared with the RANSAC method. SVR based on quadratic programming optimization can efficiently deal with more than 50 percent outliers and delivers more consistent results than RANSAC in our experiments. The linear combination representation can use SVR in a straightforward manner while previous factorization-based or subspace separation methods cannot. Experimental results are presented using real video sequences to demonstrate the effectiveness of our LC+SVR approaches, including a quantitative comparison of SVR and RANSAC.