A Novel Parameter Estimation Algorithm for the Multivariate t-Distribution and Its Application to Computer Vision
We present a novel algorithm for approximating the parameters of a multivariate t-distribution. At the expense of a slightly decreased accuracy in the estimates, the proposed algorithm is significantly faster and easier to implement compared to the maximum likelihood estimates computed using the expectation-maximization algorithm. The formulation of the proposed algorithm also provides theoretical guidance for solving problems that are intractable with the maximum likelihood equations. In particular, we show how the proposed algorithm can be modified to give an incremental solution for fast online parameter estimation. Finally, we validate the effectiveness of the proposed algorithm by using the approximated t-distribution as a drop in replacement for the conventional Gaussian distribution in two computer vision applications: object recognition and tracking. In both cases the t-distribution gives better performance with no increase in computation.
KeywordsApproximate Algorithm Multivariate Gaussian Distribution Incremental Algorithm Scale Matrix Parameter Estimation Algorithm
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- 1.Aeschliman, C., Park, J., Kak, A.C.: A Probabilistic Framework for Joint Segmentation and Tracking. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (2010)Google Scholar
- 4.Iscaps, C.: Pets2006 (2006), http://www.cvg.rdg.ac.uk/pets2006/data.html
- 5.Khan, Z., Balch, T., Dellaert, F.: MCMC-based particle filtering for tracking a variable number of interacting targets. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1805–1918 (2005)Google Scholar
- 7.Lange, K.L., Little, R.J.A., Taylor, J.M.G.: Robust statistical modeling using the t distribution. Journal of the American Statistical Association, 881–896 (1989)Google Scholar
- 9.Meng, X.L., van Dyk, D.: The EM algorithm–an old folk-song sung to a fast new tune. Journal of the Royal Statistical Society. Series B (Methodological), 511–567 (1997)Google Scholar
- 14.Simoncelli, E.P.: Statistical modeling of photographic images. In: Handbook of Image and Video Processing, pp. 431–441 (2005)Google Scholar