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Multivariate Relevance Vector Machines For Tracking

Multivariate Relevance Vector Machines For Tracking. UNIVERSITY OF CAMBRIDGE. Graz, Austria. A. Thayananthan, R. Navaratnam, B. Stenger, P. H. S. Torr and R. Cipolla. Learning a Sparse One-to-Many Mapping. Contributions. An extension of the RVM algorithm to multivariate outputs (MVRVM)

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Multivariate Relevance Vector Machines For Tracking

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  1. Multivariate Relevance Vector Machines For Tracking UNIVERSITY OF CAMBRIDGE Graz, Austria A. Thayananthan, R. Navaratnam, B. Stenger, P. H. S. Torr and R. Cipolla Learning a Sparse One-to-Many Mapping Contributions • An extension of the RVM algorithm to multivariate outputs (MVRVM) • An EM type algorithm for learning a sparse one-to-many mapping • Application to the pose estimation problem • Mapping from image features to state space is one-to-many. • Mutually exclusive regions in state space can correspond to overlapping regions in feature space. • Learn several mapping functions from feature space to different state space regions. MVRVM • Original RVM algorithm is limited to 1D outputs • MVRVM: principled extension of RVM to multivariate output (code available!) • Assumption: independent Gaussian noise, independent weights EM for learning K MVRVMs Input: Output: E-step: Estimate parameters using MVRVM training M-step: Estimate assignment probabilities of samples to each MVRVM Model : Prior : grouping weights along output dimensions Likelihood : Data 1st Iteration grouping weights along output dimensions error for each sample Posterior : 10th Iteration 4th Iteration Marginal Likelihood :

  2. Multivariate Relevance Vector Machines For Tracking (2) UNIVERSITY OF CAMBRIDGE Graz, Austria Application to Pose Estimation Results • MVRVM functions predict poses • Predicted poses are used to project 3D model • Likelihoods are calculated for predicted poses State space: 4D Training samples: 5 000 MVRVMs: 10 Relevant Vectors:389 Robust Representation of Image Features Basis functions Hausdorff vs Shape Context State space: 8D Training samples: 10 000 MVRVMs: 10 Relevant Vectors: 455 • Basis function vector is obtained by matching templates with edges. • Error for different features: Hausdorff fractions and shape context histograms State space: 8D Training samples:13 000 MVRVMs: 4 Relevant Vectors: 118 Tracking Framework • Posterior: piecewise Gaussian with L components • Predict each of the L components • Perform RVM regression to obtain K hypotheses • Evaluate likelihood computation for each hypothesis • Compute the posterior distribution for each of LxK components • Select L components to propagate to next time step by selecting from different modes State space: 9D Training samples: 50 000 MVRVMs: 50 Relevant Vectors: 984

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