Sparse Bayesian Learning for Efficient Visual Tracking
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Sparse Bayesian Learning for Efficient Visual Tracking
O. Williams, A. Blake & R. Cipolloa
PAMI, Aug. 2005.
Presented by Yuting Qi
Machine Learning Reading Group
Duke University
06/24/2005
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Overview
• Motivations - an extension of SVT
• Bayesian tracking with RVM
• Overall system
• Experimental results
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Motivations• Support vector tracking (SVT) [1]
– Training a SVM classifier through the labeled image database;
– For a given test image, the tracked object region is located by maximizing the SVM score.
– Using first-order Taylor expansion, Ifinal is the linear transformation of image gradient, Ix & Iy.
[1] Shai Avidan, “Support vector tracking”, IEEE Tran. On PAMI, Aug, 2004
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[u,v]: motion vector
Ifinal: correct object region;
I: all possible regions;
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Motivations
• Limitations of SVT– Is the optimization efficient using different kernels?– Is the optimization function suitable?– Smoothing image gradient may decrease performance;
• Properties of RVM Tracker– Fully probabilistic regression for displacement;– Observations of displacement are fused temporally with
motion prediction;– Online tracking;
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Bayesian Tracking with RVM• Building a displacement expert-RVM
– Train an RVM to learn the relationship between images and motion. For a test image region x, RVM returns the displacement :
– Mapping from image space to state space.– 4 dimensional state space:
• Translation in x, y, rotation, scaling• Each dimension building one RVM
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• Creating training dataset– Given a seed image I containing the labeled ROI λ;– Generating training examples {z} from I:
• Sampling random displacements from a uniform distribution:
• Corresponding state:
• Generating example zi from state u
– Real training examples:
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• Learning the expert– Given N training examples: {zi, ti}, i=1,…,N. – The relationship between subimages zi and displacem
ent ti is
– Considering additive processing noise:
– Learning
– Posterior is also Gaussian:
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• Tracking with the expert– Given the test image I, initial state u0
– Get ROI x by sampling I around u0.
– The expert outputs the probability distribution of the corresponding displacement
– Assume the state transition probability is:
– Plug those into Kalman-Bucy filter for tracking
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Gaussian innovation
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State predict
Innovation
State update
• Tracking algorithm
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Overall System
• A validator is adopted to achieve the tracking robustness.• Absence of the verification of the tracked object triggers
a exhaustive search over the input image by the classifiers.
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Face Tracking Results
• Row (1): deformation• Row (2): occlusion (lost track in the last frame)• Row (3): lighting variation
(1)
(2)
(3)
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Hand Tracking Results
Cars Tracking Results
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Long-term Tracking Results
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Conclusions
• Develop a tracker using sparse probabilistic regression by RVMs.
• RVM can be trained from a single image (generating training set).
• Robustness is obtained by the object verification.