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An Adaptive Learning Method for Target Tracking across Multiple Cameras Kuan-Wen Chen, Chih-Chuan Lai, Yi-Ping Hung, Chu-Song Chen National Taiwan University CVPR2008 Reporter: Chia-Hao Hsieh 2009/1/19

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Outline Introduction Visual cues for tracking across camera – Spatio-Temporal Relationships – Brightness Transfer Functions Experimental Results

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Introduction Adaptive learning method Tracking targets across multiple cameras with disjoint views Using prior knowledge – Camera network topology Sudden lighting changes

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Spatio-Temporal Relationships Prior knowledge of camera network topology Which pair of cameras are adjacent The blind regions are closed or open – Advantage Decrease computation complexity Help remove the redundant links

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Spatio-Temporal Relationships Batch + Adaptive learning method Batch learning phase – Estimate entry/exit zones for each single image – Model each entry/exit zones as a GMM, and use EM to estimate parameter of GMM Adaptive learning phase – Learn the transition probability for each possible link

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Spatio-Temporal Relationships transition probability Valid link – If exceeds double of the median value

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Spatio-Temporal Relationships Problems – Misclassify two zones into one single zone Update the entry/exit zones by using on-line K-means approximation Propose some operators – Zone Addition, Zone Merging, Zone Split

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Brightness Transfer Functions In [7], m x m matrix – The appearance is modeled as an m-bin histogram Propose an unsupervised learning method – Low dimensional subspace – Using spatio-temporal information and Markov chain Monte Carlo (MCMC) sampling [7] Tracking objects across cameras by incrementally learning inter-camera color calibration and patterns of activity. In ECCV, 2006

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Brightness Transfer Functions Model – Normalized cumulative histogram H i, H j. – The percentage of image points in O i with brightness less than or equal to B i is equal to the percentage of image points in O j with brightness less than or equal to B j. – f ij is the BTF for every pair of observations O i and O j in the training set

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Brightness Transfer Functions Learning – Probabilistic Principal Component Analysis PPCA – f ij can be written as BTF can be learnt with less data The average reconstruction error decreases when the number of learning data increases

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Criterion for BTF estimation The transformed histogram gives a much better match as compared to direct histogram matching A correct BTF learnt by using correct correspondences would have a more diverse reconstruction error distribution and lower errors than the one learnt by using incorrect correspondences

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Criterion for BTF estimation criterion p(π) for BTF estimation similarity(pair i ): the similarity score of the ith corresponding pair, which is calculated by (1- reconstruction_error(pair i ))

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Spatio-temporal information and MCMC sampling BTF is learnt – without hand-labeled correspondence – by sampling from the training data set – By choosing the best BTF according to the criterion – NOT practical to sample all of the permutations directly

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Spatio-temporal information and MCMC sampling For example – n observations – n! matching permutations – But, n pairs at most the correct correspondence Sample by using Markov Chain Monte Carlo and Metropolis-Hastings algorithm

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Experimental Results

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Makris’s method This paper

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Experimental Results faster learning rate. Gilbert and Bowden’s method never learns a stable BTF in the testing period

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Experimental Results Tracking Results The overall tracking accuracy is 89.4% by using unseen ground-truth of half an hour

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Experimental Results Outdoor environment Performs well and achieves high tracking accuracy in both indoor and outdoor environment

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Conclusion Unlike the other approaches assuming that the monitored environments remain unchanged Incrementally refine the clustering results of the entry/exit zones Learns the appearance relationship in a short period of time – Combing the spatio-temporal information and efficient MCMC sampling Can re-build the appearance relationship models soon after sudden lighting changes

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