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

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

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

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

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

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

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

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

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

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

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

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 ))

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

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

Experimental Results

Makris’s method This paper

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

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

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

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