An Adaptive Learning Method for Target Tracking across Multiple Cameras

Kuan-Wen Chen, Chih-Chuan Lai, Yi-Ping Hung, Chu-Song ChenNational Taiwan University

CVPR2008

Reporter: Chia-Hao Hsieh2009/1/19

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 topologyWhich pair of cameras are adjacentThe 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 Hi, Hj.

– The percentage of image points in Oi with brightness less than or equal to Bi is equal to the percentage of image points in Oj with brightness less than or equal to Bj.

– fij is the BTF for every pair of observations Oi and Oj in the training set

Brightness Transfer Functions

• Learning– Probabilistic Principal Component Analysis PPCA– fij 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(pairi): the similarity score of the ith

corresponding pair, which is calculated by (1-reconstruction_error(pairi))

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

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