Theoretical Foundation of the Collaborative Approach
Many attempts at analyzing complex motions reduce the problem dimensionality by finding independent motion parameters, and are unfortunately cornered when the intrinsic complexity of the motion is indeed too high to be easily handled. On the contrary, by relaxing and describing the complex motion in a high dimensional space, we represent it as a random field where each site encodes a simpler subpart motion that is associated locally with its own image measurements.

We have shown that this Markov network model leads to very efficient solutions based on the collaborations among a set of distributed and interlaced visual inference processes of individual subpart motions. To have a solid foundation of this new collaborative approach, we have conducted a theoretical study and obtained many exciting results using probabilistic variational analysis. We show that the mechanism of collaboration is governed by a set of fixed-point equations that elegantly describe the interactions among subparts and the posterior of the motion is obtained at equilibria. This is a generalized Bayesian Law for a random network, where the posterior of an individual is determined by three factors: its local prior, its local likelihood, and the neighborhood prior (or the messages from its neighbors).

Collaborative schemes vary in different ways of message composition. Although related to Belief Propagation (BP), our variational methods have advantages for loopy networks. We obtain further in-depth theoretical results. Gang Hua and I have proven that the maximum a posteriori (MAP) estimate can be found when nicely incorporating a deterministic annealing scheme into the fixed-point iterations. Our most recent study shows that the belief inconsistency can be evaluated by the characteristics of different fixed points.


Publication:
  1. Gang Hua and Ying Wu, "Variational Maximum a Posteriori by Annealed Mean Field Analysis", IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol.27, No.11, pp.1747-1781, Nov., 2005.  [PDF]

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  2. Gang Hua and Ying Wu, "Sequential Mean Field Variational Analysis of Structured Deformable Shapes", Computer Vision and Image Understanding, Vol.101, No.2., pp.87-99, Feb., 2006.  [PDF]

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  3. Gang Hua, Ying Wu and Zhimin Fan, "Measurement Integration Under Inconsistency for Robust Tracking", in Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR 06), New York City, NY, June 17-22, 2006.  [PDF]

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  4. Zhimin Fan and Ying Wu, "Multiple Collaborative Kernel Tracking", in Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR'05), San Diego, CA, June 20-26, 2005.  [PDF]

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  5. Ting Yu and Ying Wu, "Decentralized Multiple Target Tracking using Netted Collaborative Autonomous Trackers", in Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR'05), San Diego, CA, June 20-26, 2005.  [PDF]

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  6. Gang Hua, Ming-Hsuan Yang and Ying Wu, "Learning to Estimate Human Poses with Data Driven Belief Propagation", in Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR'05), San Diego, CA, June 20-26, 2005.  [PDF]

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  7. Ying Wu, Gang Hua and Ting Yu, "Tracking Articulated Body by Dynamic Markov Network", In Proc. IEEE Int'l Conf. on Computer Vision (ICCV'03), pp.1094-1101, Nice, France, Oct., 2003.  [PDF]
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Updated 7/2006. Copyright © 2001-2006 Ying Wu