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Multi-scale Markovian Modelisation in Image Segmentation and Remote Sensing

Members: Zoltan Kato Funded by PhD Scholarship of the French Government Partners: Pastis Group, INRIA - Sophia Antipolis, France (Josiane Zerubia and Mark Berthod) Related Projects: Cellular Neural Networks for Markov Random Field Image Segmentation Multicue Image and Video Segmentation: a Multi-layer MRF Framework Automatic Color Image Segmentation via Reversible Jump MCMC Lifetime: 1991 - 1995

Description

The main concern of this project is Markovian modelization in early vision. We consider low level vision tasks in a common framework, called image labeling, where the problem is reduced to assigning labels to pixels. Our approach is probabilistic, using Markov Random Fields (MRF) and Bayesian estimation, in particular Maximum A Posteriori (MAP) estimation. The advantage of MRF modelization is that a priori information can be "coded" locally through clique potentials. We also discuss pyramidal MRF models, which reduce the computing time and increase the quality of final results. Parameter estimation is an important problem in real-life applications in order to implement completely data-driven algorithms. We apply some methods to the estimation of monogrid model-parameters and propose a new algorithm for the hierarchical model.

All MRF models result in a non-convex energy function. The minimization of this function is done by Simulated Annealing or deterministic relaxation. We also investigate the possible parallelization techniques of optimization algorithms.

Our main result is a new hierarchical MRF model and a Multi-Temperature Annealing algorithm proposed for the energy minimization of the model. The convergence of the MTA algorithm has been proved towards a global optimum in the most general case, where each clique may have its own local temperature schedule.

Software

A demo program implementing the supervised monogrid model is also available for download.

Results

Following are some results on synthetic as well as on real satellite images. On the latter ones, red contours show region boundaries detected by our algorithm while green contours, where available, show the ground truth boundaries specified by an expert. On the synthetic image, we also show the evolution of Simulated Annealing while minimizing the MRF energy.

Results on satellite images

Noisy synthetic experiment

Noisy synthetic image	MRF segmentation result	Evolution of Simulated Annealing

Publications

1. Zoltan Kato. Multi-scale Markovian Modelisation in Computer Vision with Applications to SPOT Image Segmentation. PhD Thesis, INRIA, Sophia Antipolis, France, December 1994. Note: Available in English and French.
2. Zoltan Kato, Josiane Zerubia, and Mark Berthod. Unsupervised Parallel Image Classification Using Markovian Models. Pattern Recognition, 32(4):591-604, April 1999.
3. Mark Berthod, Zoltan Kato, Shan Yu, and Josiane Zerubia. Bayesian Image Classification Using Markov Random Fields. Image and Vision Computing, 14:285-295, 1996.
4. Zoltan Kato, Mark Berthod, and Josiane Zerubia. A Hierarchical Markov Random Field Model and Multi-Temperature Annealing for Parallel Image Classification. Computer Vision, Graphics and Image Processing: Graphical Models and Image Processing, 58(1):18-37, January 1996.
5. Mark Berthod, Zoltan Kato, and Josiane Zerubia. DPA: A Deterministic Approach to the MAP. IEEE Transactions on Image Processing, 4(9):1312-1314, September 1995.
6. Zoltan Kato, Josiane Zerubia, and Mark Berthod. Bayesian Image Classification Using Markov Random Fields. In Ali Mohammad-Djafari and Guy Demoment, editors, Maximum Entropy and Bayesian Methods, pages 375-382. Kluwer Academic Publisher, 1993.
7. Zoltan Kato, Josiane Zerubia, and Mark Berthod. Unsupervised Parallel Image Classification Using a Hierarchical Markovian Model. In Proceedings of International Conference on Computer Vision, Cambridge, MA, USA, pages 169-174, June 1995. IEEE.
8. Josiane Zerubia, Zoltan Kato, and Mark Berthod. Multi-Temperature Annealing: A New Approach for the Energy-Minimization of Hierarchical Markov Random Field Models. In Proceedings of International Conference on Pattern Recognition, volume 1, Jerusalem, Israel, pages 520-522, October 1994. IAPR.
9. Zoltan Kato, Mark Berthod, and Josiane Zerubia. Multiscale Markov Random Field Models for Parallel Image Classification. In Proceedings of International Conference on Computer Vision, Berlin, Germany, pages 253-257, May 1993. IEEE.