Desheng Liu, Maggi Kelly and Peng Gong Dept. of Environmental Science, Policy & Management

1. Classifying Multi-temporal TM Imagery Using Markov Random Fields and Support Vector Machines Desheng Liu, Maggi Kelly and Peng Gong Dept. of Environmental Science, Policy & Management University of California, Berkeley May 18, 2005

2. Outline • Introduction • Two aspects of Multi-temporal Imagery • Classification Models • Methods • Support Vector Machines • Markov Random Fields • Spatio-temporal Classification • Results • Conclusions

3. Introduction Two Aspects of Multi-temporal Imagery • Spatial Dependence • Pixels are not I.I.D. • Spatial Autocorrelation • Temporal Correlation • Land Use • Phenology • Disturbance T Y X

4. Introduction Classification Models • Non-contextual Model • Contextual Models • Spatial • Temporal • Spatio-temporal

5. Introduction Generative Spatio-temporal Models • Estimation of conditional probability • Maximum Likelihood Classifier (MLC) • Support Vector Machines (SVM) • Modeling spatio-temporal context • Markov Random Fields (MRF)

6. Methods ρ ρ ξi ξj SVM: A Graphic View (1) • Linear Cases:find the optimal linear separating boundary with (a) maximum margin ρ(b) best trade-off between maximum margin ρand minimum classification errors ξ (a) (b)

7. Methods SVM: A Graphic View (2) • Non-Linear Cases:find the optimal linear separating boundary in a transformed higher dimensional feature space Φ(x)

8. Methods SVM: A Mathematic View (1) Binary Cases: • Training samples: • Decision function: • Discriminant function • Linear cases: • Nonlinear cases: • Probability output:

9. Methods SVM: A Mathematic View (2) Multi-category Cases: • Combination of binary SVM • “One-versus-one” • “One-versus-all” • Probability output • Pairwise coupling of binary probability outputs • Soft-max function

10. Methods Time 1 Time 2 Markov Random Fields • Markov Random Fields(MRF) ---Probabilistic image models which define the inter-pixel contextual information in terms of the conditional priorprobability of a pixel given its neighboring pixels

11. Methods MAP-MRF • Bayes’ Decision Rule:Maximum a posterior (MAP) • MAP-MRF: the joint formulation of MAP and MRF MAP-MRF

12. Methods Spatio-temporal Classification Conditional Probability Conditional Prior Markov Random Fields Support Vector Machines MAP-MRF

13. Methods Implementation Algorithm Iterative Conditional Mode (ICM) iteratively estimate the class label of each pixel given the estimates of all its neighbors

14. Results Data and Study Site San Bernardino National Forest, CA TM Imagery of June 11, 1997

15. Results Data and Study Site San Bernardino National Forest, CA TM Imagery of June 10, 2002

16. Results 2002 1997 TM Image TM Image SVM SVM Initialization Initialization Classification Classification Conditional Conditional (intermediate) (intermediate) probability probability Convergence? MAP - MRF Convergence? MAP - MRF No No Fire Perimeter Yes Yes Classification (Final) Classification (Final) Classification Flow

17. Results Training/Test Samples

18. Results Classification Accuracies of TM 1997

19. Results Classification Accuracies of TM 2002

20. Results Convergence Rate

21. Results Bare Land Conifer Conifer Open Hardwood Hardwood Open Herbaceous Shrub Residential Water MLC-Spatio-Temp Original Image MLC 1997 SVM-Spatio-Temp SVM

22. Results MLC-Spatial-Temp Original Image MLC SVM-Spatial-Temp SVM Bare Land Conifer Conifer Open Hardwood Hardwood Open Herbaceous Shrub Residential Water 2002

23. Conclusions • SVM are much better in the processing of spectral data than MLC for the initialization of the iterative algorithm. • MRF are efficient probabilistic models for the analysis of spatial / temporal contextual information. • The combination of SVM and MRF unifies the strengths of two algorithms and leads to an improved integration of the spectral, spatial and temporal components of multi-temporal remote sensing imagery.

24. Acknowledgements • USDA Forest Service • NASA Earth System Science Graduate Student Fellowship

25. Thank you!