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

2. OutlineOutline I.Introduction 1.Two aspects of Multi-temporal Imagery 2.Classification Models II.Methods 1.Support Vector Machines 2.Markov Random Fields 3.Spatio-temporal Classification III.Results IV.Conclusions

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

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

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

6. 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 ρ and minimum classification errors ξ ρ Methods ρ ξjξj ξiξi (a)(b)

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

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

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

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

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

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

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

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

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

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

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 1997 Original ImageMLC MLC-Spatio-Temp SVM SVM-Spatio-Temp Bare Land Conifer Conifer Open Hardwood Hardwood Open Herbaceous Shrub Residential Water

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

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!