1. www.nr.no earthobs.nr.no Temporal Analysis of Forest Cover Using a Hidden Markov Model Arnt-Børre Salberg and Øivind Due Trier Norwegian Computing Center Oslo, Norway IGARSS 2011, July 27

2. www.nr.no earthobs.nr.no Outline ► Motivation ► Hidden Markov model ▪Concept ▪Class sequence estimation ▪Transition probabilities, clouds, and atmosphere ► Application: Tropical forest monitoring ► Conclusion

3. www.nr.no earthobs.nr.no Introduction ► Time-series of images needed in order to detect changes of the spatial forest cover ► Time-series analysis requires methodology that ▪handles the natural variability between in images ▪overcome problems with cloud cover in optical images (and missing data in Landsat-7) ▪handles atmospheric disturbances ▪does not propagate errors from one time instant to the next

4. www.nr.no earthobs.nr.no Introduction: Change detection ► Naive ▪Simply create forest cover maps from two years, and compare ▪Errors in both maps are added. Not a good idea! ► Time series analysis ▪Model what is going on by using all available images from the two years (and before, between, and after)

5. www.nr.no earthobs.nr.no Hidden Markov Model (HMM) ► HMM used to model each location on ground as being in one of the following classes:  = {forest, sparse forest, grass, soil} ► Markov property: P(  t |  t-1,…,  1 ) = P(  t |  t-1 )

6. www.nr.no earthobs.nr.no Hidden Markov Model (HMM) ► Bayes rule for Markov models ► P(  t |  t-1 ) : class transition probability class 1class 2 P(1|1) P(2|1) class 3 P(3|1)

7. www.nr.no earthobs.nr.no Class sequence estimation ► Two popular methods for finding the class sequence  1.Most likely class sequence 2.Minimum probability of class error

8. www.nr.no earthobs.nr.no Most likely class sequence (MLCS) ► Finds the class sequence that maximizes the likelihood →maximum likelihood estimate ► The optimal sequence is efficiently found using the Viterbi-algorithm

9. www.nr.no earthobs.nr.no Viterbi algorithm Forest Sparse forest Grass Soil Forest Sparse forest Grass Soil Possible states at time t Possible states at time t+1 Most probable sequence of previous states for each state at time t The best sequence ending at state c, given the observations x 1, …, x t The probability of jumping from state c to state k (this is dependent on the time interval) The probability of observing the actual observation, given that the state is k

10. www.nr.no earthobs.nr.no Minimum probability of class error ► If we are interested in obtaining a minimum probability of error class estimate (at time instant t), the MLCS method is not optimal, but the maximum a posteriori (MAP) estimate is ► The MAP estimate at time instant t ►  t found using the forward-backward algorithm

11. www.nr.no earthobs.nr.no Class transition probabilities ► Landsat: Minimum time interval between two subsequent acquisitions is 16 days ► Let P 0 (  t =m|  t =m’) = P 0 (m|m’) denote the class transition probability corresponding to 16 days ► Class transition probability for any 16·  t interval …in matrix form

12. www.nr.no earthobs.nr.no Clouds ► Clouds prevent us from observing the Earth’s surface ► Clouds may be handled using two different strategies 1.Cloud screening and masking of cloud- contaminated pixels as missing observations 2.Include a cloud class in the HMM modeling framework …in this work we only consider strategy 1. ► Cloud screening performed using a SVM

13. www.nr.no earthobs.nr.no Data distributions, class transition probabilities, co-registration ► Landsat image data (band 1-5,7) modeled using class dependent multivariate Gaussian distributions ► Mean vector and covariance matrix estimated from training data ► Class transition probabilities assumed fixed ▪May be estimated from the data (e.g. Baum- Welch) ► Precise co-registration needed

14. www.nr.no earthobs.nr.no Atmospheric disturbance Ground surface reflectance Atmosphere Top of the atmosphere reflectance  We apply a re-training methodology for handling image data variations (IGARSS’11, MO4.T05)  LEDAPS calibration (surface reflectance) will be investigated

15. www.nr.no earthobs.nr.no Landsat 5 TM images (166/63) Amani, Tanzania 1985-03-091986-08-191986-06-161986-10-061987-08-06 1995-02-171995-05-242008-06-12 2009-11-222009-11-062009-12-08 2009-07-01 2010-02-10 1995-02-01

16. www.nr.no earthobs.nr.no Results - Forest cover maps 16 2010-02-101995-02-171986-06-16 Forest Sparse forest Soil Grass Worldview-2 2010-03-04

17. www.nr.no earthobs.nr.no Results - Forest cover change 17 2010-02-10 1995-02-171986-06-161995-02-011986-10-061986-08-19 2009-07-012009-11-222009-12-08WV2 2010-03-25

18. www.nr.no earthobs.nr.no Landsat 5 TM images (227-062) Santarém, Brazil 1988-09-041989-08-221992-07-291993-05-291995-06-04 1996-07-082004-08-312005-07-012005-07-172006-08-05 2007-06-212008-06-232008-09-112009-07-122009-07-28

19. www.nr.no earthobs.nr.no Results - Forest cover maps Santarém, Brazil 19 2008-06-23 1997-07-271986-07-29 2007-06-23

20. www.nr.no earthobs.nr.no Results - Forest cover change maps Santarém, Brazil 20 2008-06-23 1997-07-271986-07-29 2007-06-23

21. www.nr.no earthobs.nr.no Multsensor possibilities ► Multitemporal observations from other sensors (e.g., radar) may naturally be modeled in the hidden Markov model ▪Only the sensor data distributions are needed, e.g. ► The multisensor images need to be geocoded to the same grid 21

22. www.nr.no earthobs.nr.no Temporal forest cover sequence ► Multisensor Hidden Markov model 22 CLASSES tt  t-1  t+1 ytyt y t-2  t-2 ytyt y t+1 y t-1 Optical SAR TIME OBSERVATIONS

23. www.nr.no earthobs.nr.no Conclusions ► Time series analysis of each pixel based on a hidden Markov model ► Finds the most likely sequence of land cover classes ► Change detection based on classified sequence ▪Does not propagate errors since the whole sequence is classified simultaneously. ▪Regularized by the transition probabilities. ► Handles cloud contaminated images ► Multisensor possibilities 23

24. www.nr.no earthobs.nr.no Acknowledgements The experiment presented here was supported by a research grant from the Norwegian Space Centre. 24