temporal_analysis_forest_cover_using_hmm.ppt
- 1. 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. Outline Motivation Hidden Markov model Concept Class sequence estimation Transition probabilities, clouds, and atmosphere Application: Tropical forest monitoring Conclusion
- 3. 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. 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. 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. Hidden Markov Model (HMM) Bayes rule for Markov models P( t | t-1 ) : class transition probability class 1 class 2 P(1|1) P(2|1) class 3 P(3|1)
- 7. Class sequence estimation Two popular methods for finding the class sequence Most likely class sequence Minimum probability of class error
- 8. 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. 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. 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. 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. Clouds Clouds prevent us from observing the Earth’s surface Clouds may be handled using two different strategies Cloud screening and masking of cloud-contaminated pixels as missing observations Include a cloud class in the HMM modeling framework … in this work we only consider strategy 1 . Cloud screening performed using a SVM
- 13. 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. Atmospheric disturbance We apply a re-training methodology for handling image data variations (IGARSS’11, MO4.T05) LEDAPS calibration (surface reflectance) will be investigated Ground surface reflectance Atmosphere Top of the atmosphere reflectance
- 15. Landsat 5 TM images (166/63) Amani, Tanzania 1985-03-09 1986-08-19 1986-06-16 1986-10-06 1987-08-06 1995-02-17 1995-05-24 2008-06-12 2009-11-22 2009-11-06 2009-12-08 2009-07-01 2010-02-10 1995-02-01
- 16. Results - Forest cover maps 2010-02-10 1995-02-17 1986-06-16 Worldview-2 2010-03-04 Forest Sparse forest Soil Grass
- 17. Results - Forest cover change 2010-02-10 1995-02-17 1986-06-16 1995-02-01 1986-10-06 1986-08-19 2009-07-01 2009-11-22 2009-12-08 WV2 2010-03-25 Clouded observation Clouded observation Clouded observation
- 18. Landsat 5 TM images (227-062) Santarém, Brazil 1988-09-04 1989-08-22 1992-07-29 1993-05-29 1995-06-04 1996-07-08 2004-08-31 2005-07-01 2005-07-17 2006-08-05 2007-06-21 2008-06-23 2008-09-11 2009-07-12 2009-07-28
- 19. Results - Forest cover maps Santarém, Brazil 2008-06-23 1997-07-27 1986-07-29 2007-06-23
- 20. Results - Forest cover change maps Santarém, Brazil 2008-06-23 1997-07-27 1986-07-29 2007-06-23
- 21. 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
- 22. Temporal forest cover sequence Multisensor Hidden Markov model CLASSES t t-1 t+1 y t y t-2 t-2 y t y t+1 y t-1 Optical Optical Optical Optical SAR SAR TIME OBSERVATIONS
- 23. 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
- 24. Acknowledgements The experiment presented here was supported by a research grant from the Norwegian Space Centre.