Temporal Analysis of Forest Cover Using a Hidden Markov Model Arnt-Børre Salberg and Øivind Due Trier  Norwegian Computing...
Outline <ul><li>Motivation </li></ul><ul><li>Hidden Markov model  </li></ul><ul><ul><li>Concept </li></ul></ul><ul><ul><li...
Introduction <ul><li>Time-series of images needed in order to detect changes of the spatial forest cover </li></ul><ul><li...
Introduction: Change detection <ul><li>Naive </li></ul><ul><ul><li>Simply create forest cover maps from two years, and com...
Hidden Markov Model (HMM) <ul><li>HMM used to model each location on ground as being in one of the following classes: </li...
Hidden Markov Model (HMM) <ul><li>Bayes rule for Markov models </li></ul><ul><li>P(  t |  t-1 )  : class transition prob...
Class sequence estimation <ul><li>Two popular methods for finding the class sequence   </li></ul><ul><ul><li>Most likely ...
Most likely class sequence (MLCS) <ul><li>Finds the  class sequence  that maximizes the likelihood </li></ul><ul><ul><li>-...
Viterbi algorithm Forest Sparse forest Grass Soil Forest Sparse forest Grass Soil Possible states at time  t Possible stat...
Minimum probability of class error <ul><li>If we are interested in obtaining a  minimum probability of error class estimat...
Class transition probabilities <ul><li>Landsat:  Minimum time interval between two subsequent acquisitions is 16 days </li...
Clouds <ul><li>Clouds prevent us from observing the Earth’s surface  </li></ul><ul><li>Clouds may be handled using two dif...
Data distributions, class transition probabilities, co-registration <ul><li>Landsat image data (band 1-5,7) modeled using ...
Atmospheric disturbance <ul><li>We apply a re-training methodology for handling image data variations (IGARSS’11, MO4.T05)...
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 ...
Results - Forest cover maps 2010-02-10 1995-02-17 1986-06-16 Worldview-2  2010-03-04 Forest Sparse forest Soil Grass
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 2009-11-22 200...
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 2004-08-3...
Results - Forest cover maps Santarém, Brazil 2008-06-23 1997-07-27 1986-07-29 2007-06-23
Results - Forest cover change maps Santarém, Brazil 2008-06-23 1997-07-27 1986-07-29 2007-06-23
Multsensor possibilities <ul><li>Multitemporal observations from other sensors (e.g., radar) may naturally be modeled in t...
Temporal forest cover sequence <ul><li>Multisensor Hidden Markov model </li></ul>CLASSES  t  t-1  t+1 y t y t-2  t-2 y...
Conclusions <ul><li>Time series analysis of each pixel based on a hidden Markov model </li></ul><ul><li>Finds the most lik...
Acknowledgements <ul><li>The experiment presented here was supported by a research grant from the Norwegian Space Centre. ...
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temporal_analysis_forest_cover_using_hmm.ppt

  1. 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. 2. Outline <ul><li>Motivation </li></ul><ul><li>Hidden Markov model </li></ul><ul><ul><li>Concept </li></ul></ul><ul><ul><li>Class sequence estimation </li></ul></ul><ul><ul><li>Transition probabilities, clouds, and atmosphere </li></ul></ul><ul><li>Application: Tropical forest monitoring </li></ul><ul><li>Conclusion </li></ul>
  3. 3. Introduction <ul><li>Time-series of images needed in order to detect changes of the spatial forest cover </li></ul><ul><li>Time-series analysis requires methodology that </li></ul><ul><ul><li>handles the natural variability between in images </li></ul></ul><ul><ul><li>overcome problems with cloud cover in optical images (and missing data in Landsat-7) </li></ul></ul><ul><ul><li>handles atmospheric disturbances </li></ul></ul><ul><ul><li>does not propagate errors from one time instant to the next </li></ul></ul>
  4. 4. Introduction: Change detection <ul><li>Naive </li></ul><ul><ul><li>Simply create forest cover maps from two years, and compare </li></ul></ul><ul><ul><li>Errors in both maps are added. Not a good idea! </li></ul></ul><ul><li>Time series analysis </li></ul><ul><ul><li>Model what is going on by using all available images from the two years (and before, between, and after) </li></ul></ul>
  5. 5. Hidden Markov Model (HMM) <ul><li>HMM used to model each location on ground as being in one of the following classes: </li></ul><ul><ul><li>  = { forest, sparse forest, grass, soil } </li></ul></ul><ul><li>Markov property: P(  t |  t-1 ,…,  1 ) = P(  t |  t-1 ) </li></ul>
  6. 6. Hidden Markov Model (HMM) <ul><li>Bayes rule for Markov models </li></ul><ul><li>P(  t |  t-1 ) : class transition probability </li></ul>class 1 class 2 P(1|1) P(2|1) class 3 P(3|1)
  7. 7. Class sequence estimation <ul><li>Two popular methods for finding the class sequence  </li></ul><ul><ul><li>Most likely class sequence </li></ul></ul><ul><ul><li>Minimum probability of class error </li></ul></ul>
  8. 8. Most likely class sequence (MLCS) <ul><li>Finds the class sequence that maximizes the likelihood </li></ul><ul><ul><li>-> maximum likelihood estimate </li></ul></ul><ul><li>The optimal sequence is efficiently found using the Viterbi -algorithm </li></ul>
  9. 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. 10. Minimum probability of class error <ul><li>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 </li></ul><ul><li>The MAP estimate at time instant t </li></ul><ul><li> t found using the forward-backward algorithm </li></ul>
  11. 11. Class transition probabilities <ul><li>Landsat: Minimum time interval between two subsequent acquisitions is 16 days </li></ul><ul><li>Let P 0 (  t =m|  t =m’) = P 0 (m|m’) denote the class transition probability corresponding to 16 days </li></ul><ul><li>Class transition probability for any 16·  t interval </li></ul><ul><ul><li>… in matrix form </li></ul></ul>
  12. 12. Clouds <ul><li>Clouds prevent us from observing the Earth’s surface </li></ul><ul><li>Clouds may be handled using two different strategies </li></ul><ul><ul><li>Cloud screening and masking of cloud-contaminated pixels as missing observations </li></ul></ul><ul><ul><li>Include a cloud class in the HMM modeling framework </li></ul></ul><ul><ul><li>… in this work we only consider strategy 1 . </li></ul></ul><ul><li>Cloud screening performed using a SVM </li></ul>
  13. 13. Data distributions, class transition probabilities, co-registration <ul><li>Landsat image data (band 1-5,7) modeled using class dependent multivariate Gaussian distributions </li></ul><ul><li>Mean vector and covariance matrix estimated from training data </li></ul><ul><li>Class transition probabilities assumed fixed </li></ul><ul><ul><li>May be estimated from the data (e.g. Baum-Welch) </li></ul></ul><ul><li>Precise co-registration needed </li></ul>
  14. 14. Atmospheric disturbance <ul><li>We apply a re-training methodology for handling image data variations (IGARSS’11, MO4.T05) </li></ul><ul><li>LEDAPS calibration (surface reflectance) will be investigated </li></ul>Ground surface reflectance Atmosphere Top of the atmosphere reflectance
  15. 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. 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. 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. 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. 19. Results - Forest cover maps Santarém, Brazil 2008-06-23 1997-07-27 1986-07-29 2007-06-23
  20. 20. Results - Forest cover change maps Santarém, Brazil 2008-06-23 1997-07-27 1986-07-29 2007-06-23
  21. 21. Multsensor possibilities <ul><li>Multitemporal observations from other sensors (e.g., radar) may naturally be modeled in the hidden Markov model </li></ul><ul><ul><li>Only the sensor data distributions are needed, e.g. </li></ul></ul><ul><li>The multisensor images need to be geocoded to the same grid </li></ul>
  22. 22. Temporal forest cover sequence <ul><li>Multisensor Hidden Markov model </li></ul>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. 23. Conclusions <ul><li>Time series analysis of each pixel based on a hidden Markov model </li></ul><ul><li>Finds the most likely sequence of land cover classes </li></ul><ul><li>Change detection based on classified sequence </li></ul><ul><ul><li>Does not propagate errors since the whole sequence is classified simultaneously. </li></ul></ul><ul><ul><li>Regularized by the transition probabilities. </li></ul></ul><ul><li>Handles cloud contaminated images </li></ul><ul><li>Multisensor possibilities </li></ul>
  24. 24. Acknowledgements <ul><li>The experiment presented here was supported by a research grant from the Norwegian Space Centre. </li></ul>

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