temporal_analysis_forest_cover_using_hmm.ppt
TRANSCRIPT
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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
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Outline
► Motivation
► Hidden Markov model ▪ Concept
▪ Class sequence estimation
▪ Transition probabilities, clouds, and atmosphere
► Application: Tropical forest monitoring
► Conclusion
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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
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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)
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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)
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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)
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Class sequence estimation
► Two popular methods for finding the class sequence 1. Most likely class sequence
2. Minimum probability of class error
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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
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Viterbi algorithm
Forest
Sparseforest
Grass
Soil
Forest
Sparseforest
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
x1, …, xt
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
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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
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Class transition probabilities
► Landsat: Minimum time interval between two subsequent acquisitions is 16 days
► Let P0(t=m|t=m’) = P0(m|m’) denote the class transition probability corresponding to 16 days
► Class transition probability for any 16·t interval
…in matrix form
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Clouds
► Clouds prevent us from observing the Earth’s surface
► Clouds may be handled using two different strategies1. 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
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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
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Atmospheric disturbance
Ground surface reflectance
Atmosphere
Top of the atmospherereflectance
We apply a re-training methodology for handling image data variations (IGARSS’11, MO4.T05)
LEDAPS calibration (surface reflectance) will be investigated
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Landsat 5 TM images (166/63)Amani, Tanzania
1985-03-09 1986-08-191986-06-16 1986-10-06 1987-08-06
1995-02-17 1995-05-24 2008-06-12
2009-11-222009-11-06 2009-12-08
2009-07-01
2010-02-10
1995-02-01
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Results - Forest cover maps
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2010-02-101995-02-171986-06-16
ForestSparse forest
SoilGrass
Worldview-2 2010-03-04
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Results - Forest cover change
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2010-02-10
1995-02-171986-06-16 1995-02-011986-10-061986-08-19
2009-07-01 2009-11-22 2009-12-08 WV2 2010-03-25
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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
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Results - Forest cover mapsSantarém, Brazil
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2008-06-231997-07-271986-07-29 2007-06-23
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Results - Forest cover change mapsSantarém, Brazil
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2008-06-231997-07-271986-07-29 2007-06-23
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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
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matrixcoherency theis , class| ttZ kp ZZ
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Temporal forest cover sequence
► Multisensor Hidden Markov model
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CLASSES tt-1 t+1
ytyt-2
t-2
yt yt+1yt-1
OpticalOptical
Optical OpticalSAR SAR
TIME
OBSERVATIONS
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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
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Acknowledgements
The experiment presented here was supported by a research grant from the Norwegian Space Centre.
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