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.

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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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