Desheng%20Liu,%20Maggi%20Kelly%20and%20Peng%20Gong

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Classifying Multi-temporal TM Imagery Using
Markov Random Fields and Support Vector Machines
Desheng Liu, Maggi Kelly and Peng Gong Dept. of
Environmental Science, Policy
Management University of California, Berkeley May
18, 2005
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Outline

• Introduction
• Two aspects of Multi-temporal Imagery
• Classification Models
• Methods
• Support Vector Machines
• Markov Random Fields
• Spatio-temporal Classification
• Results
• Conclusions

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Two Aspects of Multi-temporal Imagery
Introduction
T

• Spatial Dependence
• Pixels are not I.I.D.
• Spatial Autocorrelation
• Temporal Correlation
• Land Use
• Phenology
• Disturbance

Y
X
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Classification Models
Introduction

• Non-contextual Model
• Contextual Models
• Spatial
• Temporal
• Spatio-temporal

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Generative Spatio-temporal Models
Introduction

• Estimation of conditional probability
• Maximum Likelihood Classifier (MLC)
• Support Vector Machines (SVM)
• Modeling spatio-temporal context
• Markov Random Fields (MRF)

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Methods
SVM A Graphic View (1)

• Linear Cases find the optimal linear separating
  boundary with (a) maximum margin ? (b) best
  trade-off between maximum margin ? and
  minimum classification errors ?

(a)
(b)
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Methods
SVM A Graphic View (2)

• Non-Linear Cases find the optimal linear
  separating boundary in a transformed higher
  dimensional feature space

F(x)
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SVM A Mathematic View (1)
Methods
Binary Cases

• Training samples
• Decision function
• Discriminant function
• Linear cases
• Nonlinear cases
• Probability output

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SVM A Mathematic View (2)
Methods
Multi-category Cases

• Combination of binary SVM
• One-versus-one
• One-versus-all
• Probability output
• Pairwise coupling of binary probability outputs
• Soft-max function

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Markov Random Fields
Methods

• Markov Random Fields (MRF) --- Probabilistic
  image models which define the inter-pixel
  contextual information in terms of the
  conditional prior probability of a pixel given
  its neighboring pixels

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MAP-MRF
Methods

• Bayes Decision Rule Maximum a posterior (MAP)
• MAP-MRF the joint formulation of MAP and MRF

MAP-MRF
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Spatio-temporal Classification
Methods
Conditional Probability
Conditional Prior
Markov Random Fields
Support Vector Machines
MAP-MRF
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Methods
Implementation Algorithm
Iterative Conditional Mode (ICM) iteratively
estimate the class label of each pixel given the
estimates of all its neighbors
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Data and Study Site
Results
TM Imagery of June 11, 1997
San Bernardino National Forest, CA
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Data and Study Site
Results
San Bernardino National Forest, CA
TM Imagery of June 10, 2002
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Classification Flow
Results
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Results
Training/Test Samples
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Classification Accuracies of TM 1997
Results
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Classification Accuracies of TM 2002
Results
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Convergence Rate
Results
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1997
Results
MLC-Spatio-Temp
Original Image
MLC
SVM-Spatio-Temp
SVM
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2002
Results
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Conclusions

• SVM are much better in the processing of spectral
  data than MLC for the initialization of the
  iterative algorithm.
• MRF are efficient probabilistic models for the
  analysis of spatial / temporal contextual
  information.
• The combination of SVM and MRF unifies the
  strengths of two algorithms and leads to an
  improved integration of the spectral, spatial and
  temporal components of multi-temporal remote
  sensing imagery.

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Acknowledgements

• USDA Forest Service
• NASA Earth System Science Graduate
  Student Fellowship

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