Classifying Multi-temporal TM Imagery Using Markov Random Fields and Support Vector Machines
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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. Outline. Introduction

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Desheng liu maggi kelly and peng gong dept of environmental science policy management

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


Desheng liu maggi kelly and peng gong dept of environmental science policy management

Outline Fields and Support Vector Machines

  • Introduction

    • Two aspects of Multi-temporal Imagery

    • Classification Models

  • Methods

    • Support Vector Machines

    • Markov Random Fields

    • Spatio-temporal Classification

  • Results

  • Conclusions


Two aspects of multi temporal imagery

Introduction Fields and Support Vector Machines

Two Aspects of Multi-temporal Imagery

  • Spatial Dependence

    • Pixels are not I.I.D.

    • Spatial Autocorrelation

  • Temporal Correlation

    • Land Use

    • Phenology

    • Disturbance

T

Y

X


Classification models

Introduction Fields and Support Vector Machines

Classification Models

  • Non-contextual Model

  • Contextual Models

    • Spatial

    • Temporal

    • Spatio-temporal


Generative spatio temporal models

Introduction Fields and Support Vector Machines

Generative Spatio-temporal Models

  • Estimation of conditional probability

    • Maximum Likelihood Classifier (MLC)

    • Support Vector Machines (SVM)

  • Modeling spatio-temporal context

    • Markov Random Fields (MRF)


Desheng liu maggi kelly and peng gong dept of environmental science policy management

Methods Fields and Support Vector Machines

ρ

ρ

ξi

ξj

SVM: A Graphic View (1)

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

(a)

(b)


Desheng liu maggi kelly and peng gong dept of environmental science policy management

Methods Fields and Support Vector Machines

SVM: A Graphic View (2)

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

Φ(x)


Svm a mathematic view 1

Methods Fields and Support Vector Machines

SVM: A Mathematic View (1)

Binary Cases:

  • Training samples:

  • Decision function:

  • Discriminant function

    • Linear cases:

    • Nonlinear cases:

  • Probability output:


Svm a mathematic view 2

Methods Fields and Support Vector Machines

SVM: A Mathematic View (2)

Multi-category Cases:

  • Combination of binary SVM

    • “One-versus-one”

    • “One-versus-all”

  • Probability output

    • Pairwise coupling of binary probability outputs

    • Soft-max function


Markov random fields

Methods Fields and Support Vector Machines

Time 1

Time 2

Markov Random Fields

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


Map mrf

Methods Fields and Support Vector Machines

MAP-MRF

  • Bayes’ Decision Rule:Maximum a posterior (MAP)

  • MAP-MRF: the joint formulation of MAP and MRF

MAP-MRF


Spatio temporal classification

Methods Fields and Support Vector Machines

Spatio-temporal Classification

Conditional Probability

Conditional Prior

Markov Random Fields

Support Vector Machines

MAP-MRF


Desheng liu maggi kelly and peng gong dept of environmental science policy management

Methods Fields and Support Vector Machines

Implementation Algorithm

Iterative Conditional Mode (ICM)

iteratively estimate the class label of each pixel given the estimates of all its neighbors


Data and study site

Results Fields and Support Vector Machines

Data and Study Site

San Bernardino National Forest, CA

TM Imagery of June 11, 1997


Data and study site1

Results Fields and Support Vector Machines

Data and Study Site

San Bernardino National Forest, CA

TM Imagery of June 10, 2002


Classification flow

Results Fields and Support Vector Machines

2002

1997

TM Image

TM Image

SVM

SVM

Initialization

Initialization

Classification

Classification

Conditional

Conditional

(intermediate)

(intermediate)

probability

probability

Convergence?

MAP

-

MRF

Convergence?

MAP

-

MRF

No

No

Fire

Perimeter

Yes

Yes

Classification

(Final)

Classification

(Final)

Classification Flow


Desheng liu maggi kelly and peng gong dept of environmental science policy management

Results Fields and Support Vector Machines

Training/Test Samples


Classification accuracies of tm 1997

Results Fields and Support Vector Machines

Classification Accuracies of TM 1997


Classification accuracies of tm 2002

Results Fields and Support Vector Machines

Classification Accuracies of TM 2002


Convergence rate

Results Fields and Support Vector Machines

Convergence Rate


Desheng liu maggi kelly and peng gong dept of environmental science policy management

Results Fields and Support Vector Machines

Bare Land

Conifer

Conifer Open

Hardwood

Hardwood Open

Herbaceous

Shrub

Residential

Water

MLC-Spatio-Temp

Original Image

MLC

1997

SVM-Spatio-Temp

SVM


Desheng liu maggi kelly and peng gong dept of environmental science policy management

Results Fields and Support Vector Machines

MLC-Spatial-Temp

Original Image

MLC

SVM-Spatial-Temp

SVM

Bare Land

Conifer

Conifer Open

Hardwood

Hardwood Open

Herbaceous

Shrub

Residential

Water

2002


Conclusions
Conclusions Fields and Support Vector Machines

  • 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.


Acknowledgements
Acknowledgements Fields and Support Vector Machines

  • USDA Forest Service

  • NASA Earth System Science Graduate Student Fellowship


Desheng liu maggi kelly and peng gong dept of environmental science policy management

Thank you! Fields and Support Vector Machines