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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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slide1

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

slide2

Outline

  • 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

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

Classification Models
  • Non-contextual Model
  • Contextual Models
    • Spatial
    • Temporal
    • Spatio-temporal
generative spatio temporal models

Introduction

Generative Spatio-temporal Models
  • Estimation of conditional probability
    • Maximum Likelihood Classifier (MLC)
    • Support Vector Machines (SVM)
  • Modeling spatio-temporal context
    • Markov Random Fields (MRF)
slide6

Methods

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)

slide7

Methods

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

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

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

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

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

MAP-MRF

spatio temporal classification

Methods

Spatio-temporal Classification

Conditional Probability

Conditional Prior

Markov Random Fields

Support Vector Machines

MAP-MRF

slide13

Methods

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

Data and Study Site

San Bernardino National Forest, CA

TM Imagery of June 11, 1997

data and study site1

Results

Data and Study Site

San Bernardino National Forest, CA

TM Imagery of June 10, 2002

classification flow

Results

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
slide17

Results

Training/Test Samples

slide21

Results

Bare Land

Conifer

Conifer Open

Hardwood

Hardwood Open

Herbaceous

Shrub

Residential

Water

MLC-Spatio-Temp

Original Image

MLC

1997

SVM-Spatio-Temp

SVM

slide22

Results

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