Preprocessing Techniques for Image Analysis Applications

Hong Zhang

Preprocessing

• High dimensionality

• Limited sample size

• A simple argument: Rao-Blackwell

)var()var(

)](|)([))((

1

1

xTxExT

Preprocessing

• Normalization / transformation

• Feature extraction / elimination

• Kernel design

Medical Imaging Applications

Image Processing

Feature Extraction

Kernel Design

image SVM

Mammography

Mathematical Morphology

• Erosion• Dilation• Opening• Closing

• Tophat• Watershed• Reconstruction• Skeletonization

Calcification Detection

Cell Image

Segmentation

Simple Features

• Area• Length• Elongation• Eccentricity• Compactness

• Mean• Variance• Density• Fractal dimension• Moments

Kernel Invariance

),(),(

),(),(

qpkqTpk

qpkTqTpk

Translation Invariance

Rotation Invariance

The Fourier Kernel

NnNdseszf insn ,)(

1

0

2

N

nnn gfwzK

1

''),(

iref

f

1

0translation

rotation

3D Problems

• Harmonic analysis on locally compact Abelian group

• S2 is not a topological group

• SO(3) is not Abelian

• Torus

• Quaternion

G

dxxfxf )()()(ˆ

Circulating Tumor Cells

Automatic CTC Detection

Canonical Correlation Analysis

Functional MRI

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yxyx

wCwwCw

wCw

''

'Maximize correlation

Flow Cytometry

Distance Measures

• Bhattacharyya affinity

• Nearest neighbor error

• Mahalanobis distance

• Kullback-Leibler divergence

• Jeffreys’ divergence

),(),( qpeqpk

Kernel on Distributions

||||

|2/)(|ln2

1)(

2)(

8

1),(

)/log()/log(),(

),(

21

2112

1

2112

),(

MMMMqp

dxpqqqppqp

eqpk

TB

KL

qp

Clustering

• Gaussian mixture

• K-means

• EM algorithm

• Regularization