1

Two Realizations of Probability Anomaly Detector with Different Vector Quantization Algorithms

Anna Denisova

Samara State Aerospace University

2

Anomaly detection for hyperspectral imagesAnomaly is a small partition of data with some characteristics significantly

different from background.

Hyperspectral image Anomaly detection method Anomaly measure image

Mai

n is

sues

1. High dimension2. Physical meaning of

image pixels

1. No prior information about target objects

2. Background model3. Anomaly measure

Post processing

Anomaly detection methods classification

Gaussian Mixture(GMM-GLRT, Cluster

based anomaly detector)

Linear spectral mixture (OSP and

SSP Detectors)

Local normal model (RXD)

Non parametric background model

(Kernel RX-Detector)

Local normal model in feature space

(SVDD)

3

Probability anomaly detector (PAD)Input image

1. Vector quantization

2. Calculating histogram using hash function

3. Calculating probabilities

4. Aggregation

Output image

Thresholding

Anomaly value:

innIi

qPAggregatennP21 ,

21 1,

.)(

,

,

,,

,

21

21

pixelquantizedofyprobabilitqP

functionnaggregatioAggregate

windownaggregatioinpixeliforvaluequantizedq

nnpositionwithwindownaggregatiofor

scoordinateofsetnnIwhere

i

thi

4

PAD with uniform quantization (PAD UQ)PAD UQ:Uniform quantizing with K levels for each image component l.

Integer hash functions:• modulo hashing

•multiplicative modulo hashing

•Hash functions for strings (Horner algorithm)

Kxxxnnx

nnqll

lll

minmax

min2121

,,

MKqqf in

ii mod)(

1

0

MKqqf in

ii mod)(

1

0

5

PAD with agglomerative clusterzationPAD AC:New vector quantization algorithm based on agglomerative clusterization.Properties:1. Quantization values are the centers of clusters.2. Number of clusters M is fixed.3. Cluster size threshold – ε 4. Output – a codebook Q of size M.

M, ε, 0,0,11xxxQ сс

mсxnnxd ,, 21true false

MQ •Include x in Cm•Recalculate xCm

•Increase ε•Merge clusters with d<ε

•Add new cluster with center in x

Initialization

Sequentially for each pixel

6

Experimental research

Source image Embedding mask Image with anomaliesAVIRIS, 224 spectral bands, 145x145

AVIRIS, 360 spectral bands, 145x145

Images with anomalies Embedding mask

Synthetic hyperspectral images,99 spectral bands, 128x128

7

Experimental research of PAD UQK Biexponential ACF Gauss ACF

TP FP TP FP

2 1 0.098 1 0.104

3 1 0.378 1 0.387

4 1 0.471 1 0.504

Hash function K=2

TP FPModulo hash 1 0.10119

Multiplicative modulo hash 0.8 0.00005

Horner algorithm 1 0.10630

high

mid

dle

low

Corr

elati

on le

vel

Biexponential ACF Gauss ACF

8

Experimental research of PAD AC

0.010.02

0.03

0.0400000000000001

0.05000000000000010

0.00050.001

0.00150.002

0.0025

M=10M=20M=30М=40M=50

ε

FP

0.01 0.02 0.03 0.04 0.050

0.0005

0.001

0.0015

0.002

0.0025

M=10M=20M=30M=40M=50

ε

FP

Biexponential ACF Gauss ACFhi

ghm

iddl

elo

w

Corr

elati

on le

vel

high

mid

dle

low

9

Experimental research of aggregation and noise

3×3, TP 3×3, FP 5×5, TP 5×5, FP 7×7, TP 7×7, FP0

0.5

1

1.5

PAD UQ

Minimum Median Sigma filtr

Anomaly size, Probability type (TP or FP)Prob

abili

ty v

alue

(TP

or F

P)

3×3, TP 3×3, FP 5×5, TP 5×5, FP 7×7, TP 7×7, FP0

0.51

1.5

PAD AC

without aggregation minimummedian

Anomaly size, Probability type (TP or FP)

Prob

abili

ty v

alue

(TP

or F

P)

3×3, TP

3×3, FP

5×5, TP

5×5, FP

7×7, TP

7×7, FP

0

0.2

0.4

0.6

0.8

1

1.2

PAD AC for noised images

∞25015015

Anomaly size, Probability type (TP or FP)

Prob

abili

ty v

alue

(TP

or F

P)

10

Experimental research on real images

Input image №1 PAD AC (M=15, EPS=1) RXD

Not detected signature (red on the left chart), detected signature (red on the right chart)

and background signature (green)

0.0010.003

0.0050.007

0.0090.011

0.0130.015

0.0170.019

00.10.20.30.40.50.60.70.80.9

PAD AC (M=15, EPSILON=1), TPRXD, TPPAD AC (M=15, EPSILON=1), FPRXD, FP

Threshold

11

Experimental research on real images

Input image №2 PAD AC (M=90, EPS=1) RXD

Region 2 (Yellow), Region 1 (Green), Background (Red)

12

0.0010.003

0.0050.007

0.0090.011

0.0130.015

0.0170.019

0

0.2

0.4

0.6

0.8

1

1.2

PAD AC (M=90, EPSILON=1), TPRXD, TPPAD AC (M=90, EPSILON=1), FPRXD, FP

Threshold

12

ConclusionProposed two realizations of PAD anomaly detection algorithm

PAD UQ and PAD AC:• PAD UQ inefficient in presence of noise and highly depends on

correlation properties of background. • Further development of PAD AC consists in production

modifications with PCA.• PAD AC noise resistant and fewer dependant from image

correlation.• PAD AC requires automatic procedure of initial error and

codebook size estimation to be applied on real images.

Questions?