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Two Realizations of Probability Anomaly Detector with Different Vector Quantization Algorithms
Anna Denisova
Samara State Aerospace University
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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)
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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
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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
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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
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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
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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)
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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
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Experimental research on real images
Input image №2 PAD AC (M=90, EPS=1) RXD
Region 2 (Yellow), Region 1 (Green), Background (Red)
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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
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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?
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