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METHODS FOR TARGET DETECTION IN SAR IMAGES
Kaan Duman Supervisor: Prof. Dr. A. Enis Çetin December 18, 2009 Bilkent University Dept. of Electrical and Electronics Engineering
Introduction
Target Detection in SAR Images using Region Covariance (RC) and Codifference Using various distance metrics and SVM Classifiers Comparisons with PCA method
Use of Directional Filters (DFs) on Target Detection Methods l1 norm distance metric SVM classifiers
Conclusions
Outline
Introduction Synthetic Aperture Radar (SAR) sensors can produce images of scenes in
all weather conditions at any time of day and night.
Many algorithms are developed for SAR ATR (Automatic Target Recognition) algorithms are provided in the literature.
Methods presented here can be used for detection or discrimination stage of SAR ATR.
Region covariance and codifference matrix features are used in the SAR ATR target detection problem.
SAR images are pre-processed with directional filters in order to decrease the computational cost of the algorithm.
Experimental results using the MSTAR SAR database are presented at the end of each part.
PART I
Target Detection in SAR Images Using Region Covariance (RC) and Codifference
Feature Vector Extraction of ROI
For each pixel in the region of interest (ROI):
where,
• i is the index of the feature vector (i = 1,2,…,7), • k is the label of a pixel, • (x , y) is the position of a pixel, • I is intensity of a pixel (since gray-scale images are used in this study), • d(I(x,y)) /dx is the horizontal and d(I(x,y))/dy is the vertical first derivative of the ROI calculated with the filter [-1 0 1], • d2(I(x,y))/dx2 is the horizontal and d2(I(x,y))/dy2 is the vertical second derivative of the ROI calculated with the filter [-1 2 -1],
Example: For a 4 by 4 region, k = 1,2,…16; x = 1,2,3,4; y = 1,2,3,4 .
€
zk = x y I(x,y) dI(x,y)dx
dI(x,y)dy
d2I(x,y)dx 2 d
2I(x,y)dy 2
⎡
⎣ ⎢
⎤
⎦ ⎥
T
€
zk = zk(i)[ ]T
Region Covariance (RC) Matrix
where, n is the total number of pixels in the ROI cR(i,j) is the (i, j)th component of the covariance matrix
Advantages of using RC matrix: Invariant to a degree of scale and illumination change Provides an averaging filter to filter out the naturally occurring
speckle noise in SAR images.
Region Codifference Matrix
where, the scalar multiplication is replaced by an additive
operator ⊕. The operator ⊕ is basically a summation operation but the sign of the result behaves similar to the multiplication operation:
for real numbers a and b.
€
CR = cR (i, j)[ ] =1n −1
zk (i)⊕ zk ( j) −1n
zk (i)⊕ zk ( j)k=1
n
∑k=1
n
∑k=1
n
∑⎡
⎣ ⎢
⎤
⎦ ⎥
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
Stages of the Target Detection Algorithm
€
ρ2(C1,C2) = log2(λi(C1) − λi(C2))i=1
p
∑
€
ρ3(C1,C2 ) = C1( i, j) −C2( i, j)( )j=1
p
∑⎡
⎣ ⎢
⎤
⎦ ⎥
i=1
p
∑
€
ρ4(C1,C2 ) =C1( i, j) −C2( i, j)
C2( i,i)
⎛
⎝ ⎜
⎞
⎠ ⎟
j=1
p
∑⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥ i=1
p
∑
€
ρ5(C1,C2 ) =C1( i, j) −C2( i, j)(C1( i,i) + C2( i,i))
⎛
⎝ ⎜
⎞
⎠ ⎟
j=1
p
∑⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥ i=1
p
∑
Used distance metrics: Involving computation of eigenvalues:
1) Gen. Eig. Dist. Met. 2) Dis. Eig. Dist. Met.
Based on l1 norms: 3) l1 Norm Dist. Met. 4) Norm. l1 Norm Dist. Met.
5) 2nd Norm. l1 Norm Dist. Met.
where, C1, C2 are the covariance or codifference matrices of regions R1 (from test images) and R2 (from training images), respectively.
A sample covariance or codifference matrix where the bounded region shows the necessary features for the decision algorithm:
Stages of the Target Detection Algorithm
MSTAR SAR Database Examples of 128-by-128 and cropped 64-by-64 target and
clutter images (ROIs):
MSTAR SAR Database Number of images used in the training and testing studies:
Experimental results include: Detection Accuracy: (number of correctly detected target images) / (number of total test images)
False Alarm: (number of clutter images detected as target images) / (number of total clutter images)
Experimental Results The target detection accuracies (%) obtained with the RC and codifference
methods using defined distance metrics and SVM classifiers:
97.5 98 98.5 99 99.5 100 100.5
1
2
3
4
5
6
Target detection accuracies (%)
Using region covariance (RC) method
128 by 128 images64 by 64 images
97.5 98 98.5 99 99.5 100 100.5
1
2
3
4
5
6
Target detection accuracies (%)
Using region codifference method
128 by 128 images64 by 64 images
Decision MethodsPreferred:
SVM classifiers
2nd Norm. l1 norm dist.
Norm. l1 norm dist.
l1 norm dist. met.
Dis. eig. dist. met.
Gen. eig. dist. met.
SVM classifiers
2nd Norm. l1 norm dist.
Norm. l1 norm dist.
l1 norm dist. met.
Dis. eig. dist. met.
Gen. eig. dist. met.
Experimental Results The false alarm rates (%) obtained with the RC and codifference methods
using defined distance metrics and SVM classifiers:
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
1
2
3
4
5
6
False alarm rates (%)
Using region covariance (RC) method
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
1
2
3
4
5
6
False alarm rates (%)
Using region codifference method
128 by 128 images64 by 64 images
128 by 128 images64 by 64 images
Decision MethodsPreferred:
2nd Norm. l1 norm dist.
SVM classifiers
Norm. l1 norm dist.
l1 norm dist. met.
Dis. eig. dist. met.Gen. eig. dist. met.
SVM classifiers2nd Norm. l
1 norm dist.
Norm. l1 norm dist.
l1 norm dist. met.
Dis. eig. dist. met.
Gen. eig. dist. met.
Using k-NN (k – Nearest Neighbor) Algorithm
The target detection accuracies (%) obtained for increasing k values using l1 norm distance metric on RC and codifference methods:
10 20 30 40 50 60 70 80 90 10097.5
98
98.5
99
99.5
100
k values
Targ
et d
etec
tion
accu
raci
es (%
)
Using RC method on 128 by 128 imagesUsing codifference method on 128 by 128 imagesUsing RC method on 64 by 64 imagesUsing codifference method on 64 by 64 images
Using k-NN (k – Nearest Neighbor) Algorithm
The false alarm rates (%) obtained for increasing k values using l1 norm distance metric on RC and codifference methods:
10 20 30 40 50 60 70 80 90 1000
2
4
6
8
10
12
14
k values
Fals
e al
arm
rate
s (%
)
Using RC method on 128 by 128 imagesUsing codifference method on 128 by 128 imagesUsing RC method on 64 by 64 imagesUsing codifference method on 64 by 64 images
Using PCA (Principal Component Analysis)
Number of images used in training and testing studies for the PCA method
Target detection accuracies and false alarm rates achieved using PCA method
Comparisons with Commonly Used PCA Method
Target detection accuracies and false alarm rates achieved with the new database: Using l1 norm distance metric
Using SVM as a classifier
PART II
Use of Directional Filters (DFs) on Target Detection Methods
The “Two-Stage” Target Detection System
ROIs in SAR images are filtered using 2-D directional filters (DFs) in the pre-processing stage.
After the images are put into sub-categories by the output of the DFs, they are classified with the RC and codifference methods using l1 norm distance metric and SVM classifiers.
Directional Filters (DFs)
Used to classify target and clutter images in the database according to their orientations in the pre-processing stage.
Distributing images into sub-categories decreases the number of distance calculation based on l1 norms.
Design of the DFs:
Block Diagram of the Pre-processing Stage
Target Detection Strategy
Block diagram of the target detection stage applied in each sub-category using (a) l1 norm distance metric (b) SVM classifiers
Experimental Results Sample 64-by-64 target images selected by DFs 1-10
Experimental Results The results of various two-stage set-ups working on 10 sub-categories
Experimental Results The results of various two-stage set-ups working on 8 sub-categories
Experimental Results The total target detection accuracies (%) obtained with the
two-stage set-ups for different numbers of sub-categories
1 2 3 4 5 6 7 8 9 1098.2
98.4
98.6
98.8
99
99.2
99.4
99.6
99.8
100
Number of sub categories
Targ
et d
etec
tion
accu
raci
es (%
)
Using RC method with l1 norm distance metric
Using RC method with SVM classifiersUsing codifference method with l1 norm distance metric
Using codifference method with SVM classifiers
Experimental Results The total false alarm rates (%) obtained with the two-stage
setups for different numbers of sub-categories
1 2 3 4 5 6 7 8 9 100
0.2
0.4
0.6
0.8
1
1.2
1.4
Number of sub categories
Fals
e al
arm
rate
s (%
)
Using RC method with l1 norm distance metric
Using RC method with SVM classifiersUsing codifference method with l1 norm distance metric
Using codifference method with SVM classifiers
Experimental Results The results of various two-stage set-ups working on 10 sub-
categories with the new database
Using k-NN (k – Nearest Neighbor) Algorithm
The total target detection accuracies (%) obtained for increasing k values using 10 sub-categories for the two-stage system. l1 norm distance metric is used.
2 4 6 8 10 12 14 16 18 2097
97.5
98
98.5
99
99.5
100
k values
Targ
et d
etec
tion
accu
raci
es (%
)
Using RC methodUsing codifference method
Using k-NN (k – Nearest Neighbor) Algorithm
The total false alarm rates (%) obtained for increasing k values using 10 sub-categories for the two-stage system. l1 norm distance metric is used.
2 4 6 8 10 12 14 16 18 200
1
2
3
4
5
6
7
8
9
k values
Fals
e al
arm
rate
s (%
)
Using RC methodUsing codifference method
Conclusions
The use of RC and codifference methods for SAR image classification problems are investigated using various distance metrics and SVM classifiers.
To further reduce the computational complexity of the algorithm, DFs are used in a pre-processing stage, in order to divide the images into sub-categories.
The codifference methods provide higher detection accuracies and lower false alarm rates than RC methods, besides having lower computational costs.
The distance metrics involving l1 norms provide superior classification results than other metrics used.
For real-time applications, the SAR image classification method based on SVM using codifference features has the lowest computational complexity.
