autoregressive model for multi-pass sar change detection ... · detection for wide-area...
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Autoregressive Model for Multi-Pass SAR
Change Detection Based on Image Stacks
Bruna Gregory Palm
September 4, 2018
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Outline
• Introduction/Motivation;
• Data description;
• AR model;
• Experimental Results;
• Application;
• Conclusions.
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Introduction
SAR change detection is usually used to detect changes in time between
to images.
Generally, the changes are natural disasters or deforestation and installa-
tions [1, 2, 3].
Currently used algorithms are mainly designed for two SAR images retrieved
at different instants.
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Introduction
However, the use of the SAR image stack (more than two images observed
in different times) emerges as a research topic on SAR change detection.
The stacks are based on the fact that the passes, the heading angles of
the platform, and the incident angles, are almost identical [4].
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Introduction
Figure 1: Images samples of the stack.
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Data description
The data used for this study were delivered by CARABAS II [5], a Swedish
ultra-wideband VHF SAR system.
The data included eight images with almost identical flight geometry, but
with four different targets deployments in the ground scene [6, 5].
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Data description
Each image is represented by a matrix of 3000×2000 pixels, corresponding
to an area of 6 km2.
The ground scene is dominated by forest with pine trees. Fences, power
lines and roads were also present in the scene.
Some military vehicles were deployed in the SAR scene and placed in a
manner to facilitate their identifications in the tests [5].
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Data description
Figure 2: Image of the terrain vehicles used as targets during the experiment,
presented in [5].
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Data description
Figure 3: Image of location and orientation of the targets presented in [5].
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Data description
Figure 4: Image of location and orientation of the targets presented in [5].
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Data description
Figure 5: CARABAS-II images.
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AR model
A time series is any set of observations, y [n], observed over a specific time,
n.
These series are analysed by means of the temporal dependence, being able
to make predictions.
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AR model
The AR models can be defined as follow:
y [n] = −p∑
k=1
a[k]y [n − k] + u[n], (1)
where y [n] is the amplitude value of each pixel in one image, a[k] are
the autoregressive terms, u[n] is white noise, and p is the order of the
model [7].
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AR model
The predicted image is given by
y [N + h] = −p∑
k=1
a[k]y [N + h − k], (2)
where a[k] are the estimate of a[k].
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AR model
The estimated autoregressive terms a[k] are the solutions of the following
equation systemryy [0] ryy [1] . . . ryy [p − 1]
ryy [1] ryy [0] . . . ryy [p − 2]...
.... . .
...
ryy [p − 1] ryy [p − 2] . . . ryy [0]
a[1]
a[2]...
a[p]
= −
ryy [1]
ryy [2]...
ryy [p]
,
where ryy [·] is the autocorrelation function.
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Experimental Results
The resolution of the CARABAS II system is approximately 3 × 3 m2.
Since a pixel represents a 1×1 m2, considering an one-dimensional model,
the closest pixels will be more correlated than the others. Thus, we
used p = 1 in the AR models.
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Experimental Results
Based on the fitted model, we obtained the forecast of one step ahead for
each pixel.
This forecasting provides a new image representing the ground estimation
of the SAR scene.
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Experimental Results
Figure 6: Prediction image for the AR(1) model.
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Experimental Results
Figure 7: Difference images between interest images and prediction image.
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Experimental Results
Figure 8: Difference images between interest images and prediction image.
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Application
We considered change detections methods in the difference images.
Image
StackGround
Estimation
-
Interest
Image
AR
model
Binary
image
Change
Detection
Figure 9: Processing scheme for change detection.
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Application
Table 1: Change detection results obtained
Case of Interest Number of Detected Pd Area Number of FAR
Mission Pass known targets Targets [Km2] false alarms
1 5 25 25 1.00 6 0 0.00
2 5 25 16 0.64 6 9 1.50
3 5 25 25 1.00 6 1 0.17
4 5 25 22 0.88 6 2 0.33
1 6 25 25 1.00 6 1 0.17
2 6 25 25 1.00 6 2 0.33
3 6 25 25 1.00 6 3 0.50
4 6 25 25 1.00 6 15 2.50
Total 200 188 0.94 48 33 0.69
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Application
Number of Number of
detected targets1 false alarms
Our proposal 188 33
Reference paper 188 52
1Number of known targets = 200.
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Application
0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
FAR
0.85
0.86
0.87
0.88
0.89
0.9
0.91
0.92
0.93
0.94
0.95
Pd
Figure 10: ROC curve obtained with the proposed method.
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Conclusions
In this paper we proposed the use of an AR(1) model for a stack of eight
SAR images to retrieve a ground scene estimation.
By using this technique, it was possible to obtain a reliable representation
of the ground scene.
In CDA, we obtained competitive results of Pd and FAR when compared
with the literature.
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References i
L. M. Ulander, W. E. Pierson, M. Lundberg, P. Follo, P.-O. Frolind,
and A. Gustavsson, “Performance of VHF-band SAR change
detection for wide-area surveillance of concealed ground targets,” in
Algorithms for Synthetic Aperture Radar Imagery XI, vol. 5427.
International Society for Optics and Photonics, 2004, pp. 259–271.
K. Folkesson, G. Smith-Jonforsen, and L. M. Ulander, “Model-based
compensation of topographic effects for improved stem-volume
retrieval from CARABAS-II VHF-band SAR images,” IEEE
Transactions on Geoscience and Remote Sensing, vol. 47, no. 4, pp.
1045–1055, 2009.
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References ii
L. Ulander, A. Gustavsson, J. Fransson, M. Magnusson,
G. Smith-Jonforsen, K. Folkesson, B. Hallberg, and L. Eriksson,
“Mapping of wind-thrown forests using the VHF-band CARABAS-II
SAR,” in IEEE International Symposium on Geoscience and Remote
Sensing. IEEE, 2006, pp. 3684–3687.
R. Machado, V. T. Vu, M. I. Pettersson, P. Dammert, and
H. Hellsten, “The stability of UWB low-frequency SAR images,”
IEEE Geoscience and Remote Sensing Letters, vol. 13, no. 8, pp.
1114–1118, 2016.
M. Lundberg, L. M. Ulander, W. E. Pierson, and A. Gustavsson, “A
challenge problem for detection of targets in foliage,” in Algorithms
for Synthetic Aperture Radar Imagery XIII. International Society for
Optics and Photonics, 2006.
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References iii
L. M. Ulander, M. Lundberg, W. Pierson, and A. Gustavsson,
“Change detection for low-frequency SAR ground surveillance,” IEE
Proceedings-Radar, Sonar and Navigation, vol. 152, no. 6, pp.
413–420, 2005.
S. M. Kay, Fundamentals of Statistical Signal Processing. Detection
Theory, Volume II. Prentice Hall, 1998.
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Thank you!
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