Evaluation of a Statistical Fusion of Linear Features in SAR Data

Abstract

In this paper, we describe an extension of an automatic road extraction procedure developed for single SAR images towards multi-aspect SAR images. Extracted information from multi-aspect SAR images is not only redundant and complementary, in some cases even contradictory. Hence, multi-aspect SAR images require a careful selection within the fusion step. In this work, a fusion step based on probability theory is proposed. During fusion each extracted line primitive is assessed by means of Bayesian probability theory. The assessment is based on the attributes of the line primitive (i.e. length, straightness, etc), global context and sensor geometry. The fusion and its integration into the road extraction system are tested in a sub-urban SAR scene.

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EVALUATION OF A STATISTICAL FUSION OF LINEAR FEATURES IN SAR DATA

A. Karin Hedman, B. Stefan Hinz, C. Uwe Stilla

A. Astronomical and Physical Geodesy, B. Remote Sensing Technology, C. Photogrammetry and Remote Sensing
Technische Universitaet Muenchen, Arcisstrasse 21, 80333 Munich, Germany


ABSTRACT

In this paper, we describe an extension of an automatic
road extraction procedure developed for single SAR images
towards multi-aspect SAR images. Extracted information
from multi-aspect SAR images is not only redundant and
complementary, in some cases even contradictory. Hence,
multi-aspect SAR images require a careful selection within
the fusion step. In this work, a fusion step based on
probability theory is proposed. During fusion each extracted
line primitive is assessed by means of Bayesian probability
theory. The assessment is based on the attributes of the line
primitive (i.e. length, straightness, etc), global context and
sensor geometry. The fusion and its integration into the road
extraction system are tested in a sub-urban SAR scene.

Index Terms— SAR data, fusion, road extraction

1. INTRODUCTION

By the development of new, sophisticated SAR-
systems, automatic road extraction has reached a new
dimension. Satellite high resolution SAR data are already
provided by the German satellite TerraSAR-X and the
Italian satellite system COSMO-SkyMed. Airborne images
already provide resolution up to 1 decimeter [1].
When working with road extraction from SAR images,
one should also keep in mind the inevitable consequences of
the side-looking geometry of the SAR sensor; occlusions
caused by shadow- and layover. In case of adjacent high
buildings and narrow streets, the roads might not even be
visible on the SAR image. Strong scattering caused by
metallic objects or by adjacent vegetation occur frequently
and hinder important information about the roads.
Furthermore it is hard, even for an experienced SAR user to
distinguish between real roads and linear shadow regions.
Preliminary work has shown that the usage of SAR
images illuminated from different directions (i.e. multi-
aspect images) improves the road extraction results. This
has been tested both for real and simulated SAR scenes
[2][3].
In this paper we will discuss the results of a fusion
approach developed for multi-aspect SAR data and its
implementation into an automatic road extraction system.

2. ROAD EXTRACTION SYSTEM

The extraction of roads from SAR images is based on an
already existing road extraction approach [4][5], which was
originally designed for optical images with a ground pixel
size of about 2m [6]. The first step consists of line
extraction using Steger’s differential geometry approach [7],
which is followed by a smoothening and splitting step. By
applying explicit knowledge about roads, the line primitives
are evaluated according to their attributes such as width,
length, curvature, etc. The evaluation is performed within
the fuzzy theory. A weighted graph of the evaluated road
primitives is constructed. For the extraction of the roads
from the graph, supplementary road segments are
introduced and seed points are defined. Best-valued road
candidates serve as seed points, which are connected by an
optimal path search through the graph. The road extraction
approach is illustrated in Fig. 1.
The fusion module presented in this paper is adopted
towards multi-aspect SAR images. Instead of using fuzzy-
functions (marked in gray in Fig. 1), a probabilistic
formulation is introduced.

Line
Extraction
Attribute
Extraction
Line
Evaluation
Fusion
Optimum Path
Calculation in
Weighted
Graph
Fig. 1. Automatic Road Extraction Process

3. FUSION MODULE

A line extraction from SAR images often delivers partly
fragmented and erroneous results. Especially in forest and in
urban areas over-segmentation occurs frequently. Even an
experienced SAR user might have problems to differentiate
between true roads and linear shaped shadows. Attributes
describing geometrical and radiometric properties of the line
primitives can be helpful in the selection. However, these
attributes may be ambiguous and are not considered to be
reliable enough when used alone. Furthermore, occlusions
due to surrounding objects cause gaps in the line extraction,
which are hard to compensate.

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The concept of the fusion module presented here is that
the fusion shall make use of both sensor geometry
information as well as context information.

3.1. Fusion based on Bayesian probability theory

The underlying theory of the approach originates from
Bayesian probability theory

(
(
p X I

Bayes’ theorem follows directly from the product rule:

(
, p Y X Ip Y X I

The strength of Bayes' theorem is that it relates the
probability that the hypothesis Y is true given the data X to
the probability that we have observed the measured data X if
the hypothesis Y is true. The latter term is much easier to
estimate. All probabilities are conditional on I, which is
made to denote the relevant background information at
hand.
The main feature involved in the road extraction process
is the line primitive, which can either be identified as ROADS
(Y1), or as something else (i.e. FALSE ALARMS, SHADOWS,
RIVERS etc..). In this work we have chosen to incorporate
the two classes FALSE ALARMS (Y2), and SHADOWS (Y3). The
class FALSE ALARMS represent the relatively bright line
extractions mainly occurring in forest areas, caused by
volume scattering.
In our case the measured data X corresponds to
geometric and radiometric attributes of the line primitive -
an attribute vector. The selection of attributes of the line
primitives is based on the knowledge about roads. The
attributes used in this work are mean intensity, length, and
straightness. More attributes do not necessarily mean better
results, instead rather the opposite occur. A selection
including a few, but significant attributes is recommended.
If there is no correlation between the attributes, the
likelihood p(X|Yi) can be assumed equal to the product of
the separate likelihoods for each attribute.

(

Each separate likelihood can p(xi|Yj) be approximated by
a probability density function learned from training data as
discussed in [8]. Please note that the estimated probability
density functions should represent a degree of belief rather
than a frequency of the behavior of the training data. The
obtained probability assessment shall correspond to our
knowledge about roads.
)
()()
)
,
,
p X Y I p Y I
p Y X I
⋅
=
(1)
)()()
,p X I
=⋅
 (2)
)()() ()()
1212
,,..
jnjjjnj
p X Yp x xx Y p x Yp x Y p x Y
==
…
(4)
Since we work with multi-aspect SAR data extracted
information shall be combined from two or more SAR
scenes. Then the hypotheses above will be extended to the
assumptions whether a ROAD truly exist in the scene or not.
We need to add a third term to our measured data X; the fact
that a line has been extracted (L) or not extracted (L) from
one or more images.
Additional information of global and local context is
helpful to support or reject certain hypotheses during fusion.
Global context play here an important role and can be
incorporated in the posterior as well as the prior
probabilities. Roads are more likely to appear in urban
areas. Shadows occur frequently in forest areas, which are
likely to be mistaken as roads. Furthermore one can assume
that it is much more likely to successfully detect a road
surrounded by fields than a road in the middle of the forest.
Exploiting sensor geometry information relates to the
observation that road primitives in range direction are less
affected by shadows or layover of neighboring elevated
objects and should therefore be better evaluated than road
primitives in azimuth direction.
By incorporating the detection of the line, L, the global
context C as well as the sensor geometry as input
information, and in the end, we have the following
expression;

(
(

By means of this statement and by means of the product
rule, the expression above can be written as;

(
(
(
,()
j
p

where
p(X|CnLn,Y1,I) = the posterior probability that the data X
is measured if a ROAD exist AND surrounded by the context
Cn AND a line has been extracted. Most probably the
attributes of the line depends on the surrounding context.
Roads tend to be relatively shorter in urban areas than in
other global context areas. Since the probability density
functions of the attributes are defined by training data in all
context areas, we apply the theorem of marginalization.

(
, ,p X L Y Ip X C L Y I dC
−∞

p(Ln|Cn,Y1,I) = the posterior probability that a line
primitive is extracted, if a ROAD truly exist. This term is
varied due to both context area and the relationship between
)
)
()
11
1
111
,..,,,.., ,,..,
,..., ,,.., ,,.., ,
jnnn
nnnjj
p Y XXL L CC I
p XXLL CC Y I p Y I
∝
⋅
(5)
)
)( ) (
(
)
)
)
1
21212
1
11111
,,...,,,,... , ,...,
,,,,..,,,,,.
..,,,..., (
,
,
)
n
jnnn
jnnnjj
njjj
j
p Y XXX C CC L LL I
p X L C Y I p X L C Y I p L C Y I
p L Y C IC YC Y p Y I
p
∝
(6)
)()
, , ,
+∞
=∫
(7)

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the road’s direction and the SAR sensor geometry. By
assuming a simple geometric model (see Fig. 2), the
posterior probability p(Ln|Cn,Y1,I) is varied depending on
incidence angle of the SAR sensor, θ, and the difference
between the look angle of the SAR sensor and the direction
of the road, β. This term is especially useful by supporting
or rejecting hypotheses regarding SHADOWS and ROAD.
p(Cn| Y1,I) = the posterior probability that the context Cn
occur if a ROAD exist. This term might be hard to define, but
can be of significance in urban areas, if the main directions
of the road are known in advance. In this work, this
probability is set equal to all occasions.
p(Y1,I) = the prior or subjective probability that a road
exist in the image. Here one can take advantage of global
context. Global context regions can be derived from maps
or GIS before road extraction, or can be segmented
automatically by a texture analysis. As a start, global
context (BUILT-UP AREAS, FIELDS, FOREST and OTHER) is
extracted manually.

Fig. 2. A tree with the height h stands nearby a road with the width w
and causes a shadow, Sn. θ is the incidence angle of the SAR sensor, β is the
difference between the sensor’s look angle and the direction of the road.

3.2. Fusion of line primitives

First of all, the line primitives are sorted according to its
discriminant value

( )
(
(
1
ln , ,g x p x L Y I

The line primitive with the highest discriminant value is
chosen first. Then, all neighbouring primitives are searched
for. Those parts of the neighbouring primitives, which
satisfy overlap and collinearity criteria (i.e. buffer width and
direction difference) are assumed to be redundant
extractions and are removed. If only a part of the
neighbouring line primitive is fused, the line primitive is
clipped and the non-fused part remains in the search. Also,
lines with an all too deviant direction according to the best-
evaluated line remain. The best-evaluated primitive obtains
a probability based on (6) depending on integrating context
information or not.
Then, the primitive yielding the second highest
maximum likelihood of being ROAD is chosen and processed
with the same algorithm. The whole fusion process ends
after all primitives have been processed.

)
)
()
()
2
ln,,p x L Y I
=−
(8)
4. RESULTS AND DISCUSSION

Three tests were carried out; single SAR scene (1), two
multi-aspect SAR scenes (one illuminated from the top and
one from the upper right corner, - with 45° difference)
without (2) and with (3) context information (Figs. 3-8).
The subjective posterior and prior probabilities used in this
work can be seen in Tab. 1 and 2.
The results achieved so far are promising in terms that
the evaluation of the lines is on one hand statistically sound
and, on the other hand, it closely matches the assumptions
on the significance of different attributes with respect to
their distinctiveness. However, the results also exemplify
the complexity of road extraction from multi-aspect SAR
images. On one hand a more complete results is achieved,
but on the other hand, the correctness is rather poor in
comparison to results extracted from one single image (Tab.
1). The reason for this is the over-segmentation in
combination with the severe behavior of the Bayesian
fusion. Incorporating global context and sensor geometry
improves the correctness, but not significantly. In the future
this part can be modeled rather as a reasoning step than
assessed by means of probabilities. Still the fusion has to be
tested on larger scenes with different complexities as well as
be analyzed further in detail.

Global
context, CG
Y=ROAD
FIELD
0.3
P(Y,I)
Y=SHADOW
0.3
Y=F A
0.4
URBAN 0.4 0.3 0.3
FOREST 0.1 0.3 0.6

Table 1. Prior probabilities used in test 3.


P(L|FIELD,Y,I)
Sensor
geometry
CR
Y=ROAD Y=SHADOW
R
C
CS
S
C
L
0.9 0.73*)
0.7 0.3
L
0.1 0.27 0.3 0.7

Table 2. Posterior probabilities used in test 3. The criteria are defined
based on the model in Fig. 3, assuming h=15m and w= 10 m.
CR: Roads within a β, which gives a possible shadow less than
a 1/3 of its width w. CS: Width of shadows caused by
trees/buildings equal to the width parameter of the line
extraction. *) Estimated from training data.



One single
image
Fusion of two
images - no
context C
Fusion of two
images
incorporating
context C
Completeness 55 % 75 % 74 %
Correctness 90 % 58 % 69 %

Table 1. Completeness and correctness as defined in [6]

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Fig. 3. The ground truth and one of the SAR
images analyzed in this work

Fig. 4. Line primitives extracted from the two
SAR scenes and classified into three classes;
ROAD (green),
SHADOW (yellow),
ALARMS (red)
FALSE

Fig. 5. Classification of the line primitives after
fusion; ROAD (green), SHADOW (yellow), FALSE
ALARMS (red)

Fig. 6. Extracted roads from one single SAR
scene
Fig. 7. Extracted roads from two multi-aspect
SAR scenes
Fig. 8. Extracted roads from two multi-aspect
SAR scenes. Global context and the sensor
geometry are incorporated during the fusion
process.



4. ACKNOWLEDGEMENT

The authors would like to thank the Microwaves and
Radar Institute, German Aerospace Center (DLR) for
providing SAR data.

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