WATER/LAND SEGMENTATION FOR SAR IMAGES BASED ON GEODESIC DISTANCE
Hua Zhong, Qing Xie, L.C. Jiao, Shuang Wang27 July 2011
Key Laboratory of Intelligent Perception and Image Understandingof Ministry of Education of China, Xidian University,
Xi'an 710071, P.R. China
OutlinesOutlines
1
2
3
4
Research Background
Geodesic Distance
The Proposed Method
Experimental Results
Research BackgroundResearch Background
Characteristics of SAR
① Advantage: working without solar illumination and in all weather conditions, compared to satellite optical images.
Many applications:
For instance, imaging the Earth surface, environmental monitoring, target detection ( coastline, bridges, etc ).
Research BackgroundResearch Background
Characteristics of SAR
② Disadvantages: SAR is affected by multiplicative speckle,
gives the images a grainy appearance
makes the interpretation of SAR images a challenging task
Research BackgroundResearch Background
Why focus on water/land segmentation in SAR image?
An important application
Water/land separation in synthetic aperture radar (SAR) images is an increasingly used tool in environmental monitoring applications such as flood extent mapping or coastline extraction.
Research BackgroundResearch Background
Characteristics of Water/Land segmentation
Water/land separation is a particular case of SAR image classification, with only two classes to assign. Water surfaces:
behave as specular reflectors at radar wavelengthsappears as low intensity areas in SAR images
Land:Comparatively brighterthe rougher surrounding terraincharacterized by diffuse scattering.
The job seems easy, however, difficult, in fact, because of the influences of the depth, the complexity of water/land boundary, and the wide range of land intensities. Also the multiplicative speckle SAR images increases the difficulties,and it is difficult to reach a precise segmentation.
FrameworkFramework
Our method includes two steps: Coarse segmentation
roughly segments between water/land regions only based on the probability models for speedRefinement.
refines only the boundary areas using geodesic distance with automatically generated class labels and adaptively determined bandwidth.
We only applies the distance computation in the refine step, because the computation of geodesic distance costs most of the runtime, and the precise outlines is expected especially in those tiny details such as complex shaped shorelines, bridges and quay shipside. Boundary area with adaptive bandwidth can further accelerate the segmentation..
FrameworkFramework
What we have done?a novel method for water/land segmentation is proposed based on the framework of geodesic distance.
1. Water/land modelingaccording to the statistics of both the speckle and land covers,which leads to a fast point-wised coarse segmentation
2. Boundary area with adaptive bandwidth Based on the water/land models, the boundary area between water and land can be localized with automatically generated class labels and adaptively determined bandwidth
3. Improved geodesic distance Then the refined segmentation is implemented using an improved geodesic distance, combining the manifold idea to enlarge the inter-class differences.
Briefly review ------ Geodesic Distance
Let and be the label set for object and background, respectively. The geodesic distance is simply the smallest integral of a weight function over all possible paths from the labels to any pixel . Specifically, the distance from each of the two classes of labels to any pixel is defined as
where
where is weight function for pixel , and is the path connects any two pixels and [4].
[4] X. Bai, G. Sapiro, “Geodesic Matting: A Framework for Fast Interactive Image and Video Segmentation and Matting,” Int. J. Comput Vis., vol. 82, pp. 113-132, 2009.
Geodesic DistanceGeodesic Distance
OΩ BΩ( )d x
x
( ) min ( , ), { , }ll s O BD x d s x l∈Ω= ∈ Ω Ω
2
, 1 21 2 11 2 ,( , ) min ( ) ( )
s s
s
C i s s i isd s s Y x C x dx= ⋅∫
( )iY x ix1 2,S SC
1s 2s
1. Water/land models
The labels for both classes can be obtained offline:
: the water, assumed to follow the gamma distribution
- the land, modeled as Gaussian mixed model (GMM) , representing the widely spread intensity range of land cover.
The Proposed MethodThe Proposed Method
LΩ
WΩ
1. Water/land models
For the water label set :
The probability distribution model is used according to gamma distribution,
where is intensity of a pixel, is the equivalent noise level (ENL)
of , is the mean of pixel intensities in .
The Proposed MethodThe Proposed Method
( )WF v
1
( ) exp( )( 1)!
N N
W N
N v N vF vN I I
−⋅ ⋅= −
−
v NWΩ I WΩ
WΩ
1. Water/land models
For the land label set :
we construct as followed:
,
where and .
The mean and the std can be obtained directly through the set
The parameters and are computed from the subset , which includes the pixels with intensities larger than a threshold.
The weights and are used to balance the role of and .
The Proposed MethodThe Proposed Method
LΩ
( )LF v
1 1 2 2( ) ( ) ( )LF v k f v k f v= ⋅ + ⋅
21 1 1( ) ~ ( , )f v N μ σ 2
2 2 2( ) ~ ( , )f v N μ σ
1σ LΩ1μSΩ2μ 2σ
1k 2k1( )f v 2 ( )f v
1 2 1k k+ =
2. Boundary area with Adaptive bandwidth
Given the boundary (which can be obtained from the coarse segmentation, a sliding window is taken along with the center pixel denoted as and the radius as .
Intuitively, the bandwidth depends on two factors:
1. boundary variance
2. smoothness
The Proposed MethodThe Proposed Method
∂Ω( )N x ∂Ω
x ( )R x
2Bσ
L∇
2. Boundary area with Adaptive bandwidth
The boundary variance is defined as
which means how much the boundary can be distinguished, and helps to control the width of the current window.
is the weight for each pixel
is the Euclidean distance between pixel and the boundary .
is the weighted distance, presented as:
The Proposed MethodThe Proposed Method
( )w y
2Bσ
2
( )2
( )
( )( ( ) ( ))( )
( )
E Ey N x
B
y N x
w y d y d xx
w yσ ∈
∈
−=∑
∑
( )Ed y y ∂Ω( )Ed x
( )
( )
( ) ( )( )
( )
Ey N x
E
y N x
w y d yd x
w y∈
∈
=∑∑
y
2. Boundary area with Adaptive bandwidth
The smoothness factor reflects is defined as
where is the length of within the window .
the smaller is, the smoother the boundary is.
The Proposed MethodThe Proposed Method
L∇
∂Ω
( ) ( ) 2 ( )L x L x R x∇ = −
( )L x ∂Ω ( )N xL∇
2. Boundary area with Adaptive bandwidth
Finally, the adaptive bandwidth with the radius is obtained as
And the sliding windows along with the radius consist the
adaptive boundary area .
The Proposed MethodThe Proposed Method
* ( )R x
* ( ) max{ ( ), ( ) ( )}E BR x L x d x xσ= ∇ +
L∂Ω * ( )R x
beltΩ
The Proposed MethodThe Proposed Method
3. Improved geodesic distance
Inspired by the idea of manifold , the distance can be approximated by adding up a sequence of “short hops” between neighboring points.
Let denotes the new weight function, a factor is introduced in order to amplify the between-class distance and minify the within-class difference. is defined as
It is obviously that through we can easily amplify the difference range from to . Replacing the weight with , we can get the improved geodesic distance .
'( )iY x ρ
'( )iY x( )'( ) l iF x
iY x ρ∇=
ρ[ ]0,1 [ ]1,ρ ( )iY x '( )iY x
( )lD x
FrameworkFramework
The details: 1. Establish the models and for the water/land, respectively, as
described in section 3.1; 2. Coarse Segmentation: For each pixel , its probabilities belong to
water and land are computed according to the models, and then coarsely segmented.
3. The coarse boundary could be acquired based on the coarse segmentation result.
4. Locate the adaptive boundary area, as described in section 3.2; At each sliding window on , the pixels whose likelihood rank thelargest ones are selected as the automatically generated labels for each class.
5. Refinement: perform the improved geodesic distance in the boundary area to get the refined boundary.
Fig.1. Step results of the proposed method. (a) Real SAR image; (b) Coarse Segmentation; (c) Automatically generated labels (point labels for land and lines for water); (d) Boundaryarea with adaptive bandwidth; (e) Geodesic distance to water labels (brighter pixels meansthe shorter distance); (f) Refined results.
ExperimentsExperiments
(a) (b) (c)
(d) (e) (f)
ExperimentsExperiments
Fig. 1(b) shows coarse segmentation of Fig. 1(a) fast using only the probability modelslocalization of initial boundary area very well the automatically generated labels (Fig. 1(c)) are correct due to
the effectiveness of our probability models. Fig 1(d)-(f) show the process of refinement.
the boundary area with adaptive bandwidth in Fig.1(d) can reflect well the complexness of the boundary. ( the area around the bridges and quays has larger harbor
bandwidth, and the area along the riverside is smaller in comparison)Fig. 1(e) gives the map of the geodesic distance( the difference between water and land is very clear. )
in Fig 1(f), the tiny details of the bridges and the quays are better maintained.
Fig.2. Some example images (first line) and the segmentation results (second line)
ExperimentsExperiments
ExperimentsExperiments
Fig. 2 presents some results on the other real SAR images.
as a whole, the details are also very clear.from Fig. 2(a), we can see that though the land background is
complex, and the contour of water body is complicated with many tiny details, the proposed method accurately segments water from land regions, with the important details well maintained such as the shape of riverside and bridges, including a very thin one, which is difficult to be distinguished by human eyes. our segmentation result shows high interior uniformity in both
land area and water part. fig. 2(b) and (c) show images with quays, which locate very
close and seem hard to segment. In addition, each quay has different contour but looks similar. Our method accurately maintains the clear shape of each quay and the tiny space between quays.
ExperimentsExperiments
the linear complexity Our method has the linear complexity due to the use of
geodesic distance.On the other side, we only apply the distance computation in
the refine step to further reduce computation complexity.Also, boundary area with adaptive bandwidth can further
accelerate the segmentation. for example, the actual run time on Fig.2(c) ( with the size 190×190)
with a Matlab implementation on a Pentium 2.7GHz CPU– Our method with adaptivity boundary bandwidth: 18.18 seconds – Our method with fixed boundary bandwidth: 35.57 seconds
when applying geodesic distance for both the coarse segmentationand the refinement,
the run time increases rapidly and costs 690 seconds.
REFERENCES REFERENCES
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[3] M Silveira, S Heleno, “Water/Land Segmentation in SAR Images using Level Sets”, in Proc. ICIP 2008, San Diego, California, October 2008.
[4] X. Bai, G. Sapiro, “Geodesic Matting: A Framework for Fast Interactive Image and Video Segmentation and Matting,” Int. J. Comput Vis., vol. 82, pp. 113-132, 2009.
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