961
Beijing 2008
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008
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IFICATION
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based on
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irse sampling,
ial optimum
good as or
g methods in
most cases. The SVM method separates the classes with a
hyperplane surface to maximize the margin among them (see
Fig. 4), and m is the distance between H\ and H2, and
H is the optimum separation plane which is defined as:
w-x + b = 0, (1)
where x is a point on the hyperplane, w is a n-dimensional
vector perpendicular to the hyperplane, and b is the distance of
the closest point on the hyperplane to the origin. It can be found
as:
w• Xj+b<-1, fory. = -l (2)
w-x i +b> 1, for y. = +1
(3)
These two inequalities can be combined into:
Vz. (4)
The SVM attempts to find a hyperplane (1) with minimum
|| W 11 2 that is subject to constraint (4).
H2
Figure 4. Optimum separation plane.
The processing of finding optimum hyperplane is equivalent to
solve quadratic programming problems:
m in^|| H| 2
S.t. yXw-fix^ + b^X-^ (5)
£>0,/ = l,2,...,/
where C is penalty parameter, which is used to control the edge
balance of the error ^. Again, using the technique of Lagrange
Multipliers, the optimization problem becomes:
1 / / /
min V Z Z a i a jyiy j K ( x t .yj-X
1 /=1 № /=l
sjm Sw=°
1=1
0 < a, < C,i = 1,2,...,/ (6)
where K(x i ,y j ) = f(x i )-</)(y / )is kernel function. There are
three major kernel functions including Gaussian Radius Basis
Function (RBF), Polynomial, and Sigmoid function. The
optimum classification plane is solved through chunking, Osuna,
and SMO algorithms, and then we will only need to compute
K{x,,yj) * n the training process. The final decision function is:
f{x) = sgn(^^.«,/:(x, x,) + b) (7)
SV
When multi-class SVM is concerned, three basic methods are
available to solve the classification: One-Against-All (OAA),
One-Against-One (OAO), and Directed-Acyclic-Graph (DAG).
3.3 OBJECT OVERLAY ANALYSIS(OOA)
OOA namely polygon overlay analysis creates new features and
attribute relations by overlaying the features from two input
layers. Features from each input layer are combined to create
new output features. Attributes of each input feature are
combined from the two input layers to describe each new output
feature, thus creating new attribute relationships.
Boolean Algebra is useful for performing operations on the
attributes attached to object entities in the format of vector data.
Boolean algebra uses the logical operators AND, OR,NOT to
determine whether a particular condition is true or false. The
AND operator is the intersection of two sets - for example those
object entities that belong to both set A and set B. The OR
operator is the union of two sets - for example those entities that
belong to either set A or to set B. The NOT operator is the
difference operator identifying those object entities that belong
to A but not B.
OOA is analogous to the boolean logical operator OR, where all
elements from both input layers will be present in the output
layer,which is illustrated in the following example.
Figure 5. OOA sketch map.For areas a,f,g,l,the attributes are
1,2,3,4 from the first layer.And areas b,d,h are unchanged since
the attributes from two layers are the same, and reverse for the
rest areas.
4. TEST CASE
The proposed OLCD methodology was tested on the SPOT-5
and IKONOS images in order to assess its performance.The
result was compared to a robust pixel-level post-classification
comparison method.
4.1 Object-level change detections
The multidate segmentation was carried out from multisource
HR images using MS&RG multiscale segmentation
methodology. The segmentation parameters hs, hr were both set
at 50,20 for the before and after event image,according to the
“Try&Error” strategy. The parameter M was separately set at
250 and 300 to obtain segmented image with a minimum object
size.
After the segmentation, we selected spectra(mean) and
texture(contrast) characteristic of several objects from each
class as the training samples, taking advantage of statistic
methods and Gray Level Co-occurrence Matrix (GLCM)
filtering.During the classification processing, firstly, we scaled
the training samples and the testing samples before applying
SVM. Secondly, we chose RBF kernel, which is more suitable
to land use and land cover classification. Thirdly, we used
cross-validation and grid-search method to get the best
parameters of RBF. The highest overall accuracy on the
multi-source image information was obtained with y =0.3,0.25
and C=100, 130,respectively,where/is the width of the kernel
function, and C is the penalty parameter. At last, the training