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In: Wagner W., Szflcely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010,1 APRS, Vol. XXXVIII, Part 7B
Fig. 4. (a) Original image; (b) Ratio response map (edges
probability map); (c) Over-segmentation results
And then, Meanshift (Dorin Comaniciu, 2002) based over
segmentation algorithm is employed on the edges probability
map to divide original images into superpixies (as shown in fig.
4.c).
A superpixel captured from pre-segmentation is the smallest
unit in an image and can be assigned only a class label. Each
superpixel in images is extracted a set of features consisted of
gray histogram, SoftLBP (Ahonen T, 2007).
3.2 Linear Target Prior
Linear Target Priors (LTP) utilizes the shape of linear target to
improve the edges of classification results. This prior
information comes from the relative location between linear
targets and image pixels (or superpixels) around them. For
example, we wish to make use of the fact that all pixels
adjoining river banks are water or farmland (in a certain length).
Thus, the first is detecting the linear targets in SAR images. In
this paper, the fusion operates of D1 and D2 operates is
employed to detect linear targets (edges). And then, the LTP is
captured in the following ways.
3.2.1 Distance Map: The distances from points (pixels) to
lines (linear targets) are calculated as the method presented in
(Kumar M.P., 2005). Given lines O , the distance
d = dist(pAl) between point p and Q is the distance
between point p and point p' which is the nearest point in lines
Q to point p (as shown in fig.5.a). The distance map is shown
in fig.5.c.
I Nil A
P im ( c l/>;> Q >f (,) ) = ex P Z ¿«list ( A,fT ) Z cont ( c > A- )
7=1
cont ( c, p i , Rf
1, if Pi and c = maxlabel (Y (,) , )
(2)
other
Where, p. is LTP weight and maxlabel(l(t), •) is the
maximum class of pixels in region R = { Rq } of previous
iteration classification results Y^\ Fig.6 shows an example of
LTP map for class building, water, farmland and woodland in
SAR image. These LTP probability values map to the full range
of values in the cool-hot colormap.
Fig. 6. (a) linear target prior map for building; (b) linear
target prior map for water; (c) linear target prior map for
farmland; (d) linear target prior map for woodland.
3.3 Iterative MRF Model with LTP
The posteriori probability of the proposed model is added LTP
based on Eq.l as shown in Eq.3:
p(y, \s : )p„(y,\y„)P Lrn (y, k.n.r“)
P im (y, |s, A7“) = £ P lm (y, | p„0,y<'>)
Where, s,; is /-th superpixels in image and p,; is a pixel in Sj,
Pi.TPi is linear targets prior of Sj. The overall image posteriori
probability is:
Fig. 5. (a) sketch of distance from pixels to lines; (b)
linear target map; (c) distance map from pre-pixels to
linear tagets.
3.2.2 LTP Map: LTP is learned from the labelled image data
(classification results of previous iteration in practice), so it
changes from iteration to next iteration. Firstly, the linear target
O are divided into sub-lines with a certain length,
f> = (Oj, ...iTvsi}. And a sub-line il 7 divides its adjacent area
into K regions, we address them sub-line regions
R = {R(Qj)} k . Then, the LTP of a pixel p, for class c is
shown by Eq.2:
If,
P{Y\ 1,0., T w ,©) = n/^, k,n,y<->)
(4)
T (,+1) = argmaxj/TT 0 ^ | /,Q,T (O ,0)}
y (t+l)
A GraphCut-based optimization algorithm presented in Boykov
Y, 2001 has been used to effectively capture the global optimal
resolution of Eq.4. The training steps of the proposed Iterative
MRF model with LTP have been listed in the following:
1) Utilize edge detection template in fig.3.a to get edges
probability map of input images;
2) Over-segment the edges probability map to get
superpixels;
3) Extract features in each superpixel;
4) Training AdaBoost classifier with labeled groundtruth
data;
The testing steps of Iterative MRF model with LTP are shown
in the following: