In: Wagner W., Szekely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B
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between two points. According to this theory, the specific
solving steps are as follows:
Step 1: To obtain two-dimensional histogram of difference
image;
Step 2: According to two-dimensional histogram to Select ^
extreme points from the difference image, as is shown in Figure
5 (usually make k = 6 );
Step 3: Obtain the corresponding values of each extreme point
in the 2D-Fisher criterion function.
Step 4: Select the two extreme points (s,, /j) and (S 2 ,t 2 )
corresponding to the largest two function value, (.Sj, t ] ) as the
center and (s 2 ,f 2 ) as vertex to make a rectangle. As
shown in Figure 6, namely, the area of red rectangle
[sj —|Sj -S 2 \,S } +|jj -S2|] X [A -|fj -t 2 \,ti +|/i -/ 2 |] is
the improved scope of the solution space.
From the above analysis we can get that the improved solution
space is the original solution space.
h ~k -^1,^1+h -s 2 Q x [a +K -*2p
[0,L-l]x[0,L-l]
Figure 5. The selection of maximum in two-dimensional
histogram
Figure 6. Improvement of solution space
2) Transform two-dimensional threshold into two
one-dimensional thresholds, so as to achieve the purpose of
improving the speed of detection
Respectively make use of each pixel gray value and
neighbourhood spatial information, according to the classical
Fisher criterion function method, to solve the optimal gray
* *
threshold value S and the best neighborhood threshold t ,
both of which constitute the two-dimensional threshold
(s ,t ) of remote sensing image change detection. Then
according to the two-dimensional threshold (5 ,t ) , do change
detection of the difference images.
In method 1), the improvement of solution space of
2D-Fisher criterion function is the original solution
space [^i ~ K ~ ^21 > + K ~ ^21] x ~ K ~ 6 Mi K ~ h Q
[0,I-ljx[0,L-l]
However, we need to traverse the entire image to obtain the
two-dimensional joint probability density of pixel gray value
and its neighborhood spatial information according to the
two-dimensional histogram. After that, it has nothing to do with
the image size itself. The number of run times (one run means
the process of calculating all kinds of probability, the mean and
variance each time) of the original solution space for solving is
(1 + 2 + • —I- 256) X (1 + 2 H— • + 256) (Assuming
gray-scale of the image is 256). After improved, the number
is 4— 61 • the Intel Pentium Dual 2.0 CPU, 2G
memory environment, the time one run required is probably
0.0384^ . Since the two extreme values fall mostly on both
sides of the middle-class gray, suppose that (120,120) is
the maximum point, and (129,129) is the second, the time
is 12.4416 S the best two-dimensional threshold required. It
can be known that no matter how narrow the solution space is,
the solution time can not satisfy the needs of practical
applications. Therefore, we chose method 2).
3.3 The specific process to improve 2D-Fisher criterion function
method.
The specific process of remote sensing image change detection
makes use of the improved 2D-Fisher criterion function method
(taking two-dimensional space of choosing G-Mean for
example):
Step 1: According to the pixel gray values and formula 4, obtain
the grey level histogram of the difference image and the
histogram of the mean value of gray scale in 3x3
neighbourhood area.
Step 2: On the histogram, as well as neighborhood average gray
histogram, take advantages of classical Fisher criterion function
method to get the one-dimensional optimal threshold S and
t and the two-dimensional threshold (s ,t )
respectively.
Step 3: According to two-dimensional threshold, analyze the
various elements to generate the results of image change
detection.
For (x,y)
ifdf(x,y) >s*)&&(g(x,y) >t))
Then (x, y) d CO c
Else
{x,y)d(D n
(S , t ) is the optimal threshold of image change detection.
4. EXPERIMENT AND ANALYSIS
In the above sections, through the Fisher criterion function in
the pattern recognition theory, we propose the remote sensing
