In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Voi. XXXVIII, Part 7B 
697 
Research on Change Detection in Remote Sensing Images by using 2D-Fisher Criterion Function 
Method 
Baoming Zhang, Ke Chen,Yang Zhou, Mingxia Xie, Hongwei Zhang 
Remote Sensing Information Engineering Department, Zhen Zhou Institute of Surveying and Mapping, Zhen Zhou, China, 
E-mail: zbm2002@vip.371.net, ckl702@,163.com, zhouvang3d@163.com, xmx0424@;vahoo.cn. hongwei0691@163.com 
KEY WORDS: change detection, Fisher criterion function, Image Threshold, two-dimension histogram, remote sensing image 
ABSTRACT: 
In this paper, 2D-Fisher criterion function was introduced to change detection in remote sensing images based on classic one 
dimension fisher criterion function, and this expanded the space of grey value from one-dimension to two-dimension and greatly 
improved the image noise-sensitivity. Meanwhile, in order to enhance the computing speed, we refined the solution method of 2D 
threshold in 2D-Fisher criterion function through transforming computing method from two-dimension threshold to two 
one-dimension thresholds and greatly reduced the detection time. Refined 2D-Fisher criterion function method was suitable not only 
for the change detection in remote sensing images, but also for other aspects in data processing. 
1. INTRODUCTION 
effectively de-noising, and achieve rapid change detection. 
The auto extraction of change area is the key of the change 
detection of multi-temporal remote sensing image. It’s easy to 
compute and has a fast computation speed. So how to find a 
threshold finding method with wide range of applications, good 
results of extraction and good performance of anti-noise 
becomes one of the main content of the research on remote 
sensing image change detection. Until now, domestic and 
foreign scholars have carried out extensive research on this 
problem and proposed kinds of methods to select threshold, for 
example, maximum variance between-class, maximum entropy 
method and so on. However, whether the maximum variance 
between-class or the maximum entropy method, its rule 
function only considers maximizing the variance between-class, 
in other words to maximize the degree of separation but without 
considering the discrete level in class within. And the two 
methods are only suitable when pixel number of change class 
and no change class are not different a lot. While the number of 
the two kinds of pixels is significantly different, neither one 
method is applicable. 
A good remote sensing image change detection method should 
not only maximize the separation degree between change class 
and no change class, but also make the change class and no 
change class’s dispersion degree minimum, that is, similarity of 
pixel in every class should be maximal. As we all know, in the 
pattern recognition theory, the Fisher criterion function can be 
used to get the best projection direction of feature vector. In this 
projection direction we can get the greatest distance between 
classes and the smallest distance in class. At this time, value of 
Fisher criterion function reached the maximum. Thus, Fisher 
criterion function is a good criterion to analyze the degree of 
class separation. 
The classical Fisher criterion function method is introduced into 
remote sensing image change detection and extended its original 
one-dimensional space of gray value to the two-dimensional 
space, such as the gray value - mean neighborhood gray 
(G-Mean), gray value - the Medium value of neighborhood gray 
(G-Medium) and so on. 2D-Fisher criterion function method is 
bring forward to apply to the remote sensing image change 
detection. Because 2D-Fisher criterion function method for 
solving adaptive threshold is complex to compute, we try to 
improve remote sensing image change detection 2D-Fisher 
criterion function method proposed in this paper. So it can 
2. FISHER CRITERION FUNCTION METHOD 
The essence of solving Fisher criterion function is to solve 
optimization problems, that means using a few linear 
combination (called the discriminant or canonical variate) 
i i t 
y 1 = X, y 2 = a 2 X, • • •, y r — Cl r X in p-dimensional 
vector X = (Xj, X 2 , • • •, X p y (usually r is significantly less 
than p) to replace the original p variables Xj, X 2 , * * *, X p , in 
order to achieve the reduced-dimensional purpose, and in the 
new projection space y — Cl'x, making the largest distance 
between the various classes and the smallest in one class. As is 
shown in Figure 1, for the two categories CO n and CO c , 
assuming that all classes are characterized by two-dimensional 
distribution (A, B part in Figure 1) and project them in straight 
line Y\ and Y 2 , you can clearly see that the separation 
between classes are particularly good at the direction of straight 
line Y 2 . 
Figure 1. Projection of two-dimensional feature vector in a 
straight line 
The bi-objective problem, namely class space will be the largest 
and the smallest category from, is transformed into 
single-objective optimization problem, that makes the formula 1 
get a maximum.