The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
The Ini 
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MI(U, V) = H(U) - H(U\ V) 
= H(V)-H(V\U) (1) 
= H(U) + H(V)-H(U,V) 
Where U and V are two images to be matched. H(U) and H(V) 
are the margin entropy of U and V .respectively, and they describe 
the uncertainty of stochastic variable. The H(U,V) is the joint 
entropy of images U and V . The H(U\V) is the conditional 
entropy, which describes the total amount of uncertainty of U 
when V is known. The relationship between mutual information 
H(U,V) = -^p uv (u,v)\ogp uv (u,v) (3) 
w,v 
H(U\V) = P UV (w, v) log p w (u I v) (4) 
u,v 
Where P(u) and P(v) are the marginal probability distribution of 
variables U and V , P(u,v) is their joint probability. For grey 
image, P{u) and P(v) can be estimated by their grey histograms, 
respectively, and P(u, v) can be estimated by their joint histogram. 
MI(U, V) 
An alternative NMI(U, V) was proposed by Studholme et al (1999): 
NMI(U,V) 
H(U) + H(V) 
H(U,V) 
Figure 1. The relationship between mutual information 
and H(U),H(V),H(U,V) and H(U\V) 
and H(u), H(V), H(U,V) and Ff(t/|F) is shown in Figure 1. 
This alternative is designed to compensate for the sensitivity of MI 
to changes in image overlap. The results of their experiments 
indicate that the NMI(U,V) measure provides significantly 
improved behaviour over a range of imaging fields of view. 
In Figure 1, the circle denotes the margin entropy of image, the 
united area of two circles denotes joint entropy, and the overlap 
part of two circles is mutual information. It is shown that mutual 
information integrates margin entropy and joint entropy, and it is 
the difference of the both. Entropy is often expressed by 
probability density of variable, as follows: 
H(U) = Pu( u ) l °8Pu( u ) (2) 
U 
3. EXPERIMENT DATA AND MATCHING METHOD 
The test images are the remote sensing images captured by 
different sensors, in different season and time with different spatial 
resolution (Some are shown in Figure 2). SPOT (pan) acquired on 
December 21, 1999 with 10-meter spatial resolution are regarded 
as reference images. They all have 256x256 pixels. Corresponding 
IRS-C (pan) images acquired in July 1996 are used as the source 
images for generating input image samples for template matching. 
The spatial resolution of IRS-C (pan) image is 5.8 meter. Several 
of the input image samples with 65x65 size are obtained by 
(a) 
(b) 
(c) 
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Figure 2. Some scene images used to experiment: (a), (b) and (c) are the IRS-C source input images and corresponding 
SPOT reference images, respectively, and named by Village, Stream and Farmland, (d) is an input image cropped from 
IRS-C(pan) Farmland, and its size is 65 X 65 pixels.