th/ma09 
mporal 
ym SPIE 
    
  
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
    
INTEGRATED FUSION METHOD FOR MULTIPLE 
TEMPORAL-SPATIAL-SPECTRAL IMAGES 
Huanfeng Shen 
School of Resource and Environmental Science, Wuhan University, P.R. China 
shenhf@whu.edu.cn 
KEY WORDS: Data fusion, remote sensing, multiple temporal-spatial-spectral images 
ABSTRACT: 
Data fusion techniques have been widely resear 
ched and applied in remote sensing field. In this paper, an integrated fusion method 
for remotely sensed images is presented. Differently from the existed methods, the proposed method has the performance to 
integrate the complementary information in multip 
in one unified framework, two general image observati 
le temporal-spatial-spectral images. In order to represent and process the images 
ion models are firstly presented, and then the maximum a posteriori (MAP) 
framework is used to set up the fusion model. The gradient descent method is employed to solve the fused image. The efficacy of the 
proposed method is validated using simulated images. 
1. INTRODUCTION 
In order to get more information, image fusion techniques are 
often used to integrate the complementary information among 
different remote sensing images. By far, a great number of 
fusion methods for remote sensing images have been developed 
(Luo et al., 2002; Pohl and van Genderen, 1998). Classical 
remote — sensing image fusion techniques include 
panchromatic(PAN) / multi-spectral(MS) fusion (Joshi and 
Jalobeanu, 2010; Li and Leung, 2009), MS / hyper-spectral(HS) 
fusion (Eismann and Hardie, 2005) and multi-temporal (MT) 
fusion (Shen et al., 2009) etc. However, most fusion methods 
were developed to fuse images from two sensors, and little 
work attempted to solve the fuse problem of more sensors. In 
this paper, we propose an integrated fusion method for multiple 
temporal-spatial-spectral scales of remote sensing images. This 
method is based on the maximum a posteriori (MAP) 
framework, which has the performance to fuse images from 
arbitrary number of optical sensors. 
2. IMAGE OBSERVATION MODELS 
The image observation models relate the desired image to the 
observed images. Let x —[xj,x5..... Xp, 1 denote the desired 
image with B, being the total band number. Generally, the 
band numbers of the observed images are less than or equal 
to B,. Here we use y to denote the images whose band number 
is equal to B, and use z to denote the images whose band 
number is less than B, . Thus, the bth band of the kth image of 
y can be denoted as yy 5, and the bth band of the kth image 
of z canbe denoted as z; p - 
The observation model in terms of y; ; is represented as 
Jk,p 7 Dy kM y ky k,pXp * Phy kb (1) 
where S represents the blur matrix, M, , is the motion 
ykp 
matrix, D, , is down-sampling matrix, and mn, , represents 
the noise vector. For convenience, equation (1) can be rewritten 
as (2) by substituting the product of matrices Sy kb» My and 
D, with Ay kb 
Yk,b 7 Ay kb Xp + My Kb (2) 
The second image observation model relates the desired 
image x to the observed image z . Generally the band of z is 
wider than that of x . It has been proved that a wide-band image 
is almost a linear combination of several narrow-band images 
when the wide band approximately covers the narrow bands 
(Boggione et al., 2003; Li and Leung, 2009; Vega et al., 2009). 
Thus, if the spatial resolutions of x and z are same, the 
spectral combination model can be denoted as 
B, 
za.) — Y epa pp) tia tma) 0) 
p=l 
where c, y, is the corresponding weight of the pth band value 
xp, J) , Tgp 18 aN offset, and n, (i,j) is the noise. It can be 
expressed in matrix vector form as 
Up = Cz,k,0X + Tp,pl + M2, kb (4) 
In more general case, the model can be rewritten as 
2.5 7 D; Mz Sz (Cox ou D + Az Ep © 
Simplifying this equation by multiplying corresponding 
matrices and vectors 
Zp = Az i pX + Tok bBo kb TM kb (6) 
3. THE FUSION METHOD 
The proposed method is based on the maximum a posteriori 
(MAP) framework. For the MAP model, given the 
images y and z , the desired image can be estimated as: 
x - argmax p(x | ,2) (7) 
x 
Applying Bayes' rule, equation (7) becomes: 
de ME aX p(x)ply,z| x) (8) 
x p(y.z)