1051 
GENERALIZED MODEL FOR REMOTELY SENSED DATA PIXEL-LEVEL FUSION 
Zhang Jixian, Yang Jinghui*, Li Haitao, Yan Qin 
Chinese Academy of Surveying and Mapping, Beitaiping Road 16, Beijing 100039, P. R. China 
*: Corresponding author. Email -jhyang@casm.ac.cn. Tel: +86-10-88217730 
Commission VII, WG VII/6 
KEYWORDS: Remotely Sensed Data, Fusion, Generalized Model, Implementation, PCA 
ABSTRACT: 
A generalized model characterizing most remotely sensed data pixel-level fusion techniques is very important for theoretical analysis 
and applications. This paper focuses on the establishment of a generalized model for most data fusion methods, which is helpful to 
quantitatively analyze and quickly implement different data fusion techniques. As an example, the PCA fusion method is selected to 
demonstrate the availability of the generalized model through the generalized model based implementation. 
1. NOMENCLATURE 
XS k : the k th band of the lower resolution multispectral image; 
P a the higher resolution panchromatic band; 
P an : the degraded panchromatic band; 
P anA : approximation coefficients after n level GLP 
(Generalized Laplacian Pyramid) or a trous wavelet 
decomposition; 
w 
P D : detail coefficients after n level GLP or a trous wavelet 
decomposition; 
xs L 
k : the k th band of multispectral image resampled or 
relatively processed to have same size as the panchromatic 
band; 
xS H . 
k : the k th band of the higher resolution multispectral image 
after fusion; 
xsl xsl 
(kjj) • the pixel value of location (i,j) of the band * ; 
xs 11 . . . xs H 
• the pixel value of location (i,j) of the band k ; 
: spatial and textural details of location (i,j) extracted from 
the panchromatic band; 
CL 8 . xs L 
. the fusion coefficients modulating ( ' ,7) into ( * ' ,7) . 2 
2. INTRODUCTION 
So far, many pixel-level fusion methods (Carper, 1990, 
Shettigara, 1992, Hill, 1999, Liu,2000, Zhou, 1998, 
Ranchin,2003) for remote sensing image have been presensed 
where the multispectral image’s spatial details are enhanced by 
adopting the higher resolution panchromatic image 
corresponding to the lower resolution multispectral image. 
Therefore, the main principle of remote sensing data fusion 
focuses on the maximum enhancement of its spatial details on 
the condition of minimizing distortion of multispectral image’s 
spectral characteristics. When correlation between the 
multispectral and panchromatic images is not high, it is often a 
mutual contradiction between maintenance of spectral 
characteristics and enhancement of spatial details. Thus the 
choice of fusion algorithm is determined to emphasize spectral 
features or spatial details according to a specific application. 
Typical algorithms of remote sensing data fusion can be divided 
into three general categories (Zhang and Yang,2006): 
component substitution fusion technique (Chavez, 1991, 
Carper, 1990, Shettigara, 1992, Hill, 1999), modulation-based 
fusion technique (Chavez, 1991, Vrabel, 2000, Liu, 2000, Zhang 
and Yang,2006) and multi-scale analysis based fusion technique 
(Zhou, 1998, Ranchin,2003, N'u~nez,1999, Pradhan,2006, 
Aiazzi,2002). The typical algorithms of component substitution 
fusion technique are IHS transform fusion algorithm (Carper, 
1990), PCA transform fusion algorithm (Shettigara, 1992), LCM 
(Local Correlation Modeling) fusion algorithm (Hill, 1999) and 
RVS (Regression Variable Substitute) fusion algorithm 
(Shettigara, 1992); the fusion algorithms of the 
modulation-based technique include Brovey transform fusion 
algorithm (Vrabel,2000), SFIM (Smoothing Filter Based 
Intensity Moulation) fusion algorithm (Liu,2000) and high pass 
filter fusion algorithm (Chavez, 1991); the fusion algorithms 
based on the multi-scale analysis mainly include wavelet 
decomposition based fusion technique (Zhou, 1998, 
Ranchin,2003, N'u'nez, 1999, Pradhan,2006) and Laplacian 
pyramid decomposition based fusion technique (Aiazzi,2002). 
When various fusion algorithms are studied, an issuse whether 
these algorithms can be described by a generalized 
mathematical model (Tu,2001, Wang,2005) is ignored. The 
model can reflect the main features of the fusion process by a 
simple mathematical formula. The establishment of a 
generalized model will contribute to relatively theoretical 
analysis and fusion algorithm design in the light of a specific 
application. Also the model is beneficial to qualitative and 
quantitative analysis of fusion technology from different aspects. 
The most important aspect is that the establishment of a 
generalized model will reveal that different fusion technique