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A DIMENSIONALITY REDUCTION ALGORITHM OF HYPER SPECTRAL IMAGE 
BASED ON FRACT ANALYSIS 
SU Junying a '*, Shu Ning a 
a School of Remote Sensing and Information Engineering, Wuhan University, Luoyu Road 129#, Wuhan, Hubei, P.R. China,430079 
jysu_sjy@sina.com 
Commission VII, WG VII/3 
KEY WORDS: Hyper spectral, dimensionality reduction, spectral domain, fractal analysis, feature image 
ABSTRACT: 
A dimensionality reduction algorithm based on feature extraction of the spectral curve using fractal analysis which considering both 
the spatial characteristic and spectral characteristic of hyper spectral remote sensing image is proposed A spectral domain feature 
analysis based on fractal measurement technique is designed for hyper spectral images. Fractal characteristic of spectral curve is 
discussed. A brief description is given to explain the nonlinear mechanism resulting in fractal of spectral curve. And the spectral 
curves of same objects are presented to show the self similar. And some computational results are given to show exponential relation 
between the total length of spectral curves and the different measurement unit. A fractal dimension calculation algorithm of hyper 
spectral curve is designed. A noise remove algorithm based on wavelet transformation is done before the fractal analysis of spectral 
curve. Then a feature analysis procedure in spectral domain based on fractal measurement is also proposed to reduce dimensionality 
of hyper spectral images. The fractal dimension value is taken as the feature of spectral curve and the fractal dimension feature 
image is proposed to represent the dimensionality reduction result of hyper spectral image. Experiments of fractal dimension value 
of different objects spectral curve show fractal can be used to represent the spectral feature to reduce dimensionality of hyper 
spectral image. Finally, the application of fractal measurement of spectral domain feature analysis is briefly discussed. 
1. INTRODUCTION 
The characteristics of hyper spectral remote sensing data are 
numerous channels, high spectral resolution and large amounts 
of data, which makes it easy to discriminate objects in the scene, 
however, the vast amounts of data not only makes it difficult for 
transmission and storage, but also feature extraction and 
classification. Therefore, it is very important to reduce the 
dimension in the hyper spectral image analysis (C. Lee, 1993; A. 
Jain, 1997). As hyper spectral sensors acquire images in very 
close spectral bands, the resulting high-dimensional feature sets 
contain redundant information. Consequently, the number of 
features given as input to a classifier can be reduced without a 
considerable loss of information. Dimensionality reduction can 
general fall into feature extraction and band selection. Feature 
selection techniques generally involve both a search algorithm 
and a criterion function while feature selection is usually done 
in the image spatial space and feature transformation and 
feature extraction is used to reduce the image dimension such as 
the principal component analysis, absorption features extraction 
and spectral statistical analysis. Band selection is usually based 
on the spectral curve of hyper spectral image which can convert 
hyper spectral vector into low dimensions or one dimension. 
Due to their combinatorial complexity, band selection 
algorithms cannot be used when the number of features is larger 
than a few tens (L. Bruzzone, 1995; L. Bruzzone, 2000; C. 
Lee, 1993; C.I Chang,2006; A. Plaza,2005). And dimensionality 
reduction algorithms based on feature extraction and band 
selection can not combined spectral and spatial characteristic. 
All these dimensionality reduction algorithms have the 
disadvantages of less considering the spectral information and 
low efficiency. Fractal theory is used in many applications for 
the advantage to solve the non-linear system of the complex 
phenomenon. Thus Fractal is usually used to solve the complex 
non-linear system analysis. Fractal theory has been used in the 
remote sensing research while it does not obtain the full 
application (Qiu H L; Weng Q, 2003). Commonly, fractal 
dimension of hyper spectral remote sensing image is calculated 
by the spatial characteristic and then the fractal dimension is 
used for the band selection. And the fractal dimension value is 
calculated with spectral curve to unify the spectral information 
to the spatial distribution feature image thus it can be used to 
reduce the dimensionality of hyper spectral remote sensing 
image. 
In this paper, a dimensionality reduction algorithm based on 
feature extraction of the spectral curve using fractal analysis 
which considering both the spatial characteristic and spectral 
characteristic of hyper spectral remote sensing image is 
proposed A spectral domain feature analysis based on fractal 
measurement technique is designed for hyper spectral images. 
Fractal characteristic of spectral curve is discussed. A brief 
description is given to explain the nonlinear mechanism 
resulting in fractal of spectral curve. And the spectral curves of 
same objects are presented to show the self similar. And some 
computational results are given to show exponential relation 
between the total length of spectral curves and the different 
measurement unit. A fractal dimension calculation algorithm of 
hyper spectral curve is designed. A noise remove algorithm 
based on wavelet transformation is done before the fractal 
analysis of spectral curve. Then a feature analysis procedure in 
spectral domain based on fractal measurement is also proposed 
to reduce dimensionality of hyper spectral images. The fractal 
dimension value is taken as the feature of spectral curve and the 
fractal dimension feature image is proposed to represent the 
dimensionality reduction result of hyper spectral image. 
Experiments of fractal dimension value of different objects 
* Corresponding author. SU Junying, PhD, School of Remote Sensing and Information Engineering, Wuhan University, P.R. 
China, jysu_sjy@sina.com, 86-27-63003060