Evaluation of Endmembers Selection in Linear Spectral Unmixing


Ali Ghafouri
Faculty of Geodesy and Geomatics Eng.,
KN Toosi University of Technology,
FVali_Asr Street,
Mirdamad Cross, Tehran, Iran
ali.ghafouri@gmail.com

Abstract
Any process of subpixel classification like Linear Spectral Unmixing needs endmembers to decompose mixed pixels and determine combination fractions. It is indicated by Roberts (1998) that a wrong selection of endmembers can cause the fraction to appear negative or superpositive (more than 100%). In an n-components space it is assumed that the endmembers will occur at the vertices of the hyper-solid defined as the geometric shape bounding the pixel values in that space.

Two different methods for selecting the endmembers from the edges of this component space were employed. The first method sought to maximally include pixels from the edges of the two component distribution. Simply stated, this way selected more pixels and averaged the reflectance of more pixels that occur at the edges of the distribution. The second method included only the extreme values of the distribution edge and is termed minimally inclusive and averages less number of pixels. Both procedures were applied on an ASTER scene and results are evaluated.

The correlation coefficient between some corresponding endmembers of two methods was calculated to be between 0.96 and 0.99. The error of the estimate for both inversions is consistently below 0.02 (95%). The minimally selected inversion seems to have a somewhat higher mean and higher standard deviation from the mean. The two inversions seem to have a deviation of 0.01 on their means and 0.03 on their standard deviations, with the minimally inclusive inversion to have a lower standard deviation and mean. It also has a higher minimum and a lower maximum. The latter shows that the minimally inclusive selection produces results that better constrain the fractions to a unity range.

ASTER satellite data were used to study spectral features and classifications of land cover especially agricultural fields of north-eastern Markazi province, Iran. Ground investigation data allowed the evaluation of paper results much better.

1. Introduction
Satellite Remote Sensing has made information collection available where field surveying has fallen short because of prohibiting factors such cost, timing and terrain difficulties [8]. As a natural consequence, Remote Sensing science is in the process of developing models for identifying spatial patterns in a larger spatial and temporal context with relative high accuracy. A satellite remote sensing based approach in identifying land covers and quantifying vegetation land cover can prove very important in the fight against land degradation and vegetation loss [6]. Numerous studies have suggested ways to infer vegetation quantities from satellite imagery, most of which take advantage the high absorbance of vegetation in the visible spectrum and the high reflectance in the near infrared.

This study employed satellite Remote Sensing and the Linear Spectral Unmixing approach to evaluate the feasibility of the approach in an agricultural area. Four endmembers were selected from the image, the four main land covers pomegranate, sunflower, cotton and grass/tree. The linear unmixing model proved promising and gave reasonable results although it was discovered that the unmixing results are highly sensitive to the endmember selection approach. On this basis, some studies executed to conclude a single method of endmember selection which could have this possibility to introduce as a robust method.

2. Endmembers as Pure Reflectance Spectra
An endmember is the pure reflectance spectra that were derived by a specific target material with no mixing with any other materials. Determination of endmembers is the fundamental stage in each process of classification; because selection of endmembers is comparable to training procedure in supervised image classification, and disregarding this stage which is the primary level of each project could cause very terrible effects on the results. In linear mixture modelling, matrix E is made up by endmembers, the equation in which frac denotes the c×1 fractions vector with the proportions of the different ground cover types, DN represents an n×1 pixel vector or multispectral observation and ε is error vector [4];




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