The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXV//. Part B7. Beijing 2008 
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2.9 Combined F-Test anomaly detector (CFT) 
CFT method is based on a nonparametric model that compares 
two sets of data (random variable), background data and target 
data by using a typical inner/outer window mechanism to 
sample the image for local detection, or using full image data to 
global detection. In this method after combining two mentioned 
samples, statistical parameters of them (mean and variance) are 
estimated. Then ratio of these parameters are calculated (Z CF r) 
and tested by Fisher distribution of (1,1) degree of freedom. 
A decision threshold T is determined via defining a type I error 
for F distribution function and compared with the result of ratio. 
If Z CFT is greater than T, it means that these two sets are most 
likely sampled from different distributions. Therefore they are 
anomalous to each other. If not, they are likely sampled from 
the same distribution. 
The main assumption in this method is asymptotic behaviour of 
Fisher’s F distribution for data sets which are examined by a 
common statistical test (Rosario, 2005). 
and their performances are compared by discrete Receiver 
Operating Characteristic (ROC) curves and their area under 
curves (AUC) as appropriate criterions for evaluation of 
detection algorithms. Therefore seven threshold values are used 
to achieve confidence levels about 93% to 99% for calculating 
probability of correct detection and false alarm. 
For example figure (2) shows the visual result of local RX 
method with local window size 15, correct detected targets and 
ROC curve of this algorithm 
3. EXPERIMENTAL RESULTS 
Two sets of hyperspctral data have been used for these 
experiments. 
The first one is a real hyperspectral data (AVIRIS image of 
Cuprite region which is available in ENVI sample data) for 
visual inspection of detection results. The second one is a 
synthesized hyperspectral data for quantitative evaluation which 
was simulated by sampling of contiguous spectral curve with 20 
nanometre spectral resolution for some natural and man-made 
targets such as dry grass, sandy loam, sagebrush, galvanized 
iron and aluminium metal using ENVI spectral libraries and 
MATLAB software. This synthetic hypercube’s size was 
100x100 pixels which made up linear combination of some 
above signatures for background region and anomaly panels. 
In background region first pixel is started with 100 percent dry 
grass and 0 percent sandy loam. Then by moving to next pixel 
percentage of dry grass is decreased and percentage of sandy 
loam is increased. This process is repeated until the last pixel 
has 0 percent of dry grass and 100 percent sandy loam. Then 
anomaly pixels are added to this data in various locations. 
Anomaly panels in each column have the same pure signature 
with various sizes and they have the same signature in each row. 
All of anomaly pixels have 10 percent abundance of anomaly 
signatures such as galvanized iron and 90 percent abundance of 
background signatures. Also Gaussian noise is added to each 
pixel to achieve 30:1 signal-to-noise ratio. 
Figure (1) shows the simulated hypercube in band number 20 
(800 nanometre) and location of considered anomaly pixels in it. 
(a) (b) 
Figure 1. Simulated image in band number 20 (a), 
location of anomalies (b) 
Figure 2. Result of local RX (a), correct detected anomalies in 
99% confidence level (b), full ROC curve (c), 
comparable part of ROC curve (d) 
Local DWEST and NSWTD algorithms are tested with different 
combination of local window sizes. Figure (3) shows the best 
visual results of these methods. 
Figure 3. Global DWEST-RX (a), global DWEST (b), 
local DWEST with in/out window size 1/7 (c), 
NSWTD with in/mid/out window size 1/11/25 (d) 
Also figure (4) shows the visual results of global RX-base 
methods. 
All mentioned algorithms (in global or local manner with 
various window sizes) are implemented in MATLAB software