International Archives of the Photogrammetry, Remote Sensing and Spatial [Information Sciences, Vol XXXV, Part B4. Istanbul 2004 Intel 
class for each band have been derived from a real case study place on the y-axis. The plotted values are the averaged overall Con; 
(Fatemi, 2002). In the all cases, for generation of the pixel accuracy for a particular sample size. Repeating the sampling 75-1 
values, covariances between all of the yands were assumed to several times and taking the average eliminates the problem of 
be zero. Images have three bands that were generated by the the odd chance of obtaining an unrepresentative sample, which [n ir 
above consideration. For considering the noise that exists in all is always possible in any sampling schema. In some below 1(a) 
real images the random values of noise were added to the pixels experiments the results of investigations are discussed. tend 
in the synthetic images. Again these values of noise are imag 
according to normal distribution with certain means and 4.1 Experiment #1: Investigation of Simple Random occu 
variances. Sampling (SRS) Schema field 
error 
The area of interest in real word is Moghan and is located in The results of averaging overall accuracies with SRS method in meth 
Ardebil province of Iran. One TM (Landsat 5) image of the four images have been shown in graphs of Figure 1. 
study area acquired on 1998-06-08 is used for this study. 6 For 
bands of this image are used for producing classified map. imag 
n each 
For classification of images, based on produced reference data, each 
training samples for each class were collected. Then Maximum ef were 
Likelihood Classification based on equal prior probability of the sp 2(a) 
classes was implemented. 3 “dl over: 
SM from 
SD real 
3. SAMPLING SCHEMAS Li qum aar re REND AREE TU numl 
sample size (pixcl) 
Five sampling schemes typically are used in the accuracy a. 
assessment. These five sampling schemes are Simple Random T pue T pret i 
Sampling (SRS), Cluster Sampling (CS), Stratified Random 3 
Sampling (STRAT), Systematic Sampling (SYSTEM), and po 
Stratified Systematic Unaligned Sampling (SSUS) (Congalton, i 
1988). Simple random sampling is a method of selecting n m ; 
sample units out of N units in the population, such that every de % 
one of the possible distinct samples has an equal chance of 
being selected. Cluster sampling is a method of sampling in ; Fi 
which the sample units are not single pixels but, rather, groups A sample size (pixel) \ 
(clusters) of pixels. In this study cluster sampling is based on : dev 
random selection of clusters. Stratified random sampling is 2 x T NOR ai valu 
sampling method that divides or stratifies the population into - Nr LX > sai 
nonoverlapping subpopulations (strata). 7 1 Be 
| 
In this paper, stratification of images was done geometrically With 
and by dividing images into four equal parts. A systematic imag 
sample is one in which the sample units (pixels) are selected at 3 | | | | | | | | 2(a)) 
some equal interval over space. In stratified systematic 9s Cr ede SAN GE Suet rot nm "Pa Also 
unaligned sampling with random selecting of samples in each " sample size (pixel) vds 
strata produced from stratification of image in specified differ 
intervals, a combination of systematic and random sampling is stand 
used. s Imag 
5 (Figu 
4. INVESTIGATIONS ON SAMPLING SCHEMAS 7 
For investigating the sampling schemas used in the accuracy | I 1 “ 
assessment, each of the five sampling schemas, were simulated. Nego A NO Amor oM mH 
In each simulation overall accuracy of produced error matrix d. ple Size) = 
were calculated. Each simulation was repeated 30 times for each 1 er 
image with 50, 100, 200... 1000 samples per images for each Figure 1. Overall accuracies resulted from using SRS method fe 
sampling schema and the results were averaged together. This (each sampling schema for each sample size has been repeated 
experiment was done in three cases and results of averaging 30 times and the results have been averaged) for 3 cases in 
overall accuracies have been graphed for each image. Overall image#1 (a), image#2 (b), image#3 (c) and image#4 (d) 
accuracy was computed using the all pixels in reference data for E 
each image without sampling. Thus, it is possible to compare Figure 1(a) and Figure 1(b) that are related to images with Figu 
the results of each sampling schema simulation with these true smaller image size show that approximately with sample size (cacl 
and actual values. This comparison allowed determining the larger than 50 samples for each class, the results go towards 30ti 
best sampling schemas to use for each data set. The results of stability. In images with larger image size i.e. image#3 and 
the sampling simulations were graphically displayed with the image#4 (Figure 1(c) and Figure 1(d)), the results go towards 
overall accuracy on the y-axis and the number of samples on the stability after approximately 70 samples for each class. This The n 
x-axis. In such graphs, the actual values were also plotted on result is accordance with a rule of thumb recommended by To 
à 
each graph as a horizontal line originating from the appropriate 
1038