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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV. Part B2. Istanbul 2004
We can see that all the statistics in tablel are less than the
threshold, the conclusion is drawed that the error mean is zero.
That is to say , the error is casual, not systematic.
2.3 Error Distri* ution Test
We make a } test for proving the normal distribution of the
error of polygon area.
First, we divide them into k groups by the range of these
relative error, and count the number of samples in each group.
Secondly, Sample mean and mean square root error are
calculated. Thirdly, supposing H, is true, we calculate groups
probability P; and theroy frequence n P,, and at the last, we
2 . ~ . ~
calculate 7 using the following formula
k 2
5 —~(f, —np,) (2)
Kay
aun
5 np, f np Uy
"np,
xis I 0.0099 0.8118
5-10 72 0.0386 3.1652 | 471.407 0.15
-10<x<-5 9 01150 043
-5<x<0 I8 02186 17.9252 00748 0.00
0<x<5 29: 0095622 7215004 7.4996 2.62
5<x<10 16 02088 17.1216 116 7007
10<x<15 0.1055
15<x<20 4 0.0336 2.7552 50786 214
x220 2 0.0082 0.6724
82 4.98
tue
Table3. The result of error distribution test.
The result is shown in table 3. This table displays
2
Xoos(K ^ r - D 7» yog (5 - 2 — 1) =5.991>4.98 7 so we
accept H,, that is to say. the errors of polygonal area follow
0?
normal distribution and their mean is zero.
3. SAMPLE TECHNIQUE
3.1 Sample Design
The arca accuracy of monitoring polygons depends on change
detection techniques and image resolutions.It’s found that area
errors have a regular distribution in a certain area range (called
stratum in following sampling), so a area stratified random
sampling is applied. The approach involes subdividing the area
range into strata,and within each stratum a spectific number of
sample polygons are randomly chosen. When using LANDSAT
TM(30meter) and SPOT(10meter) images,we usually divide the
whole polygons into four stratums: under 10mu, 10-20 mu,
20~50 mu and above 50 mu,which have been proved reliable
and reasonable.
457
3.2 Sample Size
Because of the normal distribution, for a large sampling
population in which the sampling fraction n/N is negligible,in
another word, n/N does not exceed 5 or 10 percent
(Cochran, 1977,p.25), we use sampling size equation based on
OC function. The equation has the form
ax (z, +2, 15
N
9 (3)
Where n = the number of sample units,
N = the total number of units in the population,
@À = the propobility of omission,
B = the propobility of commission,
Z, =the critical normal distribution value of a,
Zn the critical normal distribution value of B,
O - a prior estimate of the population standard deviation.
Sea prior estimate of the limit of error.
It should be noted that using this formula parameter
G and O should be known beforehand.
When the population is not enough large, we can give sample
size by our experience. If the number of population is less than
50, we usually sample all the polygons in order to ensure the
reliability, If the number is not less than 50 and that the area of
the whole monitoring region is below 10 thousand mu, the
minimum sample size are 50 , but we should sample more than
75 or 100 sample units when the area of the whole monitoring
region is over 10 thousand mu.
4. ACCURACY ASSESSMENT
The accuracy assessment consists of the estimate of a single
polygon error and the whole monitoring region error. Based on
the standard normal distribution, we establish three area
accuracy indices including relative error, average relative error ,
and relative mean square root error using relative error theory ,
and using the error spread law, the formulas of single polygon
error and the whole monitoring region error are build .The
relative error expression is
where dv = relative error,
Ai =monitoring area of the ith sample unit,
Bi = reference area of the ith sample unit,
The average relative error is given as
d|v| = ZA Bf - Bi
XB
Un
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