2004 International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
'd to 3.1.1 Map Accuracy Standards (MAS) Determination: CLASSES PLANIMETRY SCALE 1:100.000 
Tego An important method for Carographic evaluations of generated MAS SE Ox Or 
ation maps is the use of Map Accuracy Standards — MAS (Galo et al., T = = 
viti ^ des A 0.5 mm | 0.3 mm 21.2132 21.2132 
the 2001), which is based on the comparison of deviations between 
: . * - c & "Zea az 2 A 
arest homologous control points casily located on the reference map B 0.8mm | 0.5mm 35.3553 35.3553 
the (Xm Ya) and the image (X, Y;) The deviations at these C l.0mm | 0.6mm 42.4264 42.4264 
root- homologous points (Ai — X4 - X, Ay 7 Y, - Y) are used to 
less compute statistics ever used to perform specific test to Table 1. Standard Error (SE) Values for Brazilian Map 
pixel evaluate the trend an the accuracy of the geometrically Accuracy Standards for the scale 1:100.000 (source: Vieira et 
xel). corrected image. In this analysis it was considered that the al., 2002) 
sons reference map is sufficiently accurate for our purposes, i.e. to 
3 F1 » 1 c 1 y . - ~ 
assess the From pli fog ng : RE 3.1.2 Generated Point Method: One drawback of some of 
According to Merchant a 2), the aim of A Pa 1S 10 the standard approaches to quality control of cartographic 
. : teseneo Go VIET py GC se the : ; id A 
check for the presence of systematic errors. This check uses the products is the difficulty of obtaining homologous points in 
(XS) sample mean of the deviations (À  , À y ). À statistical test is both representations. It is therefore necessary to consider the 
| nd ed. using. ih ld thesis that th : use of generic features to complement the control points. 
ar using the null hypothesis that the sample mean is . : : ner 
à appiiea, e YP : pe The generated point method can be applied to digitised 
| this estimating a truc (population) mean of zero. If the null finie . ; 
5 res homologous features (i.e., the same features represented in both 
994, hypothesis can be accepted at some significance level then the ; : : : 
Lu ido tobe d is that there} frena Crd] map and image) in order to generate a set of equally spaced 
conclusion to be drawn is that there is no trend or systematic ; ; ; : : 
y cone Use directi s Y and Y Je > E homologous coordinates following the path of both features. 
T irections X and Y respectively. Hi : s : 
a em m e d Test T p vs y WER The initial control points for cach features should be 
; 0 > nt’s / Test is normally used to carry out this statistica ; ; ol 
Y a The Studer eT y 3 homologous, so the relative distances (or deviations D) between 
ea test. The critical value£, ,,,, is obtained from statistical the generated homologous points are used to perform the 
ops, xu ; » NE e T ua » 
beet tables (where n is the total number of control points and a is the ere LE CN Ke that if T Is no Cui betw 
* - - ~ A ^ oO ^» e oc x € ^ 7 ^ 
confidence level, for example 0.1). If the calculated value of / Cc EE omo DEous Poe ! € SC Is we Cone 
ie" : 1 © : ap: Gtherwis necessary to : 
DAS for the deviations along the north-south dimension |fy| is less wm re Crece (o the Map, otherwise, it is Becessary to apply 
k irr a statistical analysis to in order to check the positional accuracy. 
Non than £,  ,/ and the calculated value of 7 for deviations in the A comparison between the median and standard deviation of 
ams : ji these deviations and published Map Accuracy Standards (MAS) 
n of east-west dimension |/z| is less than the tabled value / qe ue e 
: n-l.aj2 are carried out considering a specific scale. The accuracy test 
Was ; ; eg . ; à ; 5 IS 
a then the generated product (e.g., image) is free from systematic uses a Chi-square (x^) test based on the specified Standard Error 
bour T T -. ; E 
errors on the directions N and Æ respectively. The estimated (SE). The geometrically corrected image will be accepted as 
: ge E 8 accep 
values of 7y and 7; can be estimated using the following accurate if Y^p s, € Y^, o. The sample value of y^p. can be 
L equations: estimated using equation (5): 
in 
fm les) (1) > ra 7 
fg (Hag). Ap.n'? (2) X Dai 7 0r 1) . (6p np ) 5) 
where oy and oy are the standard deviations of the discrepancies ; : ; i. J 
Ar and Ay in the directions E and N respectively where, as before, 0,, is obtained from the Table 1. However, it 
y ui Accuracy analysis uses comparison of the variance of sample is not directional, and separate tests are not carried out for the N 
tions deviations ( Var( Ax), var(Ay)) to their respective pre- and E dimensions separately. The value 2, is computed from 
ately defined (tabled) values. The test is performed using a the formula a, = SE/AD 
cally hypothesis about the mean and standard deviation of the sample 
§ arc lor each of the geometric coordinates. The statistical procedure 32 Th tic À 
; ; "b: 2 s ; . ematic Accuracy 
tests employed is the Chi-square (x°) test. The accuracy of the y 
geometric: 'ected image > estimated sepe ; for ; 
th i SY con cd page em e E Gd Daly or Current accuracy assessment methods are based on non-spatial 
€ direc Ni 4 sing. st: 2 Statstlc: gy La . > S i S 
y of val ec Tons ng Te using, standard statistica icti o 98) statistics derived from the confusion or error matrix, which 
h mvolv . AIG Y + je a "V (u^ " x a 
(Tes di ving the comparison of a sample value of x (x Nd and compares the output of a classifier and known test data (Table 
ds the tabled value OC nt. a). OF QC nas) and (c5, 4) respectively. — 2j These statistics include overall accuracy, individual class 
and The values of X'wa and yg, are estimated using the accuracy, user's and producer's accuracy, and several other 
rents following equations: statistics. Although these measures are in widespread use, none 
‘hree ; E lod of them considers the spatial distribution of erroneously 
) to X Nai 7 Gr-1) . (ov /0N7) (3) classified pixels, either implicitly or explicitly. 
- - 2, 2 
y a X'Es1 7 G1). (od 7047) (4) 
. the 3.2.1 Characterising the Spatial Distribution of the 
alent where 6. and Or arc obtained from Table | and vary as a Errors: 
h the function of map scale using the One possible way to characterise the spatial distribution of the 
ce | . / errors in a thematic classification is by generating a “distance 
need formulae: 6, = 0, = SE/ 2 . The values of the Standard © uS e : a ee A it ent 
natic E : image" (see Figure 1(a)) showing the distance from individual 
ns X Jor (SE) for the Brazilian Map Accuracy Standards, for pixels to the multivariate means of the classes to which they 
cator iis IS defined by the decree n? 89.817 of 1984, which ^ have been assigned. Either the Euclidean distance or the 
ve classifies cartographic products in relation to their geometric Mahalanobis distance measure can be used. The former, 
  
  
quality (see Table 1). 
  
  
  
  
  
  
  
  
  
  
  
  
however, implies spherical clusters in feature space, while the 
latter takes into account the covariance between the features-on 
which the classification is based. The individual distances are 
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