-45- 
@ To determine the systematic (correlated) portions ax! one may calculate these for the n control 
points i as interpolated values alalogous to (13e) : 
then dx; may be subtracted from Ax; to obtain x! to be used in (13e) for the interpolation of 
Ax! ; or one may use the Ax, directly if the values of the cross covariance matrix in (13e) are 
3 
subtracted by the values of cross covariance matrix in(13g). 
The elements of the auto-covariance matrix c may best be obtained in a parametric adjustment in- 
volving all control points. Then covariances may be calculated for all combinations of distances 
between the points involved. These may be grouped into distance classes defining a covariance function 
of the form 
? (813) 
according to Kraus 
© (aij) 
according to Hirvonen and Koch. 
This function may then be applied to form the coefficients of the cross covariance matrix. 
To avaid difficulties in inverting c a regional covariance function may be determined involving 
points up to a distance r from j only or within a region. 
While this method constitutes an ideal tool for accuracy anylysis of mathematical models at a 
few points, it is too time consuming to be applied to all image points. Also it may lend itself to 
interpolation under the stated conditions it is not helpful for extrapolation. 
4. Accuracy Analysis Tests 
  
Due to the variety of methods described and used in analyses it becomes impractical to summarize 
them here, except as a quide - line for the references: 
4.1. Accuracy Tests for Satellite Images 
Analyses of Landsat (E.R.T.S.) images have first been made by Colvocoresses & Mc Ewen /18/, than 
by Báhr and Schuhr /3/, Forrest /31/, Bähr /4/, Wong /86/, Bernstein /9/, and Trinder/83/. 
Most tests have been done with bulk images, reproduced by NASA's electron beam recorder /18, 
3, 4, 86, 83, 31/. For these tests image coordinates have been measured in a comparator and these 
were related to ground coordinates of the recognized terrain features. The same applied to the 
test of precision processed images /31/. Some tests have directly been performed with computer 
compatible tapes /31, 9/. For such a comparison an "image” had to be generated using time vary- 
ing orbital data contained on the tapes. Such "images" displayed greyshade data for an area 
around a comparison point on a line printer. Counting pixel rows and columns for a point with 
known ground coordinates (the center of an identified area) the discrepancy was obtained (Forrest/31/). 
Bernstein/9/ reports on a procedure where an "image" generated in the described manner is compared 
with another stored "image" symmetrically identifying the control point coordinates. The comparison 
is made by digital image correlation technigues.