27 
1.221. The transformation of errors between the individual pairs of photographs 
The coordinate transformation between the individual pairs of photo- 
graphs is assumed to consist of two translations, one rotation and one 
scale change. The differential formulae of the coordinate transformation 
formulae are demonstrated in the expressions (17) and (18) above. 
These formulae express the relation between small errors of the inter- 
sected coordinates and the errors of the elements of transformation 
db 
dz, dy, —— and da. 
b 
The transformation of errors between two arbitrary, adjacent pairs 
of photographs à — 1,7 and 4,4 4- 1 will now be studied. 
The base à — 1,i is assumed to be fixed and temporarily free from errors. 
The errors in the points à, + 1 after the coordinate transformation 
are regarded to be caused by the errors in the transfer points 4 and 6 
from the image pair à — 1,i and the points 3 and 5 from the image pair 
i4 + 1 via the elements of the coordinate transformation. 
da. and dy, are the errors in the point à of the image pair 2,2 + 1 
db, ;_ is the error of the base 7,5 + 1 and 
de; i1 is the error of the direction of the base ?,? 4- 1. 
L,l 
The total coordinate errors in the points 3 and 5 of the image pair 
ii + 1 consist of the errors of the intersected points 4 and 6 from the 
image pair i — 1,? and the errors of the points 3 and 5 from the image 
pair 4,4 + 1. 
Corrections to the elements of the coordinate transformation are 
determined from the coordinate differences in the transfer points 
X; 4; = À 
1 
il 
(70) 
Yi—ri — Yii+r 
Errors in these coordinate differences will consequently cause errors 
in the elements of the coordinate transformations according to the 
expressions (17) and (18) above. dx and dy in the transfer points are 
according to (70) defined as 
doy = da; 114 — dRii+1s 
dys — dy; Aia — dy, is - 
(71) 
da, — da; 116 — dÆii+1s 
dy; — dy; ie di; i. 1,5 
EU Tx To 
  
CR 
zx