372 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976 
  
  
  
  
  
  
TABLE B-1. RESECTIONS IN SPACE FOLLOWED BY TABLE B-2. RELATIVE ORIENTATION FOLLOWED 
INTERSECTION OF HOMOLOGOUS Ravs. BY LEAST-SQUARE ADJUSTMENT WITH N CONTROL 
RMS SpatiaL ResipuaL rXYZ (REFERRED TO THE Points. RMS Spatial ReEsipuaAL (REFERRED TO 
IMAGE PLANE) WHEN VARYING THE NUMBER AND THE IMAGE PLANE) WHEN VARYING NUMBER AND 
DEFINITION OF CONTROL POINTS. DEFINITION OF CONTROL-POINTS. 
rXYZ (unit:um) rXYZ (unit:um) 
UMK pairs TMK pairs UMK pairs TMK pairs 
n p 101 102 ido 107 11: 12 n. p 101 102 106 107 11:10 
1 76 75 10.9 180 571 595 193 8.8 10.4 196 362 398 
4.2 89 102 12.9 19.7 34.3 41.6 
7.2 TL- 73 11.5 16.7 38.6. 60.3 
+ 90 9.4 11.8 19.1 33.4 40.9 
3 71] T1! 1.3 17.4 44.4 58.4 
4 Tl 75 TE 170 454 49.1 4 8.9 9.2 11.8 17.6 339 40.3 
: : S : : ; 1 «83 8.0 11.8 19.6 38.4 53.8 
] 77 72 9.5 154 329 34.5 
6 2 77 7.8 11.3 . 290 427 441 
16 2° 63 7.3 8.8 144 30.1 34.0 
SATT 8.0 11.5 w228 454 43.1 
3:57.05 7.1 9.0 14.4. .30.9...33.4 
4 46.92.70 9.4 1256 302 355 4 76 8.1 120 243 433 435 
; ; : 2 Ë ; 1° 86 8.5 10.2 18.9" 32.4 37.3 
] 63, 74 9.0 15.3..29.8...33.2 
16 2 85 8.9 10.1 17,0 310 36:5 
15 2 62 66 8.9 136 300 334 
+ 85 8.8 9.6 152 31.1 36.1 
3 60 67 9.1 137 298 33.0 
1.56 -66 10.0 115.286. 341 4 8.4 8.7 9.3 13.8 303 36.5 
: : ; : : s I 81 8.0 10.0 183 315 35.0 
1:55 69 *9.1: *15.0: 28.9 35.3 
15 2 76 7.9 9.8 169 321 35.3 
oS 2 58 63 8.7 136 295 33.1 
gs 77 7.8 9.2 148 32.8 36.2 
3.57. 65 9.3 149 20.1. 33.8 
à 54. 66 93 136 9286 330 4 7.3 7.9 9.2 13.0 31.7 536.5 
: ; : : : ; ] ^76 7,8 *101 *187 «31.6 365 
* (23 control points instead of 28) 28 2.76 7,5 10.0 183 305 33.3 
n: number of control points 8 77 7.7 9.7 16.7. 231.00 ‘33.1 
p: number of neighbouring targets per control point 4- 75 7.9 10.3 19.9 30.9 33.1 
  
n, p, * see Table B-1. 
tests B-1 and B-2 and number of image points for test B-3), four trials have been made with 
1, 2, 3, and 4 neighbouring targets per object point, respectively. 
One can make the following remarks: 
® There is no significant change when each control point (test B-3, image point) is defined with 
several neighboring targets. In other words, there is no significant improvement in the accuracy 
when demultiplying each ray (Figure B-2). This is not surprising if we note that the measuring 
system is in fact invariant. We are in the situation of an observer comparing the means of different 
measurement series: The random errors are eliminated and the bias is the same for each series. 
e There is a significant improvement in the accuracy when increasing the number of control points 
(tests B-1, and B-2) or relative orientation points (test B-3), on the condition of an equi-repartition 
in the whole object-volume of the supplementary points. 
Now the law of accuracy improvement we should test is the law given by Equation B-4, 
i.e., 
nXYZ = V1 + min 10 En 
where r is the number of unknown parameters, n is the number of control (or image) points, 
and m is the number of equations per point. 
(1) Test B-2 (Resections in space followed by intersection of homologous rays). 
In Test B-1, r = 22 (11 parameters per bundle) and m = 4, and Equation B-5 becomes 
hs d 
XYZ ERT A 
s on" (B-6) 
  
  
  
  
$1 S1 So 
S2 
Fic. B-2. No significant improvement in accuracy when demultiplying each ray.