TABLE 1. Corrections obtained for horizontal control points from bundle 
adjustment with and without self-calibration. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
CORRECTIONS : CORRECTIONS , 
POINT With Self-Cal. Without Self-Cal. POINT With Self-Cal. Without Self-Cal. 
AX AY AX AY AX AY: AX AY 
(ft). | (ft) (ft). |. (ft) (ft) (ft) | (ft) (ft) 
First Order Second Order 
[(a priori 0=0.5) 
Killington  -0.1 -0.6 1.0 2.4 Globe 0.9 -0.1 -0.2 1.5 
West Mount 0.0 -0.2 -0.5 -6.6 White 0.4 -0.8 -0.7 -3.9 
Mt.Anthony  -0.2 0.1 1.3 21.7 Jilson 0.0 0.9 -3.4 -6.7 
RMS: 0.1. 0.4 1.0 4.2 Ascutney -0.4 0.7 -5.2 6.2 
Hawk 0.4 0.2 -3.4 4.2 
Mt.Ephriam -1.3 -1.5 -6.8 0.7 
Second Order ; : Stowell -0.6 -0.7 -7.1 1.0 
(a priori o 21.0) Pinnacle -0.2 -0.2 -5.0 1.4 
toddar 0.2 0.2 6.0 0.9 Putney 0.2 0.5 -4.9 0.2 
Burch -0.4 -2.3 5.0 -8.4 North Pond 3.0 2.1 1.7 2.1 
TTGOT 71.7 0.8 11.2 5.3 TT7FI 0.4 -1.6 -3.2 -4.0 
Tiplady 0.9 0.2 9.1 -3.4 . TT14K - 0.8 -0.4 -1.1 -5.6 
Fleming -1.1 0.1 7.9 -3.3 Halifax 1.4 0.1 -0.6 -4.5 
Murray 0.8 -0.5 9.2 -2.0 Davis -1.6 0.3 ^ -9.4 0.4 
Vernew -0.2 -1.1 4.6" -1.9. Bald -0.6 0.2 -2.1 -1.0 
Greene -1.7 0.8 -0.9 -1.0 RMS : 0.9 1.0 4.9 3.9 
Boundary 0.3 0.2 -0.5 -4.8 
Herrick 0.0 2.4 6.7 7.4 
Northeast 0.3 -0.9 5.9 0.0 Third Order 
Niles -0.7 -0.2 2.1 1.4 (a p er 073.0) 
TTISG -0.2 -0.3 2.6 -1.5 3.2 3.7 3.0 11.7 
‘Bennington 0.0 -0.6 0.9 -3.5 ET2AAS -0.5 3.5 -3.0 9.6 
Pine Cobble 0.0 0.6 -1.9 -5.4 Garvin Hill 0.1 0.2 -1.3 7.9 
TT19T -1.8 2.4 0.3 6.7 Dingleton -0.2 3.2 -0.5 9.5 
Styles 0.1 -1.1 1.9 -1.7 Green 0.4 -3.4 -6.6 -1.2 
Bush 0.1 -0.7 0.5 -2.8 Fall -4.0 0.4 -14.4 0.6 
Haystack -0.1 0.1 -0.3 -l.7 Surry 1.3 0.1 -7.1 2.1 
Florida -0.6 1.4 -3.7 -5.5 TT7K 1.1 1.5 -1.3 -5.6 
RMS: 1.9 2.5 6.4 7.0 
  
  
adjustment caused, in turn, by a significant degree of uncompensated 
systematic error. By contrast, when the bundle adjustment with self- 
calibration is performed, the internal strain is entirely removed and 
the RMS values of the X,Y corrections for second order points become 
0.9 and 1.0 ft., respectively (or 4.4 and 4.9umat plate scale) — a 
four to fivefold improvement over the results without self-calibration. 
Generally comparable improvements were also obtained for vertical coordi- 
nates; details are not presented here because the summary of the vertical 
corrections without self-calibration had been misplaced and could not be 
located at the time of this writing. However, results for vertical cor- 
rections are at hand for the reduction with self-calibration; here, the 
RMS value of the vertical corrections turned out to be 0.5 ft, or 2.4 um 
at plate scale. A 
Because self-calibration yielded such dramatic improvements, 
it is of major interest to ascertain which parameters of the error model 
were mainly responsible for the favorable outcome. As it turned out, of 
the fifteen error coefficients that were actually exercised only five or 
six were found to be significantly different from zero and, of these, the 
totally dominant terms were those describing symmetric radial distortion. 
This was indeed a major surprise, for the precalibrated distortion function 
had been duly and correctly applied to generate appropriate corrections to 
the plate coordinates prior to the adjustment. Hence, the coefficients for 
-18- 
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