ed 
‚he 
2 
   
  
for the 
  
within ‘the "ajustment. The observation equations 
functional constraint can be shown as 
m0 C 
d À P (13) 
This could be added to the combined form of the observation 
equations for the bundle adjustment shown as 
T+Ba+tec=0 (14) 
where: C is the design matrix for the functional constraint 
C 
e disi the discrepancy vector for the functional 
constraint 
a is the alteration vector 
V is the vector of residuals 
5 is the design matrix for the observation equations of 
the bundle adjustment, and 
T is the discrepancy vector of the functions evaluated 
within the bundle adjustment. 
The function to be minimized is 
ex NE 2 LC 
à = V'HV - 21'(0 + Ba + E) - 214(C8 + ¢) (15) 
Differentiating (15) with respect to V and X and including the 
observation equations results in four equations 
a Ÿ + à = 
Bry = 0! A * 3 
a AT (16) 
V+ Bate=0 
-— C 
CA rc 
It can be ‘shown that the solution can be computed by the 
following equations [Uotila, 19731: 
i m s = De DU m C 
* z -N-1U + (N-1C'(CN-1C’)71[CH-10U m e] (17) 
or more concisely as