International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
  
3.1 Fictitious Equation Eliminate the Rank Defect 
In close-range photogrammetry, the collinearity equations are 
used to build mathematical model to carry out free network 
adjustment. The bundle freedom network adjustment utilizes 
fictitious observation values to overcome lacking of observation 
function. The least square and smallest norm condition 
determines point positions. The numbers of auxiliary 
observation data are equal to network necessary number of 
initial data so that added auxiliary observation function is in 
complete rank status. Mathematical model as follows: 
G'G=1 (6) 
AG=0 
B s 
column complete rank, exclusive result can gotten. 
G 
X = (A"PA+GG")" A" PI (8) 
To determine G matrix is ensure 4 lin complete rank state, 
GE 
the row of G matrix make up coefficient vector X a group of 
basis. The seven conditions process Helmert conversion to 
eliminate rank defect. S is G matrix normalization matrix. S 
matrix as follows: 
[ 1 0 0 os0 iK dl 0 0 Kd 0 0 
| 0 1 0:40 10. 0 SK. 05: d cR 10 vd 0 
| 0 0 1 0. 0 10 K 0:0 iR 0 0 I 
Sel Dele Saw hoses teint abe RS 0 4 
Zea De = tait tuada sen Kaunas ar Man Kae mer 
tr Ku 0 An My ey Kıch A 0, K oF. oF 0 
(Xu In: Zu 0 0 ®& Ku Mi XunZin Ri X 4 vU Z 
where: 
- — 1 / 
G7 C085, 008.4; 0, — SID K,/cos v 
, cb, cO. sik Do, = COS (10) 
Cu = lan €, COS K, 10, = — lan à sit K, 1€, =1; 
3.2 Relative control condition 
[n order to make full use of various kinds of information present 
in the object space at the time of photographing, relative control 
is often used particularly in close-range photogrammetry. There 
are some additional observation data, relative control 
information easy to add into condition equations to carry out 
whole adjustment calculation. Two kinds of method deal with 
in detail: 
3.2.1 Observation values include measured data 
Relative control including observation values, construct error 
equation from condition equation as follows: 
V,-BX-D am 
With collinearity equation's linearized as follows: 
VzAX-L (12) 
indirect adjustment methods apply in whole solve process. 
3.2. Relative control as restrict term 
Not including observation values in the relative control factor, 
relative control factor provide a restrict term for collinearity 
equation (13), and indirect adjustment model with additional 
conditions as follows: 
CX -W z0 (13) 
V=AX-L 
where: X = rectify vector of exterior orientation elements and 
object point coordinates; 
B = coefficient of error equation of relative control factor: 
D =constant vector of error equation of relative control factor; 
À = coefficient of image point coordinates error equation; 
L = constant vector of image point coordinates error equation; 
C=coefficient of restrict condition of relative control factor; 
W = constant vector of restrict condition of relative control. 
Relative control factor applied in adjustment system can partly 
change coefficient vector X status of rank defect, and can make 
the adjustment network more stably. 
4. RESULT AND CONCLUSION 
For testing and verifying correction of theory and method, 
author developed software that solve close-range model and 
three dimensions visualization based on OpenGL. Using CCD 
camera takes photo around an office building and teaching 
building to acquire dynamic sequence image data, which form 
stereo photo pair. Then carry out digital close-range 
photogrammetry process and part tests of three modeling with 
non-control point only relative control factors. Camera is 
NIKON DIX, 3008*1960 pixel, focal length: 28.9mm, 
resolution: 7.88 um, image file: TIFF, JPEG. 
41 Result 
The digital close-range photogrammetry free network bundle 
adjustment processing includes image points measure with 
stereo photo pairs, inner orientation, relative orientation of 
model, and connection of model and bundle adjustment. The 
system interface (see Fig 3-1), calculation results (see sheet 3-1) 
and three dimensions visualize result as shown (see Fig 3-2). 
  
  
  
  
    
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Fig.3-1 Software interface 
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Fig.3-2 Visualize result 
    
   
  
   
   
   
   
    
      
   
  
  
    
    
    
   
  
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4.2