- It is desirable that additional surveying observations 
(distances, angles) and geometric constraints (parallelism, 
perpendicularity, points on same line, points on same plane, 
etc.) could be incorporated into the adjustment of the mea- 
surements. 
DATA INPUT - Ground coordinates 
- Photo coordinates 
- Calibration Report 
- Lens distortion 
- Film deformation 
- Approximate e.o. 
parameters 
  
  
  
DATA 
PRE-PROCESSING 
  
  
Definition of a 
Reference Frame 
- All control points 
constant 
- Some coordinates 
constant 
- Some coordinates 
constant + geometrical 
contraints 
  
  
  
  
  
ADJUSTMENT 
OF THE DATA 
  
  
Extra Observations | 
Measured ground 
distances between 
  
  
  
DR S ct control points 
instrumentation 
- Photo 
ON-LINE coordinates 
INTERSECTIONS | - €.0- 
TO DETAIL zi0. 
POINTS - Additional 
parameters 
  
  
Drivers 
to graphic 
DATA OUTPUT 
«E packages 
Figure 1. Functions of SNAP's modules. 
The developed SNAP system is a software package which is 
based on the current state-of-the-art in Architectural 
Photogrammetry and is enhanced with a user-friendly 
interface. The general module setup is illustrated in Figure 
1, while some theoretical aspects inherent in its 
development is explained in the next paragraphs. More 
specifically, issues concerning the definition of the 
reference frame, the sequential bundle adjustment on a 
photo-wise basis and the inclusion of the photo-variant 
additional parameters are addressed. 
2.1 Formalization of observation and normal 
equations 
It is known that the photo coordinates x, y are related to 
the ground coordinates X, Y, Z through the collinearity 
conditions: 
    
R14 (X-X)-Ri? (Y-Y o) -Ri5(Z—-Z 
t ut o) * Riz( o) * Ri3( o) AI 
R3; (X-X5) - R32 (Y-Y 0) + R33 (Z-Zo) 
  
(1) 
2 R2; (X-X9) * R2? (Y-Y 9) - R23 (Z-Z) 
y=yo-f + Ay 
R31 (X—X0) + R32 (Y—Y 0) + R33 (Z-Zo) 
  
where f is the camera constant, Xo, Yo the photo coordina- 
tes of the principal point, Xo, Yo, Zo the ground coordina- 
tes of the exposure station, and R;1, R12, …, R31 are the 
elements of the rotation matrix R - R(o, q, x). Ax and Ay 
are the corrections to x and y due to remaining systematic 
errors, which are typically modeled by polynomials of the 
type Ax - £1(y, X, y), Ay £x (y, X, y) (eg. Murai S. et al, 
1984) and y, is the vector of the so-called additional para- 
meters. In SNAP a number of such models can be used. 
The linearized observation equations for point j of the i 
photograph is written as 
ax dx dx 
mn 963v 37 FE Tox 
- 8Y-]- 
yy? ij 9y Oy dy 8Z |; 
0X 0Y 02 1 
Mm 
OX OX OX OX OX Ox 6g 
9X 0q 00 0X, 0Yo 0Zo So D Ve 
+ 
dy dy dy ay ay oy |||” lak 
0X 0 dw 0X, 9Y, 9Z, lij SYo 
ôZo _i 
(2) 
or in matrix notation as 
bii = Aj Xj E Aj Xi + Di yit Vij (3) 
The observation equations for all points on the i photo is 
b; = À; X + A; % + Diyi+ Vi (4) 
where x is the correction vector to the approximate 
ground coordinates of the control points, X is the correct- 
ion vector to the approximate values of the e.o. parame- 
ters of the i th photo and y; is the vector of the additional 
parameters of the i th photo (following a general photo- 
variant approach, eg. Moniwa, 1981). For all m photogra- 
phs the form of the system is 
b, A, A, 0. 8.0 x: 
b; A, 0 A, ... 0 0 X5 
1 - X + : + 
s A; 0.0... A; 0 X; 
bn x.