24 € VF UM (39) 
t OA ner tr 
where QF is the corresponding diagonal element of Q5. 
In case we are testing a set of additional parameters y, not 
included in the available model, with corresponding coeffi- 
cient matrix D., then the statistic used is (Dermanis, 1990): 
f= q dQ a 
eta DRO.sQ Ses e 
where q is the number of the additional parameters y,, and 
àQ- VT Qoi D, [DIQ4D,] DIQV V . (41) 
When a single additional parameter y, with coefficient vec- 
tor d, is to be tested, the test statistic becomes 
f— 1 Oo 
F=r T5 S Fibra (42) 
Or 
[zl qp Q2 
ESF f S NFipri 7 pri (43) 
where 
di ZI 2 
Pe (44) 
9 dl Q; d, 
In order to finally choose the appropriate additional para- 
meters two strategies, as the most promising, can be used 
(Sarjakoski, 1984): the orthogonalization method and the 
procedure of stepwise regression analysis. The second me- 
thod is applicable in the case of photo-invariant additional 
parameters but very cumbersome in the case of photo-va- 
riant. 
The first method is based on singular value decomposition 
S-CIN,C (45) 
where C is the orthogonal matrix of eigenvectors of Ny 
and S is the diagonal matrix of eigenvalues. Then the new 
set of additional parameters a to be estimated is 
connected to the old set by 
a-Cly or y=Ca - (46) 
We are currently experimenting in order to find the most 
optimum procedure. 
4. SNAP - OPERATIONAL ASPECTS 
4.1 Hardware considerations 
The hardware components of the SNAP system were kept 
to minimum level. More specifically, a standard IBM-com- 
patible PC is suggested, with Intel 80286 or 80386 microp- 
rocessor (math-coprocessors are used when present but 
not required) with 640Mb of RAM and a hard disk. 
     
4.2 Data acquisition and pre-processing 
Today we can distinguish three main types of input devices 
as far as Architectural Photogrammetry is concerned, na- 
mely: small analytical photogrammetric instruments based 
on comparator measurements (eg. Adams MPS-2, Topcon 
PA-2000, Galileo-Siscam STEREOBIT), digitizer-based sys- 
tems (eg. Wild ELCOVISION, Rolleimetric MR2) and small 
digital stations (eg. DVP, Gagnon et.al., 1990, DIRECT, 
Patias, 1991). 
SNAP can read data (stored in a file) from anyone of the 
above sources, while at present appropriate drivers for on- 
line connection to different instruments are been deve- 
loped. Through these drivers the photo-coordinates of all 
*control" points involved in reference frame definition, in 
formation of geometrical constraints and in formation of 
surveying measurements, are read in a photo-wise manner. 
Pre-processing of the data includes incorporation of the 
camera calibration report, correction of compara- 
tor/digitizer/scanner affine errors, correction of radial lens 
distortion and finally determination of approximate values 
for the exterior orientation parameters, if they are not 
available (eg. Hâdem, 1990, Zeng and Wang, 1992). 
4.3 Data processing and stereo-plotting 
The processing of the data includes the following phases: 
Definition of the reference frame 
In order for a reference frame to be defined the user has 
the option to fix: 
- all control points coordinates 
- some of them only 
- some control points coordinates and put geometrical 
constraints, which are recognized on the object (eg. points 
on same line, or on same distance from camera, parallel 
or perpendicular lines, etc.). 
Formation of normal equations. The user can choose 
between the photo-variant or photo-invariant approach. In 
either case the normals are formed sequentially in a “first- 
come, first-serve” fashion as far the photographs is con- 
cerned. There is no restriction on the number of photogra- 
phs involved. Additionally, the inclusion of the geometrical 
constraints is sequential and thus the user can check their 
appropriateness in every step. 
Auxiliary observations. Additional surveying measu- 
rements can be incorporated into a combined adjustment 
(currently under development). 
  
Stereo-plotting. After the processing of the data, the 
i.o. and the e.o. parameters plus the additional parameters 
pertaining to each photo are computed and kept into a file. 
The plotting of the detail points is done either on-line or 
off-line by measuring the photo-coordinates (on as many 
photos) of the detail points and using the pre-saved info- 
rmation of each photo respectively. The output are ground 
coordinates of the detail points, which are displayed on the 
screen simultaneously. SNAP is then relies on popular gra- 
phics packages for editing. 
5. SNAP’S GROWTH POTENTIAL 
SNAP is an operational system based on low-cost equip- 
ment and state-of-the-art software. It combines all the cha- 
racteristics of big bundle-adjustment programs, with cove-