ar 
Ne 
he 
18 
of 
all 
J 
he 
ar 
th 
of 
hs 
of 
vertical photographs. However, in most cases, two camera 
axes are neither parallel nor perpendicular to the air base 
(C'C"). We transform images into a position that conjugate 
epipolar lines are parallel to the z-axis of the image coor- 
dinate system such that they have the same y-coordinate. 
The transformed images satisfying the epipolar condition 
are called normalized images in this paper. The normalized 
images must be parallel to the air base and must have the 
same focal length. Having chosen a focal length, there is 
still an infinite number of possible normal image positions 
(by rotating around the air base). 
3. COMPUTATION OF NORMALIZED IMAGE 
3.1 Camera Calibration 
Digital imagery can be obtained either directly by using dig- 
ital cameras, or indirectly by scanning existing aerial pho- 
tographs. In both cases, the digitizing devices (digital cam- 
era or scanner) must be calibrated to assure correct geom- 
etry. For our applications we use the rigorous calibration 
method suggested by [Chen and Schenk 92]. The method is 
a sequential adjustment procedure to circumvent the high 
correlation between DLT parameters and camera distortion 
parameters. The distortion consists of two parts: lens dis- 
tortion and digital camera error. Lens distortion is com- 
posed by radial and tangential distortion. Digital camera 
error is scan line movement distortion since EIKONIX cam- 
era used in our applications is a linear array camera. For 
more details about digital camera calibration, refer to [Chen 
and Schenk 92]. With the camera calibration, we can obtain 
a digital image free of systematic distortion. The image is 
called pizel image in this paper. 
3.2 Transforming pixel image to normalized image 
The normalized image is a pixel image in epipolar geometry 
with reference to the object space. Thus, exterior orienta- 
tion elements after absolute orientation are to be used for 
transforming the pixel image to a normalized image. The ex- 
terior orientation elements consist of three rotation angles 
and the location of perspective center in the object space 
system. The relationship between pixel image and object 
space is expressed by the collinearity equation 
ru1(X — Xe) + T12(Y — Yo) + ris(Z — Ze) 
Pra(X — Xc) * raX(Y — Ye) + raa(Z — Zc) 
0 "aX — Xc) - raX(Y — Yc) * ras(Z — Ze) 
r31(X — X¢) + r32(Y — Ye) + 733(Z — Zc) 
  
(1) 
Tp = — 
  
where z,,y, are image coordinates and ry; ---733 are ele- 
ments of an orthogonal rotation matrix R that rotates the 
object space to the image coordinate system. X¢,Yc, Zc 
are the coordinates of the projection center; X,Y, Z, the 
coordinates of object points. 
There are two steps involved in the transformation of the 
pixel images (P’, P") to normalized images( N', N"). First, 
pixel images are transformed to írue vertical images and 
from there to normalized images. Fig. 2 shows the relation- 
ship between pixel images and normalized images. 
The first transformation from pixel image to true vertical 
position simply involves a rotation with RT, where R is an 
405 
ope vs 2" 
  
X 
Figure 2: Relationship between pixel image and normalized 
image 
orthogonal rotation matrix from the object space to image 
space. Next, a transformation from true vertical to the nor- 
malized position is applied. The first angle of the rotation 
matrix Rp transforming from true vertical to the normalized 
position is K about the Z-axis, then 9 about the Y-axis, 
Q about the X-axis. The rotation angles K, 9 can be com- 
puted from the base elements B.X, BY, BZ, and (1 from the 
exterior orientation angles: 
  
BY 
K m tan EX (2) 
BZ 
$ — —tan 1 ——————ÀÀ (3) 
(BX? + BY?)'/? 
w' uw" 
where BX z X" — X', BY - Y" —Y', and BZ — Z" — Z". 
The base rotation matrix Rp will be the following. 
Rp = RaRsRx, (5) 
where 
cosK  sinK 0 
Rx = | —sinK cosK 0 
0 0 1 
cos® 0 —sin® 
0 1 0 
sin® 0 cos® 
Il 
Rs 
1 0 0 
Ra= 10 cos) sing 
0 —sin(Q cos(Q 
The base rotation matrix Rp is a combined matrix in which 
the primary rotation axis is about the Z-axis, followed by 
a rotation about the Y-axis and X-axis. Depending on the 
Q (X-axis rotation), there are many different normalized