International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
using camera pose and average distance between camera focus 
and objects that are projected to the image plane of camera. 
Since each image frame is projected to itself dependent baseline, 
we can create video mosaics from a moving and rotating 
camera. The proposed algorithm consists of 3 steps: calculation 
of optical flow through hierarchical strategy, calculation of 
camera exterior orientation using collinearity equations, and 
determination of multi-baselines. This paper realized and 
showed the proposed algorithm that can create efficient image 
mosaics in 3D space from an real image sequence. 
2. FEATURE BASED OPTICAL FLOW DETECTION 
Camera orientation is computed utilizing optical flows which 
are obtained from sparsely located feature points that are 
detected using SUSAN algorithm (Smith ef a/., 1997). Based on 
such feature points, the correlation and the contour style are 
computed and utilized to determine the best matching pair of 
feature points. The false optical flows, which are significantly 
different from others, are removed in the procedure of the 
repeated conversion using a median filter. 
3. FEATURE BASED OPTICAL FLOW DETECTION 
We discuss the camera’s exterior orientation on the 
assumption that the interior orientation of the camera has 
already been established and discuss about exterior orientation. 
If P(X,Y.Z) denote the Cartesian coordinates of a scene point 
with respect to the camera, and if (x,y) denote the corresponding 
coordinates in the image plane, the image plane is located at the 
focal length f from the focal point ox, Zl of the camera. 
The perspective projection of a scene point P(X,Y,Z) on the 
image plane at a point where p—(x, y) is expressed as follows: 
Y NS 
y AM. Y-Y, . (0) 
f Z-4, 
where À is the scale factor, X, , Y, , Z, is the camera station, 
and M isa 3 x 3 rotation matrix defined as follows: 
To eliminate the scale factor À , we divided the first and 
second component equations in Eq. 1 by the third, leading to 
the following more familiar collinearity equations: 
om X= Xm, YA rm (LZ) 
m4CX - X,)2m,(Y -Y, )ums(Z-Z,) (o 
CX. — X, ) emu (Y —- Y, )-oma(Z -Z,) 
PG - X) moY-—-Y)omac -2Z,) 
  
X 
  
y=/ 
For simplicity, the collinearity equations are shown as 
following: 
Fl [x-fuiw 
F = = ; (3) 
F y-JV/W 
where [U V W] =M|X-X, Y-Y, 
728 
3.1 DEPENDENT RELATIVE ORIENTATION 
BETWEEN THE FIRST AND SECOND IMAGE FRAMES 
To solve the relative orientation with the collinearity model, 
we can transfer the nonlinearity of the equations Eq. 4 to a 
linearized form Eq. 5 using Taylor series approximations. The 
condition equation can then be written in linearized form as: 
—F+JN+J°AN +error=F, (4) 
y manual |, 
where PF z-FG SE, X, > ear A. Z) ; 
6 t y7 x7 are initial 
values, and 
F = Fi Fri F dm JJ 
4nx] : : 
r 
A' = ^o, Ag, AK, AY, t AZ, | and 
art 5 A 
= [D AA S FA AZ NY jm are the vector 
amd ! I { i+ 
form to the approximations for the parameters, 7“ and Js 
4nx5 4nx3n 
are the matrix of the partial derivatives of the two functions in 
Eq. 4 with respect to each of the five exterior orientation 
elements and the three coordinates of the GCP, i(=3...n) is the 
index of the i” optical flows, and / is the index of the image 
frames. 
We used the first two images of an image sequence to 
determine the reference image frame. The world frame was 
typically aligned with the first image frame. The camera 
orientation at the second image frame can be calculated using 
the dependent relative orientation, Eq. 5, with the five pairs of 
manual 
optical flows and the .X L2 of the current camera station, 
which is input manually. Eq. 6 involves rewriting Eq. 5 for 
vectors, as follows: 
No. V2 A N; 
el ; (5) 
Ny N, A N, 
where N = TELS Nom JUN. oe JT. 
w= Fang =F, 
The parameter A is found as follows: 
-l T e -] 
(Ni = Nu Ny NA =m —N,Nyn,. — (6 
After a few iterations of Eq. 7, we determine the exterior 
orientation of the camera at the second frame as follows: 
|, à K Y, 21 =, % K, vs £s] se 
3.2 ABSOLUTE ORIENTATION FOR 3" to last image 
framesDEPENDENT RELATIVE ORIENTATION 
BETWEEN THE FIRST AND SECOND IMAGE FRAMES 
From the third image frame to the last image frame, the 
camera orientation can be calculated by using the GCP of three 
optical flows for three frames. 
We can calculate the camera orientation using a minimum of 
three GCPs of optical flows that are calculated by using two 
  
  
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