International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
    
  
The integration concept between an IMU and 
photogrammetry via a Kalman Filter (KF) is the 
central topic of this paper. Section 2 briefly discusses 
the photogrammetric mathematical model and its two 
problems: resection and intersection. Section. 3 
examines the solution of SLAM using 
photogrammetry in a sequential Least-Squares 
Adjustment (LSA) mode. Section 4 examines the 
integration of photogrammetry and INS in a KF. 
Conclusions are finally drawn in the last section. 
2. MATHEMATICAL MODEL OF 
PHOTOGRAMMETRY 
Equations (1) are the co-lincarity equations in 
photogrammetric mapping. They reveal the 
relationship between the image and the object 
coordinate systems: 
Ru (X-Xy)+Rız(Y-Yo)+Rız(Z-Zo) 
  
  
Fete rate RZ Ze) 
F(y)= 
yum, 4 2(X-X0)+R20(Y-Yp)+R23(Z-Z0) 
R3, (X -Xo)- Ri(Y - Yo)* R33(Z-Zo) 
(1) 
where X,y = Photo-coordinates 
X,Y,Z = Coordinates in the object frame 
¢ = Focal length 
Xo,Yo,Zg - Coordinates of projection 
centre 
xgiyg = Photo-coordinates of the 
projection of the projection centre to the 
image plane 
Rj's - Elements of the rotation matrix 
between the image and object frames 
With this model, one can solve the basic problems of 
photogrammetric mapping, namely: resection and 
intersection: 
1. Resection, whereby the position and 
attitude of an image (exterior orientation 
parameters — EOP, X9. Yg.Z9.0,0,K ) are 
determined by having at least three points 
with known coordinates in the object frame 
as well as in the image frame (Figure 2) 
2. Intersection, whereby two images, with 
known positions and attitudes, are used to 
determine the coordinates ( X;, Y;,Z; ) of 
points found on both images 
simultaneously, employing the principle of 
stereovision (Figure 3). 
Therefore, the right combination of these two 
problems yields to navigation and mapping at once. 
Chaplin, 1999, studied the motion estimation from 
stereo image sequence during GPS outages. Our 
study stems from the same source but differs in 
concept, where a KF is used to merge the outputs of a 
resection and an IMU to perform the intersection. 
  
    
   
Objects space 
      
  
  
  
Perspective centre 
(0. 0,0) 
4, 
   
(Xa. Yo, Za. ©. 0. K) 
X 
Figure 2: Resection Problem 
Image space (R) ay, 
E zr > 
g7Xou- Yin" Yijts 7E) 
Si it 
OR( 
  
  
  
  
   
   
   
  
  
  
     
       
  
    
    
    
       
Niue Yin 7k) 
Perspective centre 
(0, 0, 0) 
OR 
{Ror. Von. Ci) 
OR 
(Nos Yor, Zow, 
O n Q n. Kn) 
Image space (E) 
íxi cg Yu Na Cr } 
ArT OR Sa avan on) 
   
Perspective centre » 
(0, 0,0) 
OR 
(X, Ya cr) 
OR 
(Xu, Yoi, Zo, 01. 0 1. Ki) 
Z 
(Xo Yo 73) 
  
Figure 3: Intersection Problem 
3. PHOTOGRAMMETRY AS SLAM 
Photogrammetry by itself can be considered as a 
solution for the Simultaneous Localisation And 
Mapping (SLAM) problem, provided all necessary 
measurements can be obtained automatically. 
Considering the initial position as known, 
intersection is used to map a number of features; then 
the vehicle moves and captures images. The features 
measured from the previous position are taken as 
Ground Control Points (GCP) in the current stage to 
compute the EOPs of the cameras. 
This procedure requires certain points to consider: 
eo Recursive LSA: the LSA solution of the 
epoch k-/ is used as observations for 
epoch &, 
e (Correlations between measurements and 
unknowns are carried from one epoch to 
the other. 
This section illustrates the operation of SLAM with 
resection and intersection in a recursive approach, 
with the embedding of the time index &. To start 
with, the initialisation has to be performed by 
determining the initial EOP of the two cameras. The 
initialisation can be done in two ways: 
|l. Initialisation with. GPS/INS, which 
demands open skies for the GPS signal, or