International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
perspective) of the nonlinear perspective projection are used. 
This is accurate if the distance of the object to the camera is 
small compared to the relative depth of the object features. In 
David et. al (David et. al., 2003) the extended SoftPOSIT 
algorithm for simultaneous pose and correspondence 
determination for the case of a 3D model and its perspective 
image is illustrated. The extended SoftPOSIT algorithm uses 
line features for the matching process. Within the algorithm an 
iteration is performed, where at each step the given 2D-to-3D 
line correspondence problem is mapped to a new 
correspondence problem, which depends on the current estimate 
of the camera pose. The algorithm is then applied to improve 
the estimate of the camera pose and stops if pose and 
correspondences converge. 
2.2.3 Spatial resection for exact co-registration and geo- 
referencing: The methods described in section 2.2.2 are able to 
solve the correspondence problem, but for simplification they 
are using a weak perspective. For exact co-registration and geo- 
referencing a further iteration is necessary using the spatial 
resection approach. For this approach we assume that at least 
the correspondence problem between object and image features 
is solved. 
Y=a-X+7 
Z=ßB X+ö y=a-x+b (1) 
a a m r)en o - ze BX)- nbn - z,)- Por - Y.) > 
U du Lob aX, 27) 12,28 = PX J nals = 2.) Alp ~ 5) (2) 
  
no Nhtax, e y)en(, -8- X, B)en(a(o - Z,)- By - Y.) 
b ux 
: > fal= Y, +ax, + y) mz, zc BX, )+ noto m Z,)- Bly er Y, ) 
  
TY. 
ne Y, * Xa £y) Pala Or X,B)+ ni(a(ó = Zl pt» - Y)) 
+C 
: ni(- Y, + aX, +#)+ro(20 OT BX, )+ rn (a(6 = Z,)- Bly T Y,)) 
  
k 
Based on results of the feature matching process an exact co- 
registration of image and object space can be provided by 
spatial resection. The principle of this algorithm is to overlay 
extracted lines in the image and corresponding edges of the 3D 
CAD model to estimate the parameters of the exterior 
orientation (- position and orientation to the time of data 
collection). The camera parameters (xk, yk and ck) in equation 
(3) are fix values, estimated by a separate camera calibration 
process. The principle of the feature based spatial resection 
process is illustrated in Figure 6. 
  
  
  
  
  
  
Scene 
captured 
by user 
— 77 model (3D-CAD) 
position and orientation 
Figure 6. Principle of the feature based spatial resection 
For the feature based spatial resection initially the well-known 
collinearity equations are utilized, e.g. (Kraus, 1996). As we are 
using straight lines as tie-information, the commonly used 
collinearity equations are modified by the parameterisations (1). 
906 
The resulting equations are shown in (2) and (3). A more 
detailed mathematical description of this context can be found 
in (Schwermann, 1995). To solve the spatial resection problem, 
a least squares algorithm using the Gauss-Markov-Model was 
implemented. Here the unknown parameters (Xo, Yo, Zo, o, q, 
K) are estimated and an exact co-registration of object and 
image space can be provided. 
Up to now we assumed: (a) that the feature matching problem 
(between image and object space) is solved and (5) that 
parameters of the rough exterior orientation are available. In 
some circumstances it will be impossible to solve the matching 
problem automatically or there will be no information about the 
initial orientation parameters. For a semi automatic approach 
there exist a method to solve this problem. The collinearity 
equations clearly describe the mapping process of a 3D object 
into the image space. But in a least squares approach (as used 
for solving the spatial resection) the non-linear equations cannot 
be used without initial values. To overcome this dilemma and 
for estimation of rough (initial) exterior orientation parameters 
the feature based direct linear transformation (DLT) is usable. 
As the DLT is linear, the unknown parameters of the exterior 
orientation can be calculated directly within a least squares 
approach. The equations of the feature based DLT are shown in 
(4) and (5). 
X= (al, + AL, +L,)-Z 4 (A, + dL, + de 
(aL, * BL, * L,) Z - QL, * 8L, +1) 
“10 
  
(4) 
(aL, BL, eL) Z + +O +L.) 
To (at s Boot Zi, toL urrl] (3) 
  
Using equations (4) and (5) the unknown parameters L;-L,; can 
be obtained by a least squares approach. This offers the 
possibility to derive the exterior orientation parameters (Xo, Yo, 
Zo, ©, Q, K) from the L,-L;, parameters (KrauB, 1983), which 
can be used as initial values for the feature based spatial 
resection. The solely disadvantage of the DLT method is the 
higher order of the unknown parameters compared to the spatial 
resection method. Therefore we need a higher number of 
observations (ny, 2 6) to be able to compute the eleven DLT 
parameters. Once the DLT is solved, the initial values for the 
spatial resection approach are available. To derive the 
orientation angles (o, «, «) the rotation matrix must be set up 
using the parameters L;-L;;. Note here, that the least square 
method for computing the DLT parameters, does not 
automatically guarantee an orthogonal transformation matrix. À 
modified DLT method proposed by Hatze (Hatze, 1988) 
addresses this problem. In principle the postulate of an 
orthogonal rotation matrix should be fulfilled to guarantee a 
correct solution, but as we need the orientation parameters only 
as initial values, this postulate can be neglected if the errors are 
small. With this initial values we are able to compute the 
exterior orientation by the feature based spatial resection. 
Dependent on the available initial information different 
approaches are possible, which are depicted in Figure 7. The 
trivial requirement is the availability of an image and a suitable 
3D model of the environment. Then in principle two ways are 
possible to calculate the exterior orientation. The process can be 
started if information about the initial exterior orientation is 
available but also if this information is missing. If there is no 
initial information the problem can be solved by a semi- 
automatic approach: First of all the features must be extracted 
(automatic or manually), then they can be manually co- 
registered to the model data. After the co-registration the DLT 
method is applicable to calculate initial values of the exterior 
In 
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