International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
  
  
  
  
  
  
  
  
  
  
  
  
  
b, 5 C 
C, 
£, 
DTM (Q) 
193 dX 
E INA ete Q 
Y D, n, 
go D, D; 
POP, » dx, 
— th P', P, 
POP, ; >| dx n 
P. ?. 
  
  
  
Figure 2. Constrained matching in POPs 
Constrained matching in POPs will be described in detail in the 
following. Figure 2 depicts the situation for a pair of POPs, 
with POP, being the reference image. The object point is shown 
in its initial position (Q). During the iterative adjustment 
procedure, the object point is shifted by the vector dX, until its 
final position Ó on the true DTM is found (intermediate 
positions are not shown here). Least-squares matching is 
performed in the POPs, with the template centered on the fixed 
point P in the reference image. The matching window is 
moving in POP», centered on the approximate position (P). In 
each iteration step, the object point is projected into the POPs 
using the intersection method described in Section 2.2.1. As 
long as no consistent solution is found, the projected points P', 
and P', will not coincide with the matched positions B, and 
(P5). To achieve this, the following geometric constraints must 
be added to the MPCM system for each image: 
! 
(x,)+Ax, =x, 
+ dx, (6) 
P * Ay, = Y, T dy x 
where: (x, ) ... approximated position in the POP image 
Ax, ... LSM translation parameter 
cu ... projected object point in the POP 
dx... shift of the projected point due to an object 
point shift (see Equation (3)). 
For the reference image the LSM shift parameters are set to 
zero, which forces the object point to lie on the projection ray 
defined by b,- As the tangential plane is fixed at this point, the 
geometric constraint is strict and the projected point will 
already coincide after the first iteration. The fixed ray and the 
basis vector 5,; define the epipolar plane £5. 
In the second image, the point (P,) is shifted by the LSM 
process. The normal vector m; defining the tangential plane 
must therefore be recalculated in each iteration. As (D;) 
converges towards /),, the intersection becomes more and 
more accurate. Thus, the solution for D’, will be strict in the 
final position. The intersection line of the tangential plane with 
the epipolar plane £;» defines the epipolar line in object space. 
Applying the geometric constraint (6) to the second image 
forces the matched point to lie on the tangent line of the 
epipolar curve at point Pr 
As described above, the implementation of the epipolar 
constraint is done by adding geometric constraints for each 
image to the MPCM system. Inserting Equation (3) into (6) 
gives the modified geometric constraint for POPs. The 
constraints are introduced to the MPCM system as pseudo- 
observations with a certain weight as follows: 
  
  
  
  
|. 0G; 2 2 
(x) 74, T9 = 9 dX 96€ v +26. “A. 
OX oY 0X A {D 
06; 0G? 0G? 
y, )~y, +v] = —t-dX + —-dY + ——-dZ — Ay 
(y,) 2 3x JY c IN ( Y» 
2.2.3 Introducing the flow constraint 
As already mentioned in Section 2.1.3, additional constraints 
applied to the object coordinates can be introduced in a multi- 
temporal MPCM system. This means, that the flow vector 
f, -Q,-Q,can be constrained to a certain direction/length 
obtained from a specific flow model. 
As rock glacier flow is known to be driven mainly by gravity, 
the displacement will follow more or less the gradient direction 
of the DTM. In the reference epoch the gradient g, of the rough 
DTM is calculated at position Q,. For a second epoch, the flow 
constraint f et = () can be formulated. 
Because the Z-component is considered to be less accurate, the 
flow constraint will only be applied to the X- and Y- 
components of the flow vector. After linearization with respect 
to the object point coordinates the flow constraint can be 
introduced to the MPCM system as a pseudo-observation: 
f..gi 4v, 2-(dX,- dX,):g! *(daY, -dY,):g; (9 
Depending on the weight selected, the flow constraint will be 
more or less strict, which must be controlled by the user. If the 
weight chosen is too high, matching will fail, because of errors 
contained in the flow model. Applied with a suitable weight, 
however, the flow constraint will automatically exclude false 
matches from the measured flow vector field. 
In this Chapter a detailed description of the new matching 
algorithm implemented in the ADVM 2.0 software has been 
provided. The following Chapter will present a case study of à 
rock glacier monitoring project performed with ADVM. 
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