aning of the T-axis 
ont to the Z-axis of 
Iree axes are equal, 
cause the recorded 
| the direction of the 
generate a motion- 
1e slices at different 
o generate surfaces 
se surfaces should 
correlation between 
;s first each STC is 
oints of the motion 
section. 
)CESS 
X the motion-model 
d. : 
hosen slice is taken 
ints of interest are 
extraction operators 
1987]. To select 
holds of the feature 
al way, mean value 
; used. 
| be found. This is 
> points through the 
ne, 1993] is used to 
corresponding point. 
n of the gray value 
Yeighbourhood both 
ptical flow can be 
  
  
  
  
  
  
  
  
lescribing the local 
| element. The right 
a 1996 
The equation to be solved is 
gxo * gyo229., 
where g., gy and g; are the partial derivatives of the gray 
values. Using various points in the local 3D- 
neighbourhood the components can be determined by 
adjusting the overdetermined equation system by the 
method of least squares. 
The computed direction is used to get an approximate 
position of the corresponding point in the adjacent slice. 
Then the high precision localisation of the point is done 
by Least-Squares matching [Gruen, 1985]. Whereas the 
size of the template can be kept fixed for the STC, the 
size of the search area is varied depending on the 
variance of the computed components. If the accuracy is 
high then the search area can be small and vice versa. 
When the new point is determined the tracking process 
goes back to the least-squares-approach, until all the 
slices have been checked. 
In that way motion curves connecting corresponding 
object points, and their relations to one another can be 
found. The algorithm is applied separately to all the 
STCs. Then the relations between different STCs are 
checked in order to find the corresponding motion curves. 
In the course of this process also wrong parts of motion 
curves are detected and corrected. 
Finally the spatial intersection [Kraus, 1993] of 
corresponding motion curves results in a spatial curve, 
where the point locations depend on the time T [X(T), 
Y(T), Z(T)} 
3.2 Point Classification method 
In the second approach the feature extraction algorithm 
is applied independently to all the slices of the STC. To 
classify corresponding points all feature points of one 
slice are compared to the points of the adjacent slices. 
The computed distances are taken to build the relations 
between the feature points (Fig. 3). So, continuous 
motion curves as well as incomplete ones can be 
determined step by step. 
After this procedure has been applied to all the STCs the 
following steps are analogous to the point tracking 
method. The spatial intersection of the curve points for all 
the STCs results in the point co-ordinates X, Y, Z and T 
of the motion model. 
If we make use of the pattern projector both described 
methods can be applied in the same way. The difference 
concerning the first two cases is that points of the pattern 
do not represent any more one single object point. In 
each of the slices the projected pattern is located at a 
different position on the object, because of the movement 
of the object. As a constraint every point of one motion 
curve have to lie in one plane in the STC. This plane is 
determined by the projection centre of the camera and 
the light ray of the observed pattern point. 
This constraint can be used when searching for 
corresponding points. One further constraint can be 
introduced to the spatial intersection algorithm. 
Corresponding pattern points of the motion model have 
to be located on one straight line, namely on their light 
ray to the pattern projector. 
  
Fig. 3: Overlay of feature points in two adjacent slices. 
Feature points of the shown slice are marked as 
black dots, points of the adjacent slice as white 
dots. 
3.3 Comparison of both methods 
The computation of the second method is faster than the 
first one, but only points found by the feature extraction 
algorithm are being used for the classification process. 
So, if real feature points are not detected because of 
unfavourable thresholds settings, they cannot be 
classified and therefore will not appear in the motion 
model. In contrast, the point tracking method operates 
only in a local neighbourhood and can adapt itself more 
easily to different conditions of image contrast. 
Concerning the thresholds settings, of course for the first 
method inadequate parameters may be computed too. 
But in this case the thresholds only need to be set once 
per STC. This circumstance allows the user, if necessary, 
to refine the parameters interactively. For the point 
classification method is not useful to check each slice 
interactively, because of the great number of slices. 
The disadvantage of the point tracking method is that 
object points, which are not yet visible or not visible any 
more in the initial slice, due to the recorded movement, 
cannot be tracked and therefore also will be missed in 
the motion model. This problem can be overcome by 
choosing two or three slices as initial ones (e. g. at the 
beginning and at the end of the recorded STC) and track 
the points in two contrasting directions. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
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