4.2 Correlation Functions 
To make a decision whether to accept or reject a group of 
conjugate search patches as possible matches to the reference 
patch, a suitable correlation (similarity) value needs to be 
computed from the grey values of the reference patch and all the 
search patches. This "combined" correlation value must be a 
function of the individual correlation values for each search 
patch. A number of possible methods for determining suitable 
individual correlation values could be used. The normalized 
cross-correlation function (see for example Wong and Ho, 1986, 
for the equation) can be used to calculate a correlation 
coefficient, p, ranging from +1 to -1; +1 indicates an exact 
similarity, zero indicates no similarity and -1 indicates that the 
search patch is a negative of the reference patch. The normalized 
cross-correlation function automatically allows for a radiometric 
equalisation of the mean and standard deviation of the two 
patches. The maximum correlation value indicates the most 
similar search patch position. 
A second method is to compute the correlation value as the 
average of the absolute grey value differences between reference 
and search patch. The patches should be radiometrically equalised 
beforehand to obtain a more reliable correlation value. In this 
case the closer the correlation value is to zero the more similarity 
between the two patches. Thus, this correlation function needs to 
be minimised to find the most similar search patch position. 
Vollmerhaus (1987) describes the use of this function, which he 
calls the cross-difference-modulus-function, in some applications. 
A combined correlation value must be computed from the 
individual correlation values of each search patch. The average 
of the individual correlation values has been used in this work as 
the combined correlation value. Only this combined (average) 
correlation value is used for determining the correct match. Both 
functions mentioned here have been investigated and both show 
similar results. The normalised cross correlation function has the 
advantage that the patches do not have to be radiometrically 
equalised beforehand. Assuming that the normalised cross 
correlation function is used, the sample with the maximum 
average correlation value is chosen as the matching sample. 
4.3 Search Patch Shaping and Sampling 
A square reference patch in the reference image is imaged as a 
non-square search patch in a search image due to different image 
positions and varying surface orientation and shape. The search 
patches used in MIC can be a priori shaped to model the effects 
of the known camera geometry, however as the surface shape is 
generally not known the second effect (due to surface orientation 
and shape variation) can not be modelled. To test the MIC 
routine, three methods of search patch shaping and sampling have 
been employed: 
1. no search patch shaping, integer sampling. 
2. no search patch shaping, sub-pixel sampling. 
3. search patch shaping, sub-pixel sampling. 
Using a rounded integer value for the search patch position 
introduces a further source of error (besides the error caused by 
unmodelled search patch shaping), but significantly speeds up the 
matching procedure as no grey level interpolation (resampling) 
is required. Sub-pixel sampling is employed to improve the 
reliability of the search but at a computational cost. Using 
502 
rounded integer values is equivalent to resampling with nearest 
neighbour interpolation. In instances of highly convergent camera 
geometry or when cameras are rotated about their optical axis, 
the search patches should be shaped to eliminate the effects of 
camera geometry. As for the MPGC matching, an affine 
transformation of the search patch is used here. Three reference 
patch pixels (two corner pixels and the centre pixel) are projected 
through object space into the search images, using equal height 
values for each. The position of the centre pixel in the search 
image defines the position of both the shaped and unshaped 
search patch positions, while the positions of the two corner 
pixels define the orientation of the shaped search patch. Affine 
transformation parameters can thus be computed from the 
unshaped to the shaped search patch. All the unshaped search 
patch pixels are then transformed using these affine parameters 
and the search patch is resampled over this transformed grid at 
the sub-pixel positions. Bi-linear interpolation has been used in 
this work to compute the grey value at a sub-pixel position. 
This shaping procedure eliminates the effects of camera geometry 
on the search patch shapes for flat surfaces parallel to the XY 
plane. Deviations of the surface patch from a constant Z-value 
plane will result in unmodelled patch shape distortions. If any of 
the pixels in the reference patch have reliable known heights, for 
example from previous matches, then these can be used to 
improve the affine shaping by assuming a slanted surface patch 
at this point. This could be used well in applications which have 
very dense sampling. As a by-product of the MIC search the 
computed shaping parameters of the correct match can be used as 
provisional values in the MPGC matching to ensure convergence. 
4.4. Correlation Example 
A number of tests were performed to investigate the reliability of 
the MIC process and to compare it to traditional stereo- 
correlation techniques. In one, a flat surface containing a highly 
repetitive grid pattern was imaged by the CCD camera in 
multiple positions. As a typical example, graphs of the 
correlation values versus sample height are depicted in figure 3 
for three search images (nos. 2, 4 and 6) and their average for a 
single correlation search at one point. The reference image (no. 
1) and the three search images were taken from camera positions 
forming a rectangle. Image 6 was rotated about 45 degrees 
around its optical axis to show the effects of patch shaping. The 
set on the left represents the correlation with patch shaping and 
the set on the right without. 
The arrows in the figures depict the sample with the maximum 
correlation value in each of the search images and the average 
correlation values as well. As can be clearly seen from the patch 
shaped set on the left, the maximum of the average correlation 
values is far more unique (and thus more reliable) than for the 
individual correlation. values (which would correspond to 
traditional stereo-correlation) which often have their maximum 
at the incorrect sample position. The two sets of graphs also 
show the improvement resulting from patch shaping which 
significantly improves the correlation results for image 6 and thus 
the average as well, however it does show that the use of multiple 
images significantly improves the reliability of the matching even 
when large errors caused by unmodelled shaping parameters still 
exist. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996 
  
Two e 
the bla 
smooth 
the MI 
measur 
from tl 
precisi 
camera 
measur 
increas 
resultir