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apolating the
height at this pixel from the nearest neighbour in the DEM
image. In cases where the reference patches are distributed at
regular and frequent intervals in the reference image the use of
this simple method can be justified.
Once a height has been extrapolated for the current pixel the
remaining provisional values must be computed (see figure 1).
Firstly, the X and Y object coordinates are computed from the re-
arranged collinearity equations, using the known reference image
orientation and all the calibrated additional parameters. In a
second stage the computed X,Y,Z object coordinates are
projected into all the search images to obtain x,y image
coordinates (corrected for distortion). The image coordinates are
then transformed into the original pixel coordinate system using
the known transformation parameters. The provisional
parameters are used by the MPGC routine and if successful (the
matching results pass a run-time blunder test) the resulting height
is stored in the DEM image. If the MPGC matching failed, the
more reliable MIC routine is called to compute another estimate
for the height of this current surface point.
4. MULTI IMAGE CORRELATION
Multi-image correlation (MIC) is an extension to the traditional
grey level correlation technique. A correlation value, such as the
normalized cross-correlation coefficient, describes the similarity
between two patches, and can be used for solving correspondence
problems between images. The basic steps of most correlation
search procedures are:
1. Extract a reference patch from the reference image. The
conjugate position of this reference patch in the search
image must be determined.
2. Define a search area and specific sampling positions
(search patches) for correlation, within the search image.
3. Compute the correlation values (with respect to the
reference patch) at each of the defined sample positions.
4. Find the sample position with the maximum correlation
value. This position indicates the search patch with highest
similarity to the reference patch.
reference ray with
search steps 3 —
reference image
and patch
~J ——
search images with search patches at
geometrically consistent positions
along the epi-polar "lines"
Figure 2. The multi-image correlation (MIC) search
concept. À search step (sample) number is shown next
to the search patches and their associated object point.
When no image orientation data is used, correlation search
procedures correlate over an entire 2-D search area within the
search image. When relative orientation between two images is
known, the search patch centres can be restricted along the epi-
501
polar “line” in the search image. This procedure is often used by
photogrammetrists (see Wong and Ho, 1986; Claus, 1984 or
Dowman, 1984) to determine correspondences between two
images.
The feature which makes the developed MIC algorithm different
and more reliable is the simultaneous use of more than one
search image. The correlation search patch centres are not only
constrained along the epi-polar "lines" of the search images but
also to geometrically consistent positions within these “lines”.
Figure 2 shows both these constraints. A single correlation value
describing the similarity of these search patches to the reference
patch is computed at each of the search steps (samples). Again,
the maximum correlation value of the samples indicates the
search patch set with the highest similarity to the reference patch.
This extension is a natural progression from stereo-correlation
and shares many of the advantages of MPGC matching when
more than two images are used.
4.1 Constrained Search Space
In order to create a geometric consistency between the search
patches, it is appropriate to drive the search procedure by
generating search patch image coordinates from a varying height
coordinate along the "reference ray". The reference ray is
defined here as the imaging ray passing through the centre of the
reference patch. An example, using figure 2, is given here to the
describe the search process. The search starts at height (Z-
coordinate) 1 at point 1 along the reference ray. The X and Y
coordinates of point 1 can be computed from the re-arranged
collinearity equations. Both the search patch positions numbered
1 are calculated by back projecting point 1 into the two search
images. Image distortions are taken into account during this
computation. A correlation value, describing the similarity of
these two search patches to the reference patch, is determined.
The search height is then incremented to height number 2 and the
process repeats itself.
This is therefore a one dimensional search in object space along
the reference ray. The method ensures that all search patches are
geometrically consistent and it also allows for the implementation
of a reliable search Z-range. If relatively precise knowledge
concerning the surface shape exists, the search Z-range could be
strictly applied and even changed for each surface point. The
search height increment (step) could simply be set to a constant
value (say 1mm), however this might create an over or under
sampling depending on the image scales and geometries. Rather,
the height increment should be computed so that the search
patches are moving at approximately constant steps in the search
images. The computation suggested here is updated after each
sampling by using a simple proportion calculation to approximate
the required increment. The next height increment AZ;,;,
computed after the ith sample is given by:
AZ As,
paio As
1
AZ (1)
where AZ, is the height increment at sample i, ^s, is the required
largest image step and as; is the largest image step amongst the
search images at sample i. This ensures that all the next search
image steps are smaller than or equal to as,. For most of the
practical tests performed during this work a value of either 0.5
or 1 pixel for as, has been used.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
