' B3. Istanbul 2004
| approach, is to
of the images and
allowing a direct
ong and Faugeras,
nation of epipolar
h computer vision
why it cannot be
problems are not
> the fundamental
occur. Once again,
inner nature of the
epipolar geometry
002), is based on a
d by Orun and
hat during image
1 constant, but the
r polynomial. The
ipolar line, defined
Y; tax. Q)
nts in the left and
' parameters to be
nt in the left image
curve in the right
nt in the left image
upon which the
; to ag have to be
y substituting the
equation (2) and
1 order polynomial
th the Melbourne
aligned to epipolar
d between the two
matching strategy.
nd to have cross
95, implying well
ints were then split
is used to calculate
polynomial model.
obtain the solution
f redundancy, and
'y a least squares
points were used as
the second order
oordinates of the
0 the model, along
he right image (%),
red to the expected
| point in the right
54 check points.
oot mean Square
ixel, implying that
del is sufficiently
for matching non-
ld be successfully
lego images were
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
similarly processed. As with the Melbourne data, well matched
points (matched points with cross-correlation coefficients of
greater than 0.95) were used to determine the parameters «y to
as. This time a total of 34 points were used in the least squares
estimation process.
44 Affine projective model constraint
The affine projective model constraint is an object space
constraint. Rather than limiting the search to lines in image
space, the search is limited to lines in object space. This is done
by generating a grid of object space points (X, Y, Z) which
coincides with the coverage of the stereomodel. These points
are sequentially projected into the image space of both images
being matched, using the appropriate affine model. The image
points are then matched and the similarity measure recorded.
The process is then repeated with a new value of Z for the
object space point. The value of Z (basically the height
component of the point in object space) is varied until a highly
correlated match is found. At this point, the value of Z will be a
good estimation of the height of the terrain.
5. MATCHING STRATEGY
5.1 Candidate matching point selection
Selection of candidate matching points was carried out
automatically. A regular grid of points was projected across the
images being matched. Since each pair of images in cach data
set were georeferenced to ground coordinates (i.e. pre-aligned
with each other), the projected grids of points could be
considered as rough approximations of conjugate points, and
hence used in the first stage of the matching algorithm. This
method of initial point selection was found to be both efficient
and sufficiently accurate for the matching strategies under
investigation.
52 Matching strategy
Throughout this study, the matching strategy used for
determining the conjugate points incorporates intensity-based
matching and utilises the cross-correlation coefficient as a
similarity measure. Since this is the most appropriate strategy
for matching points in images with similar radiometric
distributions, such as stereopairs of high resolution satellite
imagery where time difference between image acquisition is
small, no other matching methodologies (such as least squares
matching or feature-based matching) were tested.
For each point to be matched, an image chip from the master
image is repeatedly projected into the slave image at various
locations around the likely candidate match point (the spatial
extent and frequency of these locations being defined by the
search space and step size respectively). The location where the
maximum value of the cross-correlation coefficient, y, is found
indicates a successful match. The cross-correlation coefficient,
Y is given by:
O vis (3)
O0
yx y)-
S
Where 0, and os are the standard deviations of the master and
slave chips being matched and oe, is the covariance of the
intersection of the master chip with the slave chip (Gonzalez
and Woods, 1992).
5.3 Hierarchical matching
Hierarchical matching is a technique often used in image
matching in order to reduce processing time. It has been
incorporated into the matching strategy used in this study by
repeating the matching process whilst progressively reducing
the search space and the step size. In the first iteration a wide
search space is used with a large step size. The result of the first
iteration (a coarse match) is used as the approximation of the
next iteration, where both the search space and the step size are
decreased. The matching is then repeated, and the result (this
time less coarse) is again passed to the next iteration. Thus in
each iteration the matching results become progressively more
refined, but processing time remains reasonable. The number of
iterations used in the matching in this study was four.
6. RESULTS
6.1 Analysis of correlation coefficients
Using the methodology described above with the two geometric
constraints (epipolar and affine), grids of points were matched
in each of the test images. The matching results for these
experiments are presented in table 2.
: No. of matched
Te ; 5 = No. ol i.
l'est site Geometric ir points with
points in :
constraint M correlation
2 coefficient > 0-8
Melbourne Epipolar 58302 37473 (64-394)
{spipalar) Affine 68199 43637 (64.094)
San Diego Epipolar 17673 6240 (35.3%)
(non-epipolar) Affine 18149 5613 (30.1%)
Table 2. Matching results
Table 2 shows the number of matched points with correlation
coefficients greater than 0.8, and the corresponding percentages
with respect to the total number of points matched, for each
combination of image and matching constraint. A number of
very interesting conclusions can be drawn from these results,
since, as it can be seen, the epipolar constraint and the affine
constraint give very similar results, but these results are very
image dependent.
The first important point to note is that use of the epipolar
constraint based on the second order polynomial used with the
San Diego data does not adversely affect the matching results.
If this model had been incorrect, then the number of well
matched points would have been much less than the 35% that
was achieved.
The second point to note is the effect of image content on the
matching algorithm. The percentages of well matched points for
the San Diego data are much lower than those for the
Melbourne data. This could be due to a number of reasons.
Firstly, the terrain varies much more steeply in the San Diego
data, meaning object space features may appear ditterently in
each of the images due to the differing incidence angle.
Secondly, the steeply varying terrain causes differing solar
reflections, meaning that ground features may have differing
radiometric signatures in each image. Finally, and probably
most importantly, the content of the San Diego images is very
