International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004
Figure 1. SPOT 5 scene of Melbourne, Australia
The affine projective model is the simplest method of relating
image space coordinates to object space coordinates without
any knowledge of the sensor model or the exterior orientation
of the sensor. Early research was carried out using moderate
resolution satellite sensors such as SPOT and MOMS (Okamoto
et al., 1999; Hattori et al., 2000), but more recently it has been
successfully applied to high resolution satellite imagery,
specifically IKONOS (Yamakawa et al., 2002, Fraser and
Yamakawa, 2004, Hanley et al., 2002). Although it requires
only a modest number of ground control points (GCPs), the
affine model has been shown to produce results to sub-pixel
accuracy. The general form of the model describing an affine
transformation from 3D object space (X, Y. Z) to 2D image space
(x, y) for a given point i is expressed as:
=
Il
Xr glo Agel i
yi = As X; zi As Y; SE AZ; = Ag
where x, y are image space coordinates; X, Y, Z are object space
coordinates; and A; to Ag are the eight affine parameters.
These eight parameters per image account for translation,
rotation, and non-uniform scaling and skew distortion. Implicit
in Equation 1 are two projections, one scaled-orthogonal and
the other skew-parallel. In the reported implementation of the
affine projective model, all model parameters are recovered
simultaneously along with triangulated ground point
coordinates in a process analogous to photogrammetric bundle
adjustment.
The affine model assumes, firstly, that the projection from
object space to image space is an affine projection and,
secondly, that lines of acquired image data are parallel to each
other. The first assumption holds true for high-resolution
satellite imaging sensors which have a very narrow field of
view of around 2° or less. Previous studies have shown the
assumption of parallel rather than perspective projection to be
sufficiently valid. The second assumption is true if the satellite
travels in a straight line, parallel to the ground during image
acquisition. Thus, the Universal Transverse Mercator projection
(UTM zone 55) was employed as the object space reference
coordinate system in the reported investigation, since the
assumption of a straight line track for the satellite, parallel to
the ‘XY plane’, is sufficiently valid within this projection
coordinate framework.
4. IMAGE MATCHING
The matching methodology implemented in this study
combines image space matching with an object space geometric
constraint, namely the affine projective model. Usually image
space matching uses a geometric constraint in image space,
such as epipolar geometry, to constrain the matching process.
The constraint is necessary to reduce the search space, which in
turn reduces processing time, as well as reducing the likelihood
of erroneous matches. The use of an object space geometric
constraint replaces the need for the epipolar constraint.
Matching points using geometric constraints in object space
rather than image space is simply another way of describing the
search for an unknown height value by moving along an image
nadir line until a highly correlated match of image pixels is
found. This method of matching has previously been described
by Benard (1984), and subsequently incorporated into many
object space matching processes (Helava, 1988; Ebner and
Heipke, 1988; Gruen and Baltsavias, 1986). The method works
by taking an object space point (Xy, Yo Zo) and projecting it,
using the affine projective model, into the image spaces of the
images being matched: (x;, yi) for image | and (x», v?) for
image 2. These two image points are then matched, in image
space, using a typical intensity-based matching strategy. The
similarity measure (in this case the cross-correlation
coefficient) for the match is recorded. A new object space point
(X Yo. Zo dZ) is then transformed into image coordinates and
matched as before. Once again the similarity measure is
recorded. The process is repeated for all values of Z; between
the lower and upper limits of Z. The value of Z; which
corresponds to the greatest similarity measure is taken as the
determined height at the point (X. Yo). The process is repeated
for all (X; Y)).
The similarity measure implemented in this matching strategy
to compare conjugate points was the cross-correlation
coefficient, y, given by (Gonzalez and Woods, 1992):
O ys
y y)-
OM4O5
where oy and os are the standard deviations of the master and
slave chips being matched, and o is the covariance of the
intersection of the master chip with the slave chip.
Since the matching strategy in this study is driven by an object
space geometric constraint, points have to be initially selected
in object space before being transformed into image space and
matched. Therefore, in order to generate the candidate matching
points, a grid of three dimensional object space points covering
the area of interest was created. These points were then
sequentially transformed into image space coordinates and
matched according to the method described above.