3.3.1 Characteristics of satellite imagery influencing
automatic height determination (case of SPOT)
The first stage in image processing is therefore to improve
the information on satellite position and view direction.
Processing aerial photographs relies on a property known
as epipolarity. This means that, after suitable rotation of one
of the photographs to bring them into alignment, it is
possible to scan along a line in the one photograph and find
matching points along a matching line in the other.
This property is important in computer processing, because
it enables a scan-line in one image to be related to a scan-
line in the other, and match points are found with a one-
dimensional search, among pixel values that are adjoining
in memory.
SPOT images do not have this property, because the scan-
line are imaged at different times from different positions,
and because of the Earth's rotation. It is often desirable to
preprocess the images in an attempt to enable epipolar
scanning. A resampling scheme based on estimated
satellite position can be performed to simplify the later step
of finding matching points in the images.
In order to bring the SPOT images into epipolarity condition
and also enabling extraction of metric information from
images, a mathematical model is used to represent the
platform/sensor imaging characteristics and other
influencing parameters like Earth'rotation and earth's
curvature.
Almost all authors use the collinearity condition equations
developed for aerial photogrammetry as the basis for their
algorithm to evaluate point heights [Carrol, 1987;
Priebbenow, 1989; Koency et al, 1987; Westin, 1990]. The
image coordinate systems need to be rotated and translated
according to the ground coordinate system.
In addition to the pixel location on image and the object
point coordinates, the collinearity equation usually contains
six elements of exterior orientation. It is important to notice
that theoretically due to the continuous movement of
platform, for each pixel there should be six different
elements. However for the relatively short period of
scanning one line of imagery, it is common to consider only
one set of six elements for each line.
The collinearity equation corresponding to one line is:
Aimage= A M P. round
Where, Aj, is the coordinates of an image point in the
image coordinate points; Pgouna iS the coordinates of the
object point in the ground coordinate system; A is a scale
factor, the ratio of distance between image points to the
distance between corresponding object points; and M is an
orthogonal three dimensional rotation matrix, allowing the
image plane to be rotated parallel to a ground system.
The orientation of one image of the SPOT satellite is
defined by the coordinates of the satellite position X,; Y,; Z,
and its orientation angles w,, ®,, and x . Because of the
movement and nonuniform gravity of the earth the satellite
does not move in a simply defined orbit, and the
coordinates of position and the orientation angles are
function of the time. Figure 4 shows the effects of these
variations [Koency et al, 1987].
776
The most direct method for functionally expressing the
exterior orientation elements for satellite based sensors is
to model the vehicle motion by orbit parameters. The
satellite position as well as its nominal heading can be
calculated as function of time, and then in the collinearity
equation while the rotational elements (0, 6, x) of exterior
orientation appear, the positional elements are now
replaced by functions of the orbital parameters.
The stereo pairs of SPOT images are taken at different
times (often within five days), so because of transitory
phenomena such as cloud, haze, etc, patterns will not
always match up between two images. Because images are
slowly sampled over a nine-second period and form
different rotation angles they are non-epipolar. Day & Muller
(1989) indicate that rotation and translation can render the
images near-epipolar, but that in practice it is not possible
to resample to true epipolarity without iterative adjustment.
Hence mathematical models that do not require true
epipolar geometry are preferred.
3.2 Algorirhm for matching
There are two basic approaches to finding matching points
in the two images. The first of these is the area-based, or
correlation method, and the second approach is feature-
based.
3.2.1 Area-based algorithm for matching points
In this method the pixel data is compared directly, searching
for the position in one image corresponding to target point
in the other. The measure used to determine the match is
based on a correlation coefficient calculated over a small
area.
3.2.2 Feature based matching algorithm for matching
points
In this method the original pixel data is simplified, retaining
only points or lines of major intensity change which will
correspond to some "features' of the landscape. Matching
then usually assumes epipolar geometry, that is for a line of
pixels in one image, a line of pixels can be found in the
other image that is collinear with it. This greatly simplifies
the matching process, reducing it to one-dimensional
search. Epipolar geometry is generally possible with aerial
photography, but is difficult to achieve accurately with
satellite imagery because each image is built up over a
nine-second period, scan-line at a time. During this period,
the satellite moves a considerable distance, and the earth
rotates. This means that, strictly, one image can not simply
be rotated to gain epipolarity.
Feature-based matching could be based on matching point
features or edge features. With the point-based approach
distinct points (interest points) are obtained from each
image and matched. In contrast, edge-based solution
identifies distinct edge from each image using an edge
detector (Otto & Chau, 1989). Edge detectors are
mathematical operators, operating on different directions.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996
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