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Mapping from Space
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Relative DEM Production from SPOT Stereo without GCP
Matching
- Selection of target point
The purpose of relative DEM production in this study is to know terrain relief roughly even though the area has no GCP. For this purpose it is necessary to know relative position of ridges and valleys. Those points on ridges and valleys are extracted by edge detection. The matching target points is
Selected at intervals of more than 3 pixels in x direction, and at intervals of 5 pixels in y direction.
Edge sampling procedure:- Sobel operator was used for edge detection in this study. Target points are selected from the points, which have the maximum value of Sobel intensity and also have 35 or more sobel intensity (s) is calculated from 3 by 3 pixels as follows:
Sobel Intensity difference is defined as the difference of maximum and minimum of Sobel intensity, which are calculated along x direction and y direction in local area of the image.
- Restriction of search area
For a target certain point in a image, window in the other image is moved in the search area to extract the best fit point. Search area should be as small as possible for efficient computer processing. Y direction of search area can be restricted by approximate epipolar line and x direction can be also restricted by maximum slop gradient. Dark blue parallelogram with the size of 4 pixels by 14 pixels in Figure 5 shows the search area determined by the following method.
Approximate epipolar line:- The gradient of approximate epipolar line is defined as the following equation (see in figure 1) :
The gradient is calculated by using a set of corresponding points in one line. This calculation is based on least-square method. The calculated gradient is used in the matching on the next line. Initial gradient is derived from the following equation (see in Figure 2):
In this study, initial gradient of right image was 0.065 for a pair of right and center images, and the one of left image for a pair of left and center images were -0.015. Gradient is computed in every matching line until the difference between calculated gradient of two consecutive matching lines becomes smaller than 0.005. An approximate epipolar line is shown as light blue band in Figure 5.
Maximum slope gradient:- Figure 3 shows search range along an approximate epipolar line. The point A' has been already matched to the point A. the point B is the next target point. When the maximum slope gradient O and a satellite geometric data are given, the point B should be projected between the point B' and the point C'. We assumed in this study that the maximum slope gradient is 45o. The restriction of search area in x direction is shown as light blue rectangle in Figure 5.
- Matching Procedures
Before the matching processing, one pair of corresponding points should be given. Matching processing is based on correlation method with search area restriction. The sizes of three matrix windows for computing correlation coefficient are 11 by 11, 15 by 15 and 29 by 29 pixels. The whole three correlation coefficients are not always calculated. Three matrics are considered to have hierarchical structure. The correlation coefficient is calculated in order from high hierarchy to low hierarchy. If the matched point is judged as poorly matched point, the correlation coefficient is calculated again in second hierarchy. The judgment of matching is based on a correlation coefficient and a distance between matched point which has correlation coefficient. 1.0 and distance 0.0 is judged as the best matched point. In the case of correlation coefficient is poor but distance has smaller value, the matching point is judged as matched point. If distance has large value but correlation coefficient is better, the matching point is also judged as matched point. In this study, the high hierarchy was 15 by 15 matrix and low was 29 by 29 matrix. These matrices were experimentally selected by assuming that small matrix was effective with large distortion and large matrix was effective with poor features in local area.15 by 15 matrix was regard as standard in matching process. These matrices were set by considering process speed. In triplet matching process, tripplet matching is performed as a combination of two stereo pair matching (a pair of Center and Right image, and a pair of Center and Left image). Common target points in the Center image are used for two stereo pairs.
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