SPOT stereo matching for DTM generation Page 1 SPOT stereo m(5)

This paper presents a matching algorithm for automatic DTM generation from SPOT images that provides dense, accurate and reliable results and attacks the problem of radiometric differences between the images. The proposed algorithm is based on a modified v

SPOT stereo matching for DTM generation

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generally smoothly changing (average slope 7 ). The 1225 DTM was derived from 252000 height values, has an accuracy of 4.1 m and a height range of 1500 m. Although it is not the most extreme case that can be encountered in Switzerland, the terrain is in most parts steep (average slope 18 ). Forests cover ca. 20% of map sheet 1224 and 35 - 40% of map sheet 1225. In the latter there are also lakes covering ca. 4% of the area. Some clouds were present. The radiometric differences were larger in map sheet 1224 which included agricultural areas. In a previous test published in Baltsavias and Stallmann, 1992b the accuracy potential of the algorithm was tested by using good approximations that were derived from the reference DTMs. For matching, the following 5 different versions were compared: Version 1: patch size 17 x 17, no geometric constraints, conformal transformation Version 2: patch size 17 x 17, constraints, conformal transformation Version 3: patch size 17 x 17, constraints, shifts only Version 4: patch size 17 x 17, constraints, conformal transformation, grey level images Version 5: patch size 9 x 9, constraints, shifts only All versions used gradient magnitude images with the exemption of version 4 that used grey level images. The aim was to compare constraints vs. no constraints, grey level vs. gradient magnitude images, conformal vs. shift transformation, and shifts with different patch sizes. The case of af ne transformation was excluded a priori because in many cases it is not stable since the selected points lie at edges and thus two scales and one shear are often not determinable. Table 1 shows the difference between the 34000 - 38000 matched points and the reference DTM, whereby the cleaned data refer to the matching results after automatic blunder detection.

Table 1

Differences of estimated heights (cleaned data) to heights bilinearly interpolated in the reference DTM (in meters) 1224 max. absolute 31.0 33.8 38.7 40.9 41.7 RMSE 7.2 8.5 9.5 9.6 10.2 mean+1.8+2.7+2.9+3.3+2.7%≥ 40 m 0.0 0.0 0.0 0.0 0.0 max. absolute 42.9 44.8 47.6 48.0 52.7 RMSE 8.9 9.4 11.2 10.0 10.7 1225 mean+1.1+1.5+1.1+2.3+1.5%≥ 40 m 0.0 0.1 0.2 0.1 0.2

In the here presented test, the same points were matched but their approximations were derived by a hierarchical approach using image pyramids. 6 pyramid levels, including

the original image were used. They were created with a decimation factor of 2 and a 3x3 Gaussian low-pass lter. Due to the non- ltering of the borders of the pyramid levels and a border for half the patch size to be used in matching, some border points could not be matched and were excluded a priori. The same points were matched in all pyramid levels. From the ve versions of the old test, version 5 was dropped and a new version 6 was used. It is similar to version 2 but instead of a conformal transformation, only two shifts and one rotation were used, since the scale was not expected to be always well-determinable as the points were lying along edges. Table 2 shows these results for the 0th pyramid level. Unsuccessfully matched points are those that needed more than 20 iterations.

Version 1 2 3 4 5

This paper presents a matching algorithm for automatic DTM generation from SPOT images that provides dense, accurate and reliable results and attacks the problem of radiometric differences between the images. The proposed algorithm is based on a modified v

SPOT stereo matching for DTM generation

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Table 2 Version

Matching versions 1224 Successfully matched points 85.0% 92.8% 97.6% 86.1% 96.0% Iterations per point 5.8 4.1 3.3 4.7 3.7 1225 Successfully matched points 89.1% 94.4% 97.4% 89.7% 96.8% Iterations per point 5.2 4.1 3.6 4.3 3.9

1 2 3 4 6

These results were analysed for automatic detection of blunders. The criteria that have been used for quality analysis are: standard deviation of unit weight from the least square matching, correlation coef cient between the template and the patch, number of iterations, x-shift (i.e. change from the approximate values), standard deviation of x-shift, y-shift, standard deviation of y-shift, and the size of the used shaping parameters. After matching, the median ( M ) and the standard deviation of the mean absolute difference from the median ( s(MAD) ) were computed for each criterion. The median and the s(MAD) were used instead of the average and the standard deviation because they are robust against blunders. For each criterion, the threshold for the rejection of a point was de ned as M+ N s(MAD). N was selected to be 3 for all criteria with the exemption of the number of iterations, the two shifts and the scale which should be left to vary more (N= 4 ). A point was rejected (i) when one of its criterion did not ful l the aforementioned threshold (relative threshold derived from the image statistics), or (ii) one of its criteria did not ful l a very loosely set threshold, e.g. for the correlation coef cient 0.2 (absolute threshold, valid for all images). The same N and absolute thresholds were used for all versions. This blunder detection scheme was successfully applied in the old test. In the current test some problems occurred. The number of the remaining points in the 0th level was signi cant decreased when the blunder detection test was applied after each pyramid level. Thus, we decided to apply the test only to the results of the 0th level. However, wrong points in the upper pyramid levels were diverging from their correct position as matching sequentially proceeded down the image pyramid. These points were typically

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