The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
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positive values, green for negative, and blue for invalid points 
(such as points in the sky). 
(a) Gaussian curvature map 
(b) Mean curvature map 
Figure 3: Gaussian and mean curvature map of SPj and SP 2 . 
Figure 4: Matching result between SP[ and SP 2 with geometric 
constraint. 
Although the SIFT method with geometric constraint already 
provides good matching results, false matches are nevertheless 
possible because lots of structures, which are similar in both 
gray scale and geometric shape, do exist in test scene. Since the 
following registration steps are sensitive to such false 
correspondences, we apply an additional filtering to the 
matches based on the RANSAC method (Fischler and Bolles, 
1981). Randomly a sample of point pairs is drawn from all 
SIFT matches. From the pair of three points a rigid body 
transformation is computed. All SIFT matches are checked 
against this transformation for consensus. The sample with the 
largest consensus is selected for registration. Figure 4 shows the 
151 matches from 301 candidate pairs of points by using 
geometric constraint. Only 116 are confirmed as valid 3D 
corresponding tie points using RANSAC (as shown in Figure 5). 
Since the rotation matrix R and translation vector T for initial 
alignment is available now, the ICP algorithm (Chen and 
Medioni, 1991) (Besl and McKay, 1992), which alternately 
establishes correspondences and refines the transformation 
parameters R and T, achieve a good performance and align two 
point cloud by minimizing the error metric derived from the 
distance between them. 
Figure 5: Best consensus matches found through RANSAC 
imported as tie points for registration. 
5. EXPERIMENTS 
As described in Section 4, the first step is preprocessing of 
reflectance intensity image. Then the SIFT features are 
extracted and matched from both reflectance images. As an 
example, Figure 6(a) shows the total number of matches from 
equalized or normalized reflectance image between SP] and all 
other scans. However, Figure 6(b) shows the number of correct 
matches from equalized or normalized reflectance image. The 
correct matches are defined as the pairs of points whose 
distance (|^ _ || 2 ) between p x and p' 2 (p' 2 = Rp 2 + T) is less 
than 0.5m. One can see the normalized images achieve better 
performance by involving more correct matches and less total 
matches. 
(a)The number of total matches (b)The number of correct 
matches 
Figure 6: Numerical comparison of the matching results 
between SP t and all other scans from histogram equalization 
and normalization using SIFT method. 
Figure 7(a) identifies the proposed geometric constraint 
improves the ratio of correct matches greatly. Figure 7(b) shows 
most correct matches are placed between 10m and 60m from 
the scanner and almost cover all around the scene. Therefore, 
we can expect accurate results by using these matches to 
calculate position and orientation parameters. Table 3 shows 
that by using geometric constraints we can safely exclude most 
of false matches and at the same time keep all the correct 
matches. The proposed method can improve the ratio of correct 
matches by a factor of more than two.