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(a) Readuals between viewpoits obtamed in
multiple registration and GPS data (by Conceptual structure of sequential alignment
GPS point
(c) Result of sequential alignment (d) After minimizing violations (overlapped with a 1/500 digital map)
Figure 9: Multiple registration using two GPS points which are located on the opposite side of the network.
range images, which are independent in registration. Violations are shown in Figure 5 as dotted lines. It can
be found that violations exist in ve neighboring range image pairs, i.e. (#26, #39) (#24,#26) (#21,#22)
(#16,#17), and (#35,#36), after sequential alignment. A result of sequential alignment is shown in Figure 6(a).
The model is shown in Z-image as de ned in Zhao and Shibasaki, 1999. Pixel size of Z-image is 1m. Obvious
inconsistency can be found in several places. Violations are minimized as addressed in section 2. A well-balanced
model of range images is obtained as shown in Figure 6(b). Change of violations in each neighboring range
image pairs is examined in Figure 7. The ve peaks after sequential alignment corresponds to the ve violations
shown in Figure 5. It can be found that after minimization, violations are not disappeared but distributed
into other range image pairs. Violations are not distributed equivalently, because a weight evaluating the
reliability of pair-wise registration is assigned in minimization. To examine the relative accuracy of the model,
a transformation matrix transforming the locations of range images in the model to the coordinate system of
GPS is estimated, where the sum of squared residuals from registered location to GPS measured locations is
minimized. Residuals between registration result and GPS data are graphed in Figure 8. Mean of residuals is
0.663m.
3.2 Multiple registration when absolute locations of several range images are known
We measure the absolute locations of several range images using GPS. With the absolute locations, all range
images can be registered to the world coordinate system. Figure 11 and Figure 12 compares the results of
registering 42 range images using two GPS points. Figure 11 shows the result where two GPS points are located
on the opposite side of the network, while Figure 12 shows the result where two GPS points are located near
to each other. In both of the cases, six violations exist in sequential alignment. They are shown as dotted lines
in the conceptual structures (see Figure 11(b) and Figure 12(b). Results of sequential alignment are shown in
1038 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
