| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2004: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2003: ¥2,200,000 (Direct Cost: ¥2,200,000)
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| Research Abstract |
In this project, we studied the problem of finding the largest common subset of given three-dimensional (3-D) point sets, P and Q, such that the subset of P corresponds to the subset of Q under similar transformation in a given allowable error, and calculating the similar transformation parameters. Simulation results show that the proposed method can find the exact correspondence of P with Q in about 186 seconds using the computer of Pentium III, 1GHz in the case of 60 points of P and Q with 30 points of the common subset, a scaling factor of 0.8, and an allowable error of 1%.
The proposed method finds every pair of similar triangles in a point set P and a point set Q, and records a same label on a side-to-side table at the location of each corresponding side pair of the triangle pair. At that time, it also records the rotation vector that is determined by the similar-triangle pair. And the label of the cell located on each side pairs in the side-to-side table is propagated to the rest if the current similar-triangle pair and the previous one share the side pair, and have the same rotation vector. Finally, the method extracts the set of the side pairs with the majority label in the side-to-side table, and obtains the point-to-point correspondences between the subset of P and Q ; the largest common subset of P and Q. In this stage, the point-to-point correspondences, however, are not one-to-one correspondences. So, the similar transformation parameters cannot be determined from them. For searching a one-to-one correspondence with minimal error from them, a method called extremal optimization was used as a post-processing. As the results of experiments, we confirmed the validity of the proposed method.
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