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This paper presents a class of minimal solutions for the 3D-to-3D registration problem in which the sensor data are 3D points and the corresponding object data are 3D planes. In order to compare the 6 degrees-of-freedom transformation between the sensor and the object, the authors need at least six points on three or more planes. They systematically investigate and develop pose estimation algorithms for several configurations, including all minimal configurations that arise from the distribution of points on planes. The degenerate configurations are also identified. They point out that many existing and unsolved 2D-to-3D and 3D-to-3D pose estimation algorithms involving points, lines, and planes can be transformed into the problem of registering points to planes.
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