We present three iterative methods for finding an optimal rotation and translation or 3-D displacement, that will bring a set of 3-D points at the closest possible location to a set of 3-D lines, the correspondence between points and lines being known. The main application is the pose estimation of a 3-D model given a 2-D projection, orthographic or perspective.
Each method attempts to minimize a sum of positive measures of the Euclidiean distance between a point and its corresponding line. The first method is a non-linear Levenberg Marquardt minimizer. The second method uses a series of linearizations. The last method is a statistically robust minimizer.
We generate random test data consisting of a bundle of lines. We select a point on each line, perturb the set of points with a known displacement and add noise to selected points. We then compare the registration results with the three methods. The robust method is less sensitive to noise than the other two. On advantage of the linear method is that it operates on as few as three points and lines.
By: André Guéziec
Published in: RC21237 in 1998
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