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Geometric matching of 3D objects: assessing the range of successfulinitial configurations

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Abstract

This paper considers the matching of 3D objects by a geometric approach based on the iterative closest point algorithm (ICP), which, starting from an initial configuration of two rigid objects, iteratively finds their best correspondence. The algorithm does not converge always to the best solution. It can be trapped in a local minimum and miss the optimum matching. While the convergence of this algorithm towards the global minimum is known to depend largely on the initial configuration of test and model objects, this paper investigates the quantitative nature of this dependence. Considering the space C of relative configurations of the two objects to be compared, we call range of successful initial configurations, or SIC-range, the subspace of C which configurations bring the algorithm to converge to the global minimum. In this paper, we present a frame for analyzing the SIC-range of 3D objects and present a number of original experimental results assessing the SIC-range of a number of real 3D objects
Published in Proceedings, International Conference on Recent Advances in 3-D Digital Imaging and Modeling 101-106, 1997
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... The latter is mostly urban [17,26] or wellstructured environment, like tunnels [15]. The robustness of registration against initial misalignment is ex-plored in [11]. This type of exploration is continued with an evaluation of icp against ndt in order to compare the valley of convergence of both methods [15]. ...
... She concludes that the norm of the difference of Euler Angles is not a distance and that the use of geodesic distance on a unit sphere is preferable. Instead of using continuous metrics, Hugli and Schutz [11] propose to use Successful Initial Configuration map, or sic-map, to display results on a 2D plot. The authors used fixed thresholds on the error to identify failure, weak success and success of the registration. ...
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... It is well-known that the ICP often converges to a local minimum which leads to bad performance. Providing a good initial alignment estimate for the ICP can draw the optimization process towards the global optimum [38]- [40]. To find such an initial estimate for the Riemannian-ICP we employ the parallel transport (PT) based alignment method of O'Yair [26] as an additional step prior to applying the ICP algorithm. ...
... It is well-known that the ICP often converges to a local minimum which leads to bad performance. Providing a good initial alignment estimate for the ICP can draw the optimization process towards the global optimum [38]- [40]. To find such an initial estimate for the Riemannian-ICP we employ the parallel transport (PT) based alignment method of O'Yair [26] as an additional step prior to applying the ICP algorithm. ...
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... In the absence of a priori knowledge or robust features, the ICP algorithm starts with one unique or, preferably, multiple different initial configurations [21]. In [22], a framework is presented for analyzing the subspace of the complete configuration space so as to force the ICP algorithm to converge to the global minimum. The method is evaluated experimentally for a number of real 3D objects. ...
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... Range data registration is tipically done by the ICP algorithm or its extensions 1, 2, 3]. Recently, i t w as proposed to approach this task by a frequency domain method 4, 5, 6 ] . ...
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... where I is the 3 × 3 identity matrix and the matrix norm M is chosen as the largest singular value of M [13].Fig. 4a) shows an example of a typical histogram of obtained by registering a set of 500 3D views taken 72 degrees apart by standard spin-images andFig. ...
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