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Worstcase and smoothed analysis of the ICP algorithm, with an application to the kmeans method
 In Proc. of the 47th Ann. IEEE Symp. on Foundations of Computer Science (FOCS
, 2006
"... We show a worstcase lower bound and a smoothed upper bound on the number of iterations performed by the Iterative Closest Point (ICP) algorithm. First proposed by Besl and McKay, the algorithm is widely used in computational geometry where it is known for its simplicity and its observed speed. The ..."
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We show a worstcase lower bound and a smoothed upper bound on the number of iterations performed by the Iterative Closest Point (ICP) algorithm. First proposed by Besl and McKay, the algorithm is widely used in computational geometry where it is known for its simplicity and its observed speed. The theoretical study of ICP was initiated by Ezra, Sharir and Efrat, who bounded its worstcase running time between Ω(n log n) and O(n 2 d) d. We substantially tighten this gap by improving the lower bound to Ω(n/d) d+1. To help reconcile this bound with the algorithm’s observed speed, we also show the smoothed complexity of ICP is polynomial, independent of the dimensionality of the data. Using similar methods, we improve the best known smoothed upper bound for the popular kmeans method to n O(k) , once again independent of the dimension. 1.
Progress in computational geometry
 Directions in Geometric Computing, pages 81  128. Information Geometers Ltd
, 1993
"... ..."
3D Shape Registration
"... Registration is the problem of bringing together two or more 3D shapes, either of the same object or of two different but similar objects. This chapter first introduces the classical Iterative Closest Point (ICP) algorithm which represents the gold standard registration method. Current limitations o ..."
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Registration is the problem of bringing together two or more 3D shapes, either of the same object or of two different but similar objects. This chapter first introduces the classical Iterative Closest Point (ICP) algorithm which represents the gold standard registration method. Current limitations of ICP are addressed and the most popular variants of ICP are described to improve the basic implementation in several ways. Challenging registration scenarios are analyzed and a taxonomy of recent and promising alternative registration techniques is introduced. Three case studies are then described with an increasing level of difficulty. The first case study describes a simple but effective technique to detect outliers. The second case study uses the LevenbergMarquardt optimization procedure to solve standard pairwise registration. The third case study focuses on the challenging problem of deformable object registration. Finally, open issues and directions for future work are discussed and conclusions are drawn. 1
Computational Aesthetics in Graphics, Visualization, and Imaging (2012), pp. 1–8 D. Cunningham and D. House (Editors) SAMBA: Steadied choreographies
"... Given the start positions of a group of dancers, a choreographer specifies their end positions and says: “Run!” Each dancer has the choice of his/her motion. These choices influence the perceived beauty (or grace) of the overall choreography. We report experiments with an automatic approach, SAMBA, ..."
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Given the start positions of a group of dancers, a choreographer specifies their end positions and says: “Run!” Each dancer has the choice of his/her motion. These choices influence the perceived beauty (or grace) of the overall choreography. We report experiments with an automatic approach, SAMBA, that computes a pleasing choreography. Rossignac and Vinacua focused on affine motions, which, in the plane, correspond to choreographies for three independent dancers. They proposed the inverse of the Average Relative Acceleration (ARA) as a measure of grace and their Steady Affine Morph (SAM) as the most graceful motion. Here, we extend their approach to larger groups. We start with a discretized (uniformly timesampled) choreography, where each dancers moves with constant speed. Each SAMBA iteration steadies the choreography by tweaking the positions of dancers at all intermediate frames towards corresponding predicted positions. The prediction for the position of dancer at a given frame is computed by using a novel combination of a distance weighted, leastsquares registration between a previous and a subsequent frame and of a modified SAM interpolation. SAMBA is fully automatic, converges in a fraction of a second, and produces pleasing and interesting motions.