Improving on the Voronoi cell based techniques of [28, 24], we give a Las Vegas Õ(2n) expected time and space algorithm for CVPP (the preprocessing version of the Closest Vector Problem, CVP). This improves on the Õ(4n) deterministic runtime of the Micciancio Voulgaris algorithm [24] (henceforth MV) for CVPP 1 at the cost of a polynomial amount of randomness (which only affects runtime, not cor...

For registration of 3-D free-form surfaces we have developed a representation which requires no knowledge of the transformation between views. The representation comprises descriptive images associated with oriented points on the surface of an object. Constructed using single point bases, these images are data level shape descriptions that are used for efficient matching of oriented points. Cor...

The problem of geometric alignment of two roughly preregistered, partially overlapping, rigid, noisy 3D point sets is considered. A new natural and simple, robustified extension of the popular Iterative Closest Point (ICP) algorithm [1] is presented, called the Trimmed ICP (TrICP). The new algorithm is based on the consistent use of the Least Trimmed Squares (LTS) approach in all phases of the ...

In this paper, we report a robust, efficient, and automatic method for matching infrared tracked markers for human motion analysis in computer-aided physical therapy applications. The challenges of this task stem from non-rigid marker motion, occlusion, and timing requirements. To overcome these difficulties, we use pair-wise distance constraints for marker identification. To meet the timing re...

The Closest Point Method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys. 2008] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this method. The main idea is that surface differentials of a surface function can be replaced with Cartesian differentials o...

The iterative closest point (ICP) algorithm is an efficient algorithm for robust rigid registration of 3D data. Results provided by the algorithm are highly dependent upon the step of finding corresponding pairs between the two sets of 3D data before registration. In this paper, a look up matrix is introduced in the point matching step to enhance the overall ICP performance. Convergence propert...

To automatically construct a three-dimensional (3-D) object model, it is necessary to merge a set of range images acquired from different views. The iterative closest point (ICP) algorithm has been widely used to find the transformation parameters between a pair of images. In this paper, a fast ICP algorithm is proposed by restricting the search space to one-dimensional (1-D) orthogonal lines t...

This paper investigates the use of Euclidean invariant features in a generalization of iterative closest point registration of range images. Pointwise correspondences are chosen as the closest point with respect to a weighted linear combination of positional and feature distances. It is shown that under ideal noise-free conditions, correspondences formed using this distance function are correct...

We show that given oracle access to a subroutine which returns approximate closest vectors in a lattice, one may find in polynomial time approximate shortest vectors in a lattice. The level of approximation is maintained; that is, for any function f , the following holds: Suppose that the subroutine, on input a lattice L and a target vector w (not necessarily in the lattice), outputs v ∈ L such...