This article presents for the first time a global method for registering 3D curves with 3D surfaces without requiring an initialization. The algorithm works with 2-tuples point+vector that consist in pairs of points augmented with the information of their tangents or normals. A closed-form solution for determining the alignment transformation from a pair of matching 2-tuples is proposed. In addition, the set of necessary conditions for two 2-tuples to match is derived. This allows fast search of correspondences that are used in an hypothesise-and-test framework for accomplishing global registration. Comparative experiments demonstrate that the proposed algorithm is the first effective solution for curve vs surface registration, with the method achieving accurate alignment in situations of small overlap and large percentage of outliers in a fraction of a second. The proposed framework is extended to the cases of curve vs curve and surface vs surface registration, with the former being particularly relevant since it is also a largely unsolved problem.
There are several approaches for the local alignment of two point clouds of which Iterative Closest Point (ICP) is probably the most prominent and broadly disseminated one @cite_16 . There are numerous variants and modifications of ICP @cite_11 @cite_20 , many of which work well in situations of refinement of curves-vs-surface or curve-vs-curve registration @cite_12 . However, all these methods are local and require proper initialisation to converge. In this article, we aim at global, fast alignment of curves and surfaces, with no prior assumptions about the initial displacement or amount of overlap.
@cite_16 @cite_12 @cite_20 @cite_11
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Despite the fact that original Iterative Closest Point(ICP) algorithm has been widely used for registration, itcannot tackle the problem when two point clouds are par-tially overlapping. Accordingly, this paper proposes a ro-bust approach for the registration of partially overlappingpoint clouds. Given two initially posed clouds, it firstlybuilds up bilateral correspondence and computes bidirec-tional distances for each point in the data shape. Based onthe ratio of bidirectional distances, the exponential functionis selected and utilized to calculate the probability value,which can indicate whether the point pair belongs to theoverlapping part or not. Subsequently, the probability val-ue can be embedded into the least square function for reg-istration of partially overlapping point clouds and a novelvariant of ICP algorithm is presented to obtain the optimalrigid transformation. The proposed approach can achievegood registration of point clouds, even when their overlappercentage is low. Experimental results tested on public da-ta sets illustrate its superiority over previous approaches onrobustness. In this paper we present a novel on-line method to recursively align point clouds. By considering each point together with the local features of the surface (normal and curvature), our method takes advantage of the 3D structure around the points for the determination of the data association between two clouds. The algorithm relies on a least squares formulation of the alignment problem, that minimizes an error metric depending on these surface characteristics. We named the approach Normal Iterative Closest Point (NICP in short). Extensive experiments on publicly available benchmark data show that NICP outperforms other state-of-the-art approaches. The authors describe a general-purpose, representation-independent method for the accurate and computationally efficient registration of 3-D shapes including free-form curves and surfaces. The method handles the full six degrees of freedom and is based on the iterative closest point (ICP) algorithm, which requires only a procedure to find the closest point on a geometric entity to a given point. The ICP algorithm always converges monotonically to the nearest local minimum of a mean-square distance metric, and the rate of convergence is rapid during the first few iterations. Therefore, given an adequate set of initial rotations and translations for a particular class of objects with a certain level of 'shape complexity', one can globally minimize the mean-square distance metric over all six degrees of freedom by testing each initial registration. One important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model, prior to shape inspection. Experimental results show the capabilities of the registration algorithm on point sets, curves, and surfaces. > The ICP (Iterative Closest Point) algorithm is widely used for geometric alignment of three-dimensional models when an initial estimate of the relative pose is known. Many variants of ICP have been proposed, affecting all phases of the algorithm from the selection and matching of points to the minimization strategy. We enumerate and classify many of these variants, and evaluate their effect on the speed with which the correct alignment is reached. In order to improve convergence for nearly-flat meshes with small features, such as inscribed surfaces, we introduce a new variant based on uniform sampling of the space of normals. We conclude by proposing a combination of ICP variants optimized for high speed. We demonstrate an implementation that is able to align two range images in a few tens of milliseconds, assuming a good initial guess. This capability has potential application to real-time 3D model acquisition and model-based tracking.