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.
More closely related with our work is the article of @cite_1 that also uses local differential information for 3D registration of curves. Two methods are proposed: the first only requires a point correspondence between curves, which considerably decreases the complexity of search, but involves the computation of third order derivatives which is impractical in real, noisy data; the second uses two correspondences, leading to a dramatic increase in the complexity. We present a more clear mathematical formulation of the problem, and provide new insights that lead to an effective search scheme.
@cite_1
2064358676 2109323956 2898182017 2049981393
In this paper, we propose a new algorithm for pairwise rigid point set registration with unknown point correspondences. The main properties of our method are noise robustness, outlier resistance and global optimal alignment. The problem of registering two point clouds is converted to a minimization of a nonlinear cost function. We propose a new cost function based on an inverse distance kernel that significantly reduces the impact of noise and outliers. In order to achieve a global optimal registration without the need of any initial alignment, we develop a new stochastic approach for global minimization. It is an adaptive sampling method which uses a generalized BSP tree and allows for minimizing nonlinear scalar fields over complex shaped search spaces like, e.g., the space of rotations. We introduce a new technique for a hierarchical decomposition of the rotation space in disjoint equally sized parts called spherical boxes. Furthermore, a procedure for uniform point sampling from spherical boxes is presented. Tests on a variety of point sets show that the proposed registration method performs very well on noisy, outlier corrupted and incomplete data. For comparison, we report how two state-of-the-art registration algorithms perform on the same data sets. We propose a novel algorithm to register multiple 3D point sets within a common reference frame using a manifold optimization approach. The point sets are obtained with multiple laser scanners or a mobile scanner. Unlike most prior algorithms, our approach performs an explicit optimization on the manifold of rotations, allowing us to formulate the registration problem as an unconstrained minimization on a constrained manifold. This approach exploits the Lie group structure of SO 3 and the simple representation of its associated Lie algebra so 3 in terms of R3. Our contributions are threefold. We present a new analytic method based on singular value decompositions that yields a closed-form solution for simultaneous multiview registration in the noise-free scenario. Secondly, we use this method to derive a good initial estimate of a solution in the noise-free case. This initialization step may be of use in any general iterative scheme. Finally, we present an iterative scheme based on Newton's method on SO 3 that has locally quadratic convergence. We demonstrate the efficacy of our scheme on scan data taken both from the Digital Michelangelo project and from scans extracted from models, and compare it to some of the other well known schemes for multiview registration. In all cases, our algorithm converges much faster than the other approaches, (in some cases orders of magnitude faster), and generates consistently higher quality registrations. This paper reviews the classical problem of free-form curve registration and applies it to an efficient RGB-D visual odometry system called Canny-VO, as it efficiently tracks all Canny edge features extracted from the images. Two replacements for the distance transformation commonly used in edge registration are proposed: approximate nearest neighbor fields and oriented nearest neighbor fields. 3-D–2-D edge alignment benefits from these alternative formulations in terms of both efficiency and accuracy. It removes the need for the more computationally demanding paradigms of data-to-model registration, bilinear interpolation, and subgradient computation. To ensure robustness of the system in the presence of outliers and sensor noise, the registration is formulated as a maximum a posteriori problem and the resulting weighted least-squares objective is solved by the iteratively reweighted least-squares method. A variety of robust weight functions are investigated and the optimal choice is made based on the statistics of the residual errors. Efficiency is furthermore boosted by an adaptively sampled definition of the nearest neighbor fields. Extensive evaluations on public SLAM benchmark sequences demonstrate state-of-the-art performance and an advantage over classical Euclidean distance fields. 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. >