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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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. > Abstract The automatic co-registration of point clouds, representing 3D surfaces, is a relevant problem in 3D modeling. This multiple registration problem can be defined as a surface matching task. We treat it as least squares matching of overlapping surfaces. The surface may have been digitized sampled point by point using a laser scanner device, a photogrammetric method or other surface measurement techniques. Our proposed method estimates the transformation parameters of one or more 3D search surfaces with respect to a 3D template surface, using the Generalized Gauss–Markoff model, minimizing the sum of squares of the Euclidean distances between the surfaces. This formulation gives the opportunity of matching arbitrarily oriented 3D surface patches. It fully considers 3D geometry. Besides the mathematical model and execution aspects we address the further extensions of the basic model. We also show how this method can be used for curve matching in 3D space and matching of curves to surfaces. Some practical examples based on the registration of close-range laser scanner and photogrammetric point clouds are presented for the demonstration of the method. This surface matching technique is a generalization of the least squares image matching concept and offers high flexibility for any kind of 3D surface correspondence problem, as well as statistical tools for the analysis of the quality of final matching results. Many modern sensors used for mapping produce 3D point clouds, which are typically registered together using the iterative closest point (ICP) algorithm. Because ICP has many variants whose performances depend on the environment and the sensor, hundreds of variations have been published. However, no comparison frameworks are available, leading to an arduous selection of an appropriate variant for particular experimental conditions. The first contribution of this paper consists of a protocol that allows for a comparison between ICP variants, taking into account a broad range of inputs. The second contribution is an open-source ICP library, which is fast enough to be usable in multiple real-world applications, while being modular enough to ease comparison of multiple solutions. This paper presents two examples of these field applications. The last contribution is the comparison of two baseline ICP variants using data sets that cover a rich variety of environments. Besides demonstrating the need for improved ICP methods for natural, unstructured and information-deprived environments, these baseline variants also provide a solid basis to which novel solutions could be compared. The combination of our protocol, software, and baseline results demonstrate convincingly how open-source software can push forward the research in mapping and navigation.