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.
In our recent work [1], [2], we proposed Point Feature Histograms (PFH) as robust multi-dimensional features which describe the local geometry around a point p for 3D point cloud datasets. In this paper, we modify their mathematical expressions and perform a rigorous analysis on their robustness and complexity for the problem of 3D registration for overlapping point cloud views. More concretely, we present several optimizations that reduce their computation times drastically by either caching previously computed values or by revising their theoretical formulations. The latter results in a new type of local features, called Fast Point Feature Histograms (FPFH), which retain most of the discriminative power of the PFH. Moreover, we propose an algorithm for the online computation of FPFH features for realtime applications. To validate our results we demonstrate their efficiency for 3D registration and propose a new sample consensus based method for bringing two datasets into the convergence basin of a local non-linear optimizer: SAC-IA (SAmple Consensus Initial Alignment). We present an algorithm for fast global registration of partially overlapping 3D surfaces. The algorithm operates on candidate matches that cover the surfaces. A single objective is optimized to align the surfaces and disable false matches. The objective is defined densely over the surfaces and the optimization achieves tight alignment with no initialization. No correspondence updates or closest-point queries are performed in the inner loop. An extension of the algorithm can perform joint global registration of many partially overlapping surfaces. Extensive experiments demonstrate that the presented approach matches or exceeds the accuracy of state-of-the-art global registration pipelines, while being at least an order of magnitude faster. Remarkably, the presented approach is also faster than local refinement algorithms such as ICP. It provides the accuracy achieved by well-initialized local refinement algorithms, without requiring an initialization and at lower computational cost.