Global Registration of 3D Point Sets via LRS Decomposition
This paper casts the global registration of multiple 3D point-sets into a low-rank and sparse decomposition problem. This neat mathematical formulation caters for missing data, outliers and noise, and it benefits from a wealth of available decomposition a
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DPIA - Universit` a di Udine, Via Delle Scienze, 208, Udine, Italy [email protected], [email protected] AST Lab - STMicroelectronics, Via Olivetti, 2, Agrate Brianza, Italy [email protected]
Abstract. This paper casts the global registration of multiple 3D point-sets into a low-rank and sparse decomposition problem. This neat mathematical formulation caters for missing data, outliers and noise, and it benefits from a wealth of available decomposition algorithms that can be plugged-in. Experimental results show that this approach compares favourably to the state of the art in terms of precision and speed, and it outperforms all the analysed techniques as for robustness to outliers. Keywords: Point-set registration · Motion synchronization completion · Low-rank and sparse matrix decomposition
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Introduction
The goal of multiple point-set registration is to find the rigid transformations that bring multiple (n ≥ 2) 3D point sets into alignment, where each rigid transformation is represented by an element of the Special Euclidean Group SE(3), namely the semi-direct product of the Special Orthogonal Group SO(3) with R3 . This is a fundamental problem in the reconstruction of 3D models of objects, covering a wide range of applications, including (but not limited to) cultural heritage, engineering modelling and virtual reality. If n = 2 then we are dealing with a pairwise (two point-sets) registration problem. The gold standard in this context is the Iterative Closest Point (ICP) Algorithm [1,2], which computes correspondences between the point sets given an estimate for the rigid transformation, then updates the transformation based on the current correspondences, and iterates through these steps until convergence – to a local minimum – is reached. See [3] for an overview of several variants of the ICP Algorithm. If n > 2 then we are dealing with a multiple point-set registration problem, which is more complex than the n = 2 case due to the high amount of parameters that have to be estimated. Among the initial attempts to address this problem are the sequential techniques introduced in [2,4], that repeatedly register a new point set into a growing model, until all the sets are considered. This approach however returns suboptimal solutions since it does not take into account all the c Springer International Publishing AG 2016 B. Leibe et al. (Eds.): ECCV 2016, Part IV, LNCS 9908, pp. 489–504, 2016. DOI: 10.1007/978-3-319-46493-0 30
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available constraints, e.g. the constraint between the last and first point set is not used if the sets are obtained using a turntable. Global methods, on the other hand, consider simultaneously all the points sets. They are able to exploit the redundancy in the constraints between pairs of point sets, to compensate and distribute the error, thereby preventing drift in the solution. Global registration can be solved in point space or in frame space. In the former case, all the rigid transformations are computed by optimizing a
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