Sensors producing 3D point clouds such as 3D laser scanners and RGB-D cameras are widely used in robotics, be it for autonomous driving or manipulation. Aligning point clouds produced by these sensors is a vital component in such applications to perform tasks such as model registration, pose estimation, and SLAM. Iterative closest point (ICP) is the most widely used method for this task, due to its simplicity and efficiency. In this paper we propose a novel method which solves the optimisation problem posed by ICP using stochastic gradient descent (SGD). Using SGD allows us to improve the convergence speed of ICP without sacrificing solution quality. Experiments using Kinect as well as Velodyne data show that, our proposed method is faster than existing methods, while obtaining solutions comparable to standard ICP. An additional benefit is robustness to parameters when processing data from different sensors.
Once the corresponding point pairs are selected the next challenge is to use this information to find the optimal transformation. Several optimisation techniques are used to minimise ICP's cost function. Fitzgibbon @cite_3 presents a method which uses a non-linear Levenberg-Marquardt method @cite_6 which combines batch gradient descent and Gauss-Newton to optimise the cost function. Levine @cite_5 uses simulated annealing to minimise the cost function.
@cite_5 @cite_6 @cite_3
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Concerns the problem of range image registration for the purpose of building surface models of 3D objects. The registration task involves finding the translation and rotation parameters which properly align overlapping views of the object so as to reconstruct from these partial surfaces, an integrated surface representation of the object. The registration task is expressed as an optimization problem. We define a function which measures the quality of the alignment between the partial surfaces contained in two range images as produced by a set of motion parameters. This function computes a sum of Euclidean distances from control points on one surfaces to corresponding points on the other. The strength of this approach is in the method used to determine point correspondences. It reverses the rangefinder calibration process, resulting in equations which can be used to directly compute the location of a point in a range image corresponding to an arbitrary point in 3D space. A stochastic optimization technique, very fast simulated reannealing (VFSR), is used to minimize the cost function. Dual-view registration experiments yielded excellent results in very reasonable time. A multiview registration experiment took a long time. A complete surface model was then constructed from the integration of multiple partial views. The effectiveness with which registration of range images can be accomplished makes this method attractive for many practical applications where surface models of 3D objects must be constructed. > From the Publisher: This is the revised and greatly expanded Second Edition of the hugely popular Numerical Recipes: The Art of Scientific Computing. The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. With over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, this book is more than ever the most practical, comprehensive handbook of scientific computing available today. The book retains the informal, easy-to-read style that made the first edition so popular, with many new topics presented at the same accessible level. In addition, some sections of more advanced material have been introduced, set off in small type from the main body of the text. Numerical Recipes is an ideal textbook for scientists and engineers and an indispensable reference for anyone who works in scientific computing. Highlights of the new material include a new chapter on integral equations and inverse methods; multigrid methods for solving partial differential equations; improved random number routines; wavelet transforms; the statistical bootstrap method; a new chapter on "less-numerical" algorithms including compression coding and arbitrary precision arithmetic; band diagonal linear systems; linear algebra on sparse matrices; Cholesky and QR decomposition; calculation of numerical derivatives; Pade approximants, and rational Chebyshev approximation; new special functions; Monte Carlo integration in high-dimensional spaces; globally convergent methods for sets of nonlinear equations; an expanded chapter on fast Fourier methods; spectral analysis on unevenly sampled data; Savitzky-Golay smoothing filters; and two-dimensional Kolmogorov-Smirnoff tests. All this is in addition to material on such basic top Abstract This paper introduces a new method of registering point sets. The registration error is directly minimized using general-purpose non-linear optimization (the Levenberg–Marquardt algorithm). The surprising conclusion of the paper is that this technique is comparable in speed to the special-purpose Iterated Closest Point algorithm, which is most commonly used for this task. Because the routine directly minimizes an energy function, it is easy to extend it to incorporate robust estimation via a Huber kernel, yielding a basin of convergence that is many times wider than existing techniques. Finally, we introduce a data structure for the minimization based on the chamfer distance transform, which yields an algorithm that is both faster and more robust than previously described methods.