Iterative point matching for registration of free-form curves
01 Jan 1992-pp 42
TL;DR: In this article, a least-squares technique is used to estimate 3D motion from the point correspondences, which reduces the average distance between curves in two sets, and yields an accurate motion estimate.
Abstract: Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in many pratical applications, some a priori knowledge exists which considerably simplifies the problem. In visual navigation, for example, the motion between successive positions is usually either small or approximately known, but a more precise registration is required for environment modeling. The algorithm described in this report meets this need. Objects are represented by free-form curves, i.e., arbitrary spaces curves of the type found in practice. A curve is available in the form of a set of chained points. The proposed algorithm is based on iteratively matching points on one curve to the closest points on the other. A least-squares technique is used to estimate 3-D motion from the point correspondences, which reduces the average distance between curves in two sets. Both synthetic and real data have been used to test the algorithm, and the results show that it is efficient and robust, and yields an accurate motion estimate. The algorithm can be easily extended to solve similar problems such as 2-D curve matching and 3-D surface matching.
Citations
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26 Oct 2011
TL;DR: A system for accurate real-time mapping of complex and arbitrary indoor scenes in variable lighting conditions, using only a moving low-cost depth camera and commodity graphics hardware, which fuse all of the depth data streamed from a Kinect sensor into a single global implicit surface model of the observed scene in real- time.
Abstract: We present a system for accurate real-time mapping of complex and arbitrary indoor scenes in variable lighting conditions, using only a moving low-cost depth camera and commodity graphics hardware. We fuse all of the depth data streamed from a Kinect sensor into a single global implicit surface model of the observed scene in real-time. The current sensor pose is simultaneously obtained by tracking the live depth frame relative to the global model using a coarse-to-fine iterative closest point (ICP) algorithm, which uses all of the observed depth data available. We demonstrate the advantages of tracking against the growing full surface model compared with frame-to-frame tracking, obtaining tracking and mapping results in constant time within room sized scenes with limited drift and high accuracy. We also show both qualitative and quantitative results relating to various aspects of our tracking and mapping system. Modelling of natural scenes, in real-time with only commodity sensor and GPU hardware, promises an exciting step forward in augmented reality (AR), in particular, it allows dense surfaces to be reconstructed in real-time, with a level of detail and robustness beyond any solution yet presented using passive computer vision.
4,184 citations
Book•
30 Sep 2010
TL;DR: Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images and takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene.
Abstract: Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of recipes, this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.
4,146 citations
12 May 2009
TL;DR: This paper modifications their mathematical expressions and performs a rigorous analysis on their robustness and complexity for the problem of 3D registration for overlapping point cloud views, and proposes an algorithm for the online computation of FPFH features for realtime applications.
Abstract: 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).
3,138 citations
TL;DR: A probabilistic method, called the Coherent Point Drift (CPD) algorithm, is introduced for both rigid and nonrigid point set registration and a fast algorithm is introduced that reduces the method computation complexity to linear.
Abstract: Point set registration is a key component in many computer vision tasks. The goal of point set registration is to assign correspondences between two sets of points and to recover the transformation that maps one point set to the other. Multiple factors, including an unknown nonrigid spatial transformation, large dimensionality of point set, noise, and outliers, make the point set registration a challenging problem. We introduce a probabilistic method, called the Coherent Point Drift (CPD) algorithm, for both rigid and nonrigid point set registration. We consider the alignment of two point sets as a probability density estimation problem. We fit the Gaussian mixture model (GMM) centroids (representing the first point set) to the data (the second point set) by maximizing the likelihood. We force the GMM centroids to move coherently as a group to preserve the topological structure of the point sets. In the rigid case, we impose the coherence constraint by reparameterization of GMM centroid locations with rigid parameters and derive a closed form solution of the maximization step of the EM algorithm in arbitrary dimensions. In the nonrigid case, we impose the coherence constraint by regularizing the displacement field and using the variational calculus to derive the optimal transformation. We also introduce a fast algorithm that reduces the method computation complexity to linear. We test the CPD algorithm for both rigid and nonrigid transformations in the presence of noise, outliers, and missing points, where CPD shows accurate results and outperforms current state-of-the-art methods.
2,429 citations
TL;DR: The main idea is to consider the objects boundaries in one image as semi-permeable membranes and to let the other image, considered as a deformable grid model, diffuse through these interfaces, by the action of effectors situated within the membranes.
2,277 citations
References
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TL;DR: In this paper, the authors describe a general-purpose representation-independent method for the accurate and computationally efficient registration of 3D shapes including free-form curves and surfaces, 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.
Abstract: 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. >
17,598 citations
01 Jan 1985
TL;DR: This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry.
Abstract: From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry...The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two."
6,525 citations
TL;DR: A closed-form solution to the least-squares problem for three or more paints is presented, simplified by use of unit quaternions to represent rotation.
Abstract: Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task . It finds applications i n stereoph and in robotics . I present here a closed-form solution to the least-squares problem for three or more paints . Currently various empirical, graphical, and numerical iterative methods are in use . Derivation of the solution i s simplified by use of unit quaternions to represent rotation . I emphasize a symmetry property that a solution to thi s problem ought to possess . The best translational offset is the difference between the centroid of the coordinates i n one system and the rotated and scaled centroid of the coordinates in the other system . The best scale is equal to th e ratio of the root-mean-square deviations of the coordinates in the two systems from their respective centroids . These exact results are to be preferred to approximate methods based on measurements of a few selected points . The unit quaternion representing the best rotation is the eigenvector associated with the most positive eigenvalue o f a symmetric 4 X 4 matrix . The elements of this matrix are combinations of sums of products of correspondin g coordinates of the points .
4,522 citations
TL;DR: An algorithm for finding the least-squares solution of R and T, which is based on the singular value decomposition (SVD) of a 3 × 3 matrix, is presented.
Abstract: Two point sets {pi} and {p'i}; i = 1, 2,..., N are related by p'i = Rpi + T + Ni, where R is a rotation matrix, T a translation vector, and Ni a noise vector. Given {pi} and {p'i}, we present an algorithm for finding the least-squares solution of R and T, which is based on the singular value decomposition (SVD) of a 3 × 3 matrix. This new algorithm is compared to two earlier algorithms with respect to computer time requirements.
3,862 citations
TL;DR: A new approach is proposed which works on range data directly and registers successive views with enough overlapping area to get an accurate transformation between views and is performed by minimizing a functional which does not require point-to-point matches.
2,850 citations