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28
Least squares 3D surface and curve matching
 ISPRS Journal of Photogrammetry and Remote Sensing
, 2005
"... The automatic coregistration 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 poin ..."
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Cited by 103 (17 self)
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The automatic coregistration 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 GaussMarkoff 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 closerange 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.
Registration of Point Cloud Data from a Geometric Optimization Perspective
, 2004
"... We propose a framework for pairwise registration of shapes represented by point cloud data (PCD). We assume that the points are sampled from a surface and formulate the problem of aligning two PCDs as a minimization of the squared distance between the underlying surfaces. Local quadratic approximant ..."
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Cited by 59 (13 self)
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We propose a framework for pairwise registration of shapes represented by point cloud data (PCD). We assume that the points are sampled from a surface and formulate the problem of aligning two PCDs as a minimization of the squared distance between the underlying surfaces. Local quadratic approximants of the squared distance function are used to develop a linear system whose solution gives the best aligning rigid transform for the given pair of point clouds. The rigid transform is applied and the linear system corresponding to the new orientation is build. This process is iterated until it converges. The pointtopoint and the pointtoplane Iterated Closest Point (ICP) algorithms can be treated as special cases in this framework. Our algorithm can align PCDs even when they are placed far apart, and is experimentally found to be more stable than pointtoplane ICP. We analyze the convergence behavior of our algorithm and of pointtopoint and pointtoplane ICP under our proposed framework, and derive bounds on their rate of convergence. We compare the stability and convergence properties of our algorithm with other registration algorithms on a variety of scanned data.
A concept for parametric surface fitting which avoids the parametrization problem
, 2003
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Aligning point cloud views using persistent feature histograms
 in International Conference on Intelligent Robots and Systems (IROS
"... Abstract — In this paper we investigate the usage of persistent point feature histograms for the problem of aligning point cloud data views into a consistent global model. Given a collection of noisy point clouds, our algorithm estimates a set of robust 16D features which describe the geometry of ea ..."
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Cited by 30 (4 self)
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Abstract — In this paper we investigate the usage of persistent point feature histograms for the problem of aligning point cloud data views into a consistent global model. Given a collection of noisy point clouds, our algorithm estimates a set of robust 16D features which describe the geometry of each point locally. By analyzing the persistence of the features at different scales, we extract an optimal set which best characterizes a given point cloud. The resulted persistent features are used in an initial alignment algorithm to estimate a rigid transformation that approximately registers the input datasets. The algorithm provides good starting points for iterative registration algorithms such as ICP (Iterative Closest Point), by transforming the datasets to its convergence basin. We show that our approach is invariant to pose and sampling density, and can cope well with noisy data coming from both indoor and outdoor laser scans. I.
Markerfree registration of terrestrial laser (b) braking in front a pedestrian (c) avoiding obstacle and pedestrian
 In Proceedings of the ISPRS Working Group V/4 Workshop 3DARCH 2005
, 2005
"... The registration of scan data often uses special markers which are placed in the scene. This leads to a reliable registration but the method is not very efficient. Therefore, we search for a registration method which works without markers. There are methods like the iterative closest point (ICP) alg ..."
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Cited by 17 (0 self)
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The registration of scan data often uses special markers which are placed in the scene. This leads to a reliable registration but the method is not very efficient. Therefore, we search for a registration method which works without markers. There are methods like the iterative closest point (ICP) algorithm which calculate the registration on the basis of the data itself. However, these algorithms have a small convergence radius and therefore a manual prealignment is necessary. In this paper, we explore a registration method called the normal distribution transform (NDT) which does not require markers, has a larger convergence radius than ICP and a medium alignment accuracy. The NDT was initially proposed in robotics for singleplane horizontal scans. We investigate three modifications to the original algorithm: a coarsetofine strategy, multiple slices, and iterative solution using the method of LevenbergMarquardt. We apply the modified algorithm to real terrestrial laser scanner data and discuss the results. 1
Fast correspondence search for 3D surface matching
 International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, 36 (Part 3/W19
, 2005
"... An algorithm for least squares matching of overlapping 3D surfaces is presented. It estimates the transformation parameters between two or more fully 3D surfaces, using the Generalized GaussMarkoff model, minimizing the sum of squares of the Euclidean distances between the surfaces. This formulatio ..."
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Cited by 12 (7 self)
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An algorithm for least squares matching of overlapping 3D surfaces is presented. It estimates the transformation parameters between two or more fully 3D surfaces, using the Generalized GaussMarkoff model, minimizing the sum of squares of the Euclidean distances between the surfaces. This formulation gives the opportunity of matching arbitrarily oriented 3D surfaces simultaneously, without using explicit tie points. Besides the mathematical model and execution aspects we pay particular interest to the reduction of the computational expenses. An efficient space partitioning method is implemented in order to speed up the correspondence search, which is the main portion of the computational efforts. The simultaneous matching of subsurface patches is given as another strategy. It provides a computationally effective solution, since it matches only relevant multisubpatches rather then the whole overlapping area. A practical example including computation times is given for the demonstration of the method. 1.
Linear leastsquares optimization for pointtoplane ICP surface registration
, 2004
"... The Iterative Closest Point (ICP) algorithm that uses the pointtoplane error metric has been shown to converge much faster than one that uses the pointtopoint error metric. At each iteration of the ICP algorithm, the change of relative pose that gives the minimal pointtoplane error is usually s ..."
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Cited by 12 (0 self)
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The Iterative Closest Point (ICP) algorithm that uses the pointtoplane error metric has been shown to converge much faster than one that uses the pointtopoint error metric. At each iteration of the ICP algorithm, the change of relative pose that gives the minimal pointtoplane error is usually solved using standard nonlinear leastsquares methods, which are often very slow. Fortunately, when the relative orientation between the two input surfaces is small, we can approximate the nonlinear optimization problem with a linear leastsquares one that can be solved more efficiently. We detail the derivation of a linear system whose leastsquares solution is a good approximation to that obtained from a nonlinear optimization. 1
Constrained 3D shape reconstruction using a combination of surface fitting and registration
, 2006
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Surface fitting and registration of point clouds using approximations of the unsigned distance function. Computer Aided Geometric Design 27
, 2010
"... Many problems in computer aided geometric design and geometry processing are stated as least– squares optimizations. Least–squares problems are well studied and widely used but exhibit immanent drawbacks such as high sensitivity to outliers. For this reason, we consider techniques for the registrati ..."
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Cited by 4 (1 self)
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Many problems in computer aided geometric design and geometry processing are stated as least– squares optimizations. Least–squares problems are well studied and widely used but exhibit immanent drawbacks such as high sensitivity to outliers. For this reason, we consider techniques for the registration of point clouds and surface fitting to point sets based on the l1norm. We develop algorithms to solve l1–registration and l1–fitting problems and explore the emerging non– smooth minimization problems. We describe efficient ways to solve the optimization programs and present results for various applications.
Reliable and RapidlyConverging ICP Algorithm Using Multiresolution Smoothing
 4th IEEE International Conference on 3D Digital Imaging and Modeling (3DIM’03), pp. 171–178, Banff, Canada, October 2003
, 2003
"... Autonomous range acquisition for 3D modeling requires reliable range registration, for both the precise localization of the sensor and combining the data from multiple scans for viewplanning computation. We introduce and present a novel approach to improve the reliability and robustness of the ICP ..."
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Cited by 2 (1 self)
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Autonomous range acquisition for 3D modeling requires reliable range registration, for both the precise localization of the sensor and combining the data from multiple scans for viewplanning computation. We introduce and present a novel approach to improve the reliability and robustness of the ICP (Iterative Closest Point) 3D shape registration algorithm by smoothing the shape’s surface into multiple resolutions. These smoothed surfaces are used in place of the original surface in a coarsetofine manner during registration, which allows the algorithm to avoid being trapped at local minima close to the global optimal solution. We used the technique of multiresolution analysis to create the smoothed surfaces efficiently. Besides being more robust, convergence is generally much faster, especially when combined with the pointtoplane error metric of Chen and Medioni. Since the pointtoplane error metric has no closedform solution, solving it can be slow. We introduce a variant of the ICP algorithm that has convergence rate close to it but still uses the closedform solution techniques (SVD or unit quaternion methods) of the original ICP algorithm.