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150
Efficient Variants of the ICP Algorithm
 INTERNATIONAL CONFERENCE ON 3D DIGITAL IMAGING AND MODELING
, 2001
"... The ICP (Iterative Closest Point) algorithm is widely used for geometric alignment of threedimensional models when an initial estimate of the relative pose is known. Many variants of ICP have been proposed, affecting all phases of the algorithm from the selection and matching of points to the minim ..."
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Cited by 718 (5 self)
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The ICP (Iterative Closest Point) algorithm is widely used for geometric alignment of threedimensional models when an initial estimate of the relative pose is known. Many variants of ICP have been proposed, affecting all phases of the algorithm from the selection and matching of points to the minimization strategy. We enumerate and classify many of these variants, and evaluate their effect on the speed with which the correct alignment is reached. In order to improve convergence for nearlyflat meshes with small features, such as inscribed surfaces, we introduce a new variant based on uniform sampling of the space of normals. We conclude by proposing a combination of ICP variants optimized for high speed. We demonstrate an implementation that is able to align two range images in a few tens of milliseconds, assuming a good initial guess. This capability has potential application to realtime 3D model acquisition and modelbased tracking.
Means and Averaging in the Group of Rotations
, 2002
"... In this paper we give precise definitions of different, properly invariant notions of mean or average rotation. Each mean is associated with a metric in SO(3). The metric induced from the Frobenius inner product gives rise to a mean rotation that is given by the closest special orthogonal matrix to ..."
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Cited by 118 (3 self)
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In this paper we give precise definitions of different, properly invariant notions of mean or average rotation. Each mean is associated with a metric in SO(3). The metric induced from the Frobenius inner product gives rise to a mean rotation that is given by the closest special orthogonal matrix to the usual arithmetic mean of the given rotation matrices. The mean rotation associated with the intrinsic metric on SO(3) is the Riemannian center of mass of the given rotation matrices. We show that the Riemannian mean rotation shares many common features with the geometric mean of positive numbers and the geometric mean of positive Hermitian operators. We give some examples with closedform solutions of both notions of mean.
Multiscale EMICP: A Fast and Robust Approach for Surface Registration
 European Conference on Computer Vision (ECCV 2002), volume 2353 of LNCS
, 2002
"... We investigate in this article the rigid registration of large sets of points, generally sampled from surfaces. We formulate this problem as a general MaximumLikelihood (ML) estimation of the transformation and the matches. We show that, in the specific case of a Gaussian noise, it corresponds to t ..."
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Cited by 107 (7 self)
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We investigate in this article the rigid registration of large sets of points, generally sampled from surfaces. We formulate this problem as a general MaximumLikelihood (ML) estimation of the transformation and the matches. We show that, in the specific case of a Gaussian noise, it corresponds to the Iterative Closest Point algorithm (ICP) with the Mahalanobis distance.
Realtime enveloping with rotational regression
 ACM Trans. Graph
, 2007
"... Enveloping (or skinning) is the process that relates a skeleton, which an animator controls, to a 3D surface mesh, which the audience sees. This process is necessary in most computer graphics applications that involve animated characters. The complexity (and speed) of enveloping solutions vary fro ..."
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Cited by 57 (4 self)
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Enveloping (or skinning) is the process that relates a skeleton, which an animator controls, to a 3D surface mesh, which the audience sees. This process is necessary in most computer graphics applications that involve animated characters. The complexity (and speed) of enveloping solutions vary from photorealistic muscle simulations used for movie production, to artifactridden heuristics such as linear blend skinning used for video games and training simulations. We propose a method for examplebased enveloping of 3D characters. We can approximate the output of muscle simulations or other highquality enveloping tools with a model that can be evaluated at speeds comparable to the fastest enveloping techniques. Our technique introduces a rotational regression model that can accurately capture common skinning behaviors such as muscle bulging, twisting, and challenging areas such as the shoulders. Our better treatment of rotational quantities is made possible by a framework that predicts mesh deformation gradients instead of mesh vertex positions. We reconstruct the vertex positions from deformation gradients in an additional step by solving a Poisson
Geometry and convergence analysis of algorithms for registration of 3D shapes
, 2006
"... The computation of a rigid body transformation which optimally aligns a set of measurement points with a surface and related registration problems are studied from the viewpoint of geometry and optimization. We provide a convergence analysis for widely used registration algorithms such as ICP, using ..."
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Cited by 43 (6 self)
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The computation of a rigid body transformation which optimally aligns a set of measurement points with a surface and related registration problems are studied from the viewpoint of geometry and optimization. We provide a convergence analysis for widely used registration algorithms such as ICP, using either closest points (Besl and McKay [2]) or tangent planes at closest points (Chen and Medioni [4]), and for a recently developed approach based on quadratic approximants of the squared distance function [24]. ICP based on closest points exhibits local linear convergence only. Its counterpart which minimizes squared distances to the tangent planes at closest points is a GaussNewton iteration; it achieves local quadratic convergence for a zero residual problem and – if enhanced by regularization and step size control – comes close to quadratic convergence in many realistic scenarios. Quadratically convergent algorithms are based on the approach in [24]. The theoretical results are supported by a number of experiments; there, we also compare the algorithms with respect to global convergence behavior, stability and running time.
Simultaneous multiple 3D motion estimation via mode finding on Lie groups
 In Proc. 10th intl. conf. on computer vision
, 2005
"... We propose a new method to estimate multiple rigid motions from noisy 3D point correspondences in the presence of outliers. The method does not require prior specification of number of motion groups and estimates all the motion parameters simultaneously. We start with generating samples from the rig ..."
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Cited by 39 (11 self)
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We propose a new method to estimate multiple rigid motions from noisy 3D point correspondences in the presence of outliers. The method does not require prior specification of number of motion groups and estimates all the motion parameters simultaneously. We start with generating samples from the rigid motion distribution. The motion parameters are then estimated via mode finding operations on the sampled distribution. Since rigid motions do not lie on a vector space, classical statistical methods can not be used for mode finding. We develop a mean shift algorithm which estimates modes of the sampled distribution using the Lie group structure of the rigid motions. We also show that proposed mean shift algorithm is general and can be applied to any distribution having a matrix Lie group structure. Experimental results on synthetic and real image data demonstrate the superior performance of the algorithm. 1.
Estimation of nonlinear errorsinvariables models for computer vision applications
 IEEE Trans. Patt. Anal. Mach. Intell
, 2006
"... Abstract—In an errorsinvariables (EIV) model, all the measurements are corrupted by noise. The class of EIV models with constraints separable into the product of two nonlinear functions, one solely in the variables and one solely in the parameters, is general enough to represent most computer visi ..."
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Cited by 34 (6 self)
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Abstract—In an errorsinvariables (EIV) model, all the measurements are corrupted by noise. The class of EIV models with constraints separable into the product of two nonlinear functions, one solely in the variables and one solely in the parameters, is general enough to represent most computer vision problems. We show that the estimation of such nonlinear EIV models can be reduced to iteratively estimating a linear model having point dependent, i.e., heteroscedastic, noise process. Particular cases of the proposed heteroscedastic errorsinvariables (HEIV) estimator are related to other techniques described in the vision literature: the Sampson method, renormalization, and the fundamental numerical scheme. In a wide variety of tasks, the HEIV estimator exhibits the same, or superior, performance as these techniques and has a weaker dependence on the quality of the initial solution than the LevenbergMarquardt method, the standard approach toward estimating nonlinear models. Index Terms—Nonlinear least squares, heteroscedastic regression, camera calibration, 3D rigid motion, uncalibrated vision. 1 MODELING COMPUTER VISION PROBLEMS SOLVING most computer vision problems requires the estimation of a set of parameters from noisy measurements using a statistical model. A statistical model provides a mathematical description of a problem in terms of a constraint equation relating the measurements to the
Examplebased control of human motion
 In 2004 A CM SIGGRAPH / Eurographics Symposium on Computer Animation
, 2004
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