On the problem of correspondence in range data and some inelastic uses for elastic nets

Joshi, Anupam; Lee, C.-H.

doi:10.1109/72.377976

Cited by 8 publications

(5 citation statements)

References 30 publications

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“…In [10] it was shown that in RPM alternating soft-assignment of correspondences and transformation is equivalent to the Expectation Maximization (EM) algorithm for GMM, where one point sets is treated as GMM centroids with equal isotropic covariances and the other point set is treated as data points. In fact, several rigid point set methods, including Joshi and Lee [11], Wells [12], Cross and Hancock [13], Luo and Hancock [6], [14], McNeill and Vijayakumar [15] and Sofka et al [16], explicitly formulate the point sets registration as a maximum likelihood (ML) estimation problem, to fit the GMM centroids to the data points. These methods re-parameterize GMM centroids by a set of rigid transformation parameters (translation and rotation).…”

Section: Rigid Point Set Registration Methodsmentioning

confidence: 99%

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Point Set Registration: Coherent Point Drift

Myronenko¹,

Song²

2010

IEEE Trans. Pattern Anal. Mach. Intell.

2,377

2,074

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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.

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Section: Rigid Point Set Registration Methodsmentioning

confidence: 99%

“…and d −1 (·) is the inverse diagonal matrix. The transformed position of y m are found according to (11) as T = T (Y, W) = Y+GW. We obtain σ 2 by equating the corresponding derivative of Q to zero…”

Section: The Coherent Point Drift (Cpd) Algorithmmentioning

confidence: 99%

Point Set Registration: Coherent Point Drift

Myronenko¹,

Song²

2010

IEEE Trans. Pattern Anal. Mach. Intell.

2,377

2,074

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“…Estimation maximization approaches. To overcome the ICP limitations, probabilistic methods [35] have been suggested, making use of GMMs, treating one point set as the GMM centroids, and the other as data points [16,42,6,23,26,14,3]. This category also includes the widely used Coherent Point Drift (CPD) method [27].…”

Section: Related Workmentioning

confidence: 99%

Provably Approximated ICP

Jubran,

Maalouf,

Kimmel

et al. 2021

Preprint

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The goal of the alignment problem is to align a (given)That is, to compute a rotation matrix 𝑅 ∈ R 3×3 and a translation vector 𝑡 ∈ R 3 that minimize the sum of paired distances ∑︀ 𝑛 𝑖=1 𝐷(𝑅𝑝 𝑖 − 𝑡, 𝑞 𝑖 ) for some distance function 𝐷. A harder version is the registration problem, where the correspondence is unknown, and the minimum is also over all possible correspondence functions from 𝑃 to 𝑄. Heuristics such as the Iterative Closest Point (ICP) algorithm and its variants were suggested for these problems, but none yield a provable non-trivial approximation for the global optimum.We prove that there always exists a "witness" set of 3 pairs in 𝑃 × 𝑄 that, via novel alignment algorithm, defines a constant factor approximation (in the worst case) to this global optimum. We then provide algorithms that recover this witness set and yield the first provable constant factor approximation for the: (i) alignment problem in 𝑂(𝑛) expected time, and (ii) registration problem in polynomial time. Such small witness sets exist for many variants including points in 𝑑-dimensional space, outlier-resistant cost functions, and different correspondence types.Extensive experimental results on real and synthetic datasets show that our approximation constants are, in practice, close to 1, and up to x10 times smaller than stateof-the-art algorithms.

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“…In addition, some probability algorithms [18], [19] have been proposed. With the development of these algorithms, it can be seen from [20]- [22] that point cloud registration has gradually been converted to a probability estimation problem. Many new algorithms have also been proposed.…”

Section: Introductionmentioning

confidence: 99%

Point Cloud Registration in Multidirectional Affine Transformation

Wang

Shu

Yang³

et al. 2018

IEEE Photonics J.

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Point clouds scanned by three-dimensional lasers may be multidirectional affine transformed when the specifications for the products, laser scanners, and thermal expansion are incompatible. If a point cloud is out of order in such a case, many existing algorithms may not be suitable to solve the problem. Therefore, this paper proposes a multidirectional affine registration (MDAR) algorithm based on the statistical characteristics and shape features of point clouds. First, we transform the problem into a problem of finding certain matrix eigenvalues. In addition, the similarity of the global vector features is introduced, and the scaling factor is calculated by maximizing the similarity. Finally, using the estimated affine factors, the multidirectional affine registration is transformed into a rigid registration. Simulation results show that the MDAR algorithm has better accuracy and less time consumption than several existing algorithms.

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On the problem of correspondence in range data and some inelastic uses for elastic nets

Cited by 8 publications

References 30 publications

Point Set Registration: Coherent Point Drift

Point Set Registration: Coherent Point Drift

Provably Approximated ICP

Point Cloud Registration in Multidirectional Affine Transformation

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