Registration of Multi-View Point Sets Under the Perspective of Expectation-Maximization

Zhu, Jihua; Guo, Rui; Li, Zhongyu; Zhang, Jing; Pang, Shanmin

doi:10.1109/tip.2020.3024096

Cited by 22 publications

(23 citation statements)

References 42 publications

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“…In this section, we compare the performance of the proposed method with three representative state-of-the-art approaches for multi-view registration, namely, JRMPC [8], TMM [20], and EMPMR [27]. The implementation of all compared methods is publicly available.…”

Section: Methodsmentioning

confidence: 99%

“…By this, global information of point sets is combined to avoid the error accumulation. Zhu et al [27] propose a method named EMPMR, which assumes that each data point is generated from a GMM whose Gaussian centroids are composed of corresponding points from other point sets. Nevertheless, GMM suffers from heavy-tail noise, and is sensitive to severe outliers due to the L 2 norm.…”

Section: Multi-view Registrationmentioning

confidence: 99%

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Robust Multi-view Registration of Point Sets with Laplacian Mixture Model

Zhang¹,

Zhao²,

Jiang³

et al. 2021

Preprint

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Point set registration is an essential step in many computer vision applications, such as 3D reconstruction and SLAM. Although there exist many registration algorithms for different purposes, however, this topic is still challenging due to the increasing complexity of various real-world scenarios, such as heavy noise and outlier contamination. In this paper, we propose a novel probabilistic generative method to simultaneously align multiple point sets based on the heavy-tailed Laplacian distribution. The proposed method assumes each data point is generated by a Laplacian Mixture Model (LMM), where its centers are determined by the corresponding points in other point sets. Different from the previous Gaussian Mixture Model (GMM) based method, which minimizes the quadratic distance between points and centers of Gaussian probability density, LMM minimizes the sparsity-induced L1 distance, thereby it is more robust against noise and outliers. We adopt Expectation-Maximization (EM) framework to solve LMM parameters and rigid transformations. We approximate the L1 optimization as a linear programming problem by exponential mapping in Lie algebra, which can be effectively solved through the interior point method. To improve efficiency, we also solve the L1 optimization by Alternating Direction Multiplier Method (ADMM). We demonstrate the advantages of our method by comparing it with representative state-of-the-art approaches on benchmark challenging data sets, in terms of robustness and accuracy.

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Section: Methodsmentioning

confidence: 99%

Section: Multi-view Registrationmentioning

confidence: 99%

Robust Multi-view Registration of Point Sets with Laplacian Mixture Model

Zhang¹,

Zhao²,

Jiang³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Several variants have been proposed to handle outliers [21], topological constraints [31], symmetrisation of the registration [9], or non rigid deformations [8]. This approach has been recently extended to the registration of multiple point clouds in [42], where a point is modeled as a mixture of Gaussians centered in the nearest neighbor points in each other point clouds. From the point of view of noise modeling, this formulation is based on an assumption of Gaussian localization uncertainty of each point [19].…”

Section: Related Workmentioning

confidence: 99%

“…Moreover, this category of methods has two major limitations already mentioned in Section 1: it is restricted to pairwise registration (excluding [42]), and since there are as many Gaussian components as points, the computational complexity can become prohibitive. The generative EM-GMM methods [12,14] have been developed to address these issues.…”

Section: Related Workmentioning

confidence: 99%

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Multiview point cloud registration with anisotropic and space-varying localization noise

Fortun¹,

Baudrier²,

Zwettler³

et al. 2022

Preprint

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In this paper, we address the problem of registering multiple point clouds corrupted with high anisotropic localization noise. Our approach follows the widely used framework of Gaussian mixture model (GMM) reconstruction with an expectation-maximization (EM) algorithm. Existing methods are based on an implicit assumption of space-invariant isotropic Gaussian noise. However, this assumption is violated in practice in applications such as single molecule localization microscopy (SMLM). To address this issue, we propose to introduce an explicit localization noise model that decouples shape modeling with the GMM from noise handling. We design a stochastic EM algorithm that considers noise-free data as a latent variable, with closed-form solutions at each EM step. The first advantage of our approach is to handle space-variant and anisotropic Gaussian noise with arbitrary covariances. The second advantage is to leverage the explicit noise model to impose prior knowledge about the noise that may be available from physical sensors. We show on various simulated data that our noise handling strategy improves significantly the robustness to high levels of anisotropic noise. We also demonstrate the performance of our method on real SMLM data.

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