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

TL;DR

This work tackles multiview point cloud registration in the presence of highly anisotropic and space-varying localization noise typical of SMLM. It introduces an explicit Gaussian noise prior and treats the noise-free data as latent, integrating this into a space-alternating EM-GMM framework to separate shape modeling from noise handling. The method yields closed-form updates for both the transformation and GMM parameters, improving robustness and GMM reconstruction compared with the baseline JRMPC, demonstrated on synthetic data and real SMLM centriole datasets. The approach enables more accurate reconstruction of nanoscale biological structures by leveraging per-point noise information and can incorporate prior sensor noise knowledge for improved registration in challenging imaging scenarios.

Abstract

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.

Figures (11)

• Figure 1: Real data of centriole acquired with dStorm Heilemann08. The two columns show two examples of point clouds, with a 90 degrees tilt of the centriole between the two views. The first row represent a view in the direction of the axis of symmetry of the centriole (top view), and the second row represents a view parallel to the axis of symmetry (side view).
• Figure 2: Illustration of our generative model for the synthesis of a point cloud $\overline{\mathbf y}_j$. It consists in sampling ${\mathbf y}_{ji}$ from (\ref{['eq:p_yji']}) (steps (a) and (b)) and then sampling $\overline{\mathbf y}_{ji}$ from (\ref{['eq:p(byji|yji)']}) (step (c)). (a) Sampling from the GMM distribution defined by the parameters $\{p_k,\boldsymbol{\mu}_k,\boldsymbol{\Sigma}_k\}_{k=1}^K$ used in \ref{['eq:p_yji']}. The GMM is here composed of two well separated Gaussians. The obtained points can be denoted as $\phi_j({\mathbf y}_{j})$ since they correspond to registered points. (b) Noise-free point cloud ${\mathbf y}_{j}$ derived by applying the transformation $\phi_j^{-1}$ to $\phi_j({\mathbf y}_{j})$. (c) Observed point cloud $\overline{{\mathbf y}}_j$ obtained as a noisy version of (b) by sampling from $p(\overline{\mathbf y}_{ji}|{\mathbf y}_{ji})$ (\ref{['eq:p(byji|yji)']}). The distribution of the noise may be anisotropic and different for each point. Here, the covariances $\overline{\boldsymbol{\Sigma}}_{ji}$ have elliptic shapes with three different orientations clearly visible in the figure: the points that belong to the lower left gaussian component have the same covariance, and the points that belong to the upper right gaussian component are divided into two groups with orthogonally oriented covariances. In the standard GMM model Evangelidis17, the generative model only consists in step (a) and (b), whereas we introduce an explicit noise model in step (c).
• Figure 3: Simulated data of the centriole (top) and triplets (bottom).
• Figure 4: Examples of simulated point clouds with different levels of anisotropic noise from the bunny (top) and centriole (bottom) models ($\sigma=0.01$ in all the examples). The point clouds are shown in the same pose.
• Figure 5: Illustration of the ground truth $\tilde{\phi}_j$ and estimated $\hat{\phi}_j$ transformations involved in the computation of our metric, in the simplified case of only two point clouds. $\phi$ represents the transformation between the ground truth and the estimated GMM.