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.

翻译：本文研究了受高各向异性定位噪声干扰的多点云配准问题。我们采用基于高斯混合模型重建与期望最大化算法的通用框架。现有方法隐含假设了空间不变的各向同性高斯噪声，但在单分子定位显微成像等实际应用中该假设往往不成立。为此，我们提出显式定位噪声模型，将高斯混合模型的形状建模与噪声处理解耦。通过设计随机期望最大化算法，将无噪数据作为隐变量处理，并在每个迭代步骤中给出闭式解。本方法的首要优势在于能处理具有任意协方差矩阵的空间变化各向异性高斯噪声；其次可通过显式噪声模型融入物理传感器提供的先验噪声知识。在多种仿真数据上的实验表明，我们的噪声处理策略显著提升了算法对高强度各向异性噪声的鲁棒性，并在真实单分子定位显微数据中验证了方法的有效性。