This work presents a novel and effective method for fitting multidimensional ellipsoids to scattered data in the contamination of noise and outliers. We approach the problem as a Bayesian parameter estimate process and maximize the posterior probability of a certain ellipsoidal solution given the data. We establish a more robust correlation between these points based on the predictive distribution within the Bayesian framework. We incorporate a uniform prior distribution to constrain the search for primitive parameters within an ellipsoidal domain, ensuring ellipsoid-specific results regardless of inputs. We then establish the connection between measurement point and model data via Bayes' rule to enhance the method's robustness against noise. Due to independent of spatial dimensions, the proposed method not only delivers high-quality fittings to challenging elongated ellipsoids but also generalizes well to multidimensional spaces. To address outlier disturbances, often overlooked by previous approaches, we further introduce a uniform distribution on top of the predictive distribution to significantly enhance the algorithm's robustness against outliers. We introduce an {\epsilon}-accelerated technique to expedite the convergence of EM considerably. To the best of our knowledge, this is the first comprehensive method capable of performing multidimensional ellipsoid specific fitting within the Bayesian optimization paradigm under diverse disturbances. We evaluate it across lower and higher dimensional spaces in the presence of heavy noise, outliers, and substantial variations in axis ratios. Also, we apply it to a wide range of practical applications such as microscopy cell counting, 3D reconstruction, geometric shape approximation, and magnetometer calibration tasks.

翻译：本研究提出了一种新颖有效的方法，用于在噪声和异常值污染的情况下将多维椭球拟合到散乱数据。我们将该问题视为贝叶斯参数估计过程，并最大化给定数据下特定椭球解的后验概率。基于贝叶斯框架内的预测分布，我们在这些点之间建立了更稳健的关联。我们引入均匀先验分布以将原始参数的搜索约束在椭球域内，从而确保无论输入如何都能获得特定于椭球的结果。随后，我们通过贝叶斯规则建立测量点与模型数据之间的联系，以增强方法对噪声的鲁棒性。由于独立于空间维度，所提方法不仅能为具有挑战性的细长椭球提供高质量拟合，还能很好地推广到多维空间。针对以往方法常忽视的异常值干扰，我们在预测分布之上进一步引入均匀分布，显著增强了算法对异常值的鲁棒性。我们提出一种{\epsilon}加速技术以大幅提升EM算法的收敛速度。据我们所知，这是首个能够在贝叶斯优化范式下、应对多种干扰执行多维椭球特定拟合的综合性方法。我们在存在强噪声、异常值及轴比大幅变化的低维与高维空间中对其进行了评估。同时，我们将其应用于多种实际场景，如显微镜细胞计数、三维重建、几何形状逼近以及磁力计校准任务。