Bayesian 3D Shape Reconstruction from Noisy Points and Normals

Reconstructing three-dimensional shapes from point clouds remains a central challenge in geometry processing, particularly due to the inherent uncertainties in real-world data acquisition. In this work, we introduce a novel Bayesian framework that explicitly models and propagates uncertainty from both input points and their estimated normals. Our method incorporates the uncertainty of normals derived via Principal Component Analysis (PCA) from noisy input points. Building upon the Smooth Signed Distance (SSD) reconstruction algorithm, we integrate a smoothness prior based on the curvatures of the resulting implicit function following Gaussian behavior. Our method reconstructs a shape represented as a distribution, from which sampling and statistical queries regarding the shape's properties are possible. Additionally, because of the high cost of computing the variance of the resulting distribution, we develop efficient techniques for variance computation. Our approach thus combines two common steps of the geometry processing pipeline, normal estimation and surface reconstruction, while computing the uncertainty of the output of each of these steps.