€1000 Noisy SDF Meshing

Motivation

Signed Distance Fields (SDF) have come into the spotlight recently since they are often used or generated by neural methods, e.g., NeRFs, 3DGS, or other deep learning methods that output surfaces. While there is already a large body of algorithms to extract explicit surfaces from SDFs, e.g., Marching Cube and its variants for triangulations, these do not handle noise, which is an inherent aspect of all sensing devices that provide the input data for the SDFs.

Description

Preliminary work was already done here, by carving space along the surfaces hit by the scanner, storing it in a sparse data structure utilizing a 2D grid with intervals, triangulating the surface adaptively based on local feature size, and visualizing the resulting surface: https://www.cg.tuwien.ac.at/research/publications/2025/schrammel-2025-b…

Extending this framework to noise will require computing a probabilistic SDF as a Gaussian distribution (mean, variance), also in a sparse grid, and then fitting triangles into a cutoff probability.

Tasks (depending on PR/BA/DA and number of students)

• Compute the Gaussian distribution at sparse grid points near the surface from the points in the scanned depth image, using its noise extent
• When using the above-implemented feature-sized triangle mesher, fit triangles into a, e.g., 3-sigma cut-off probability of the Gaussian distribution
• Evaluate the quality of the reconstructed surface compared to state-of-the-art surface reconstruction methods
• Optimize the calculations in CUDA

Requirements

• Knowledge of English (source code comments and final report have to be in English)
• Experience in geometry processing is a plus

Environment

A bonus of €500/€1000 if completed to satisfaction within an agreed time-frame of 6/12 months (PR/BA or DA)can also