Studies on 3D shape fitting with neural implicit functions

Abstract

This master’s dissertation explores how to better utilize neural implicit functions for 3D shape fitting, focusing primarily on four aspects: 1. Achieving high-fidelity shape fitting; 2. Enhancing the efficiency of shape fitting; 3. Enabling neural implicit functions to represent diverse geometric features; 4. Extracting high-quality explicit geometry from trained neural implicit functions. In the field of high-fidelity shape fitting, this research introduces the method "On Optimal Sampling for Learning signed distance function (SDF) Using multi-layer perceptrons Equipped with Positional Encoding (PE-MLPs)" (PE-Sampler). This work addresses the sampling problem in neural implicit functions for the first time and effectively resolves the wavy artifacts associated with PE-MLPs, enabling simple PE-MLP networks to achieve state-of-the-art fitting accuracy. PE-Sampler defines and computes the intrinsic frequency of the neural network. By applying the Nyquist-Shannon theorem, it provides guidance on the optimal sampling density and distribution for SDF- based neural shape fitting. Consequently, this approach achieves high-fidelity shape fitting without any noise artifacts. Empirical evaluations conducted on datasets featuring diverse geometric characteristics demonstrate the superior performance of this method compared to existing state-of-the-art algorithms for SDF fitting. In terms of efficiency and fitting diverse geometric features, this research proposes a novel method "Patch-Grid: An Efficient and Feature-Preserving Neural Implicit Surface Representation" (Patch-Grid). This is a patch-based representation, which enables neural networks to efficiently represent diverse geometric features that are challenging for vanilla neural networks, such as sharp features, thin structures, and open boundaries. By incorporating classical constructive solid geometry (CSG) into the neural SDF context, Patch-Grid alleviates the burden of characterizing diverse and complex geometric features from the neural network itself. Instead, this burden is shifted to the CSG operations, leading to significantly improved training efficiency and an expanded range of expressiveness for neural SDFs. The efficiency and accuracy of the Patch-Grid method are demonstrated through its superior performance on the ABC dataset. For explicit geometry extraction, this thesis introduces "Surface Extraction from Neural Unsigned Distance Fields"(DualMesh-UDF), an algorithm capable of extracting high-quality meshes from noisy neural unsigned distance functions(UDFs). This algorithm delves into the error characteristics of neural UDFs and, through careful algorithm design, partially overcomes the issue of unstable zero sets in neural UDFs, thereby significantly improving the quality and stability of the extraction process. Specifically, DualMesh-UDF leverages the distance values and gradient information of sampled points to project them onto the potential surface. By synthesizing the projection information from multiple sampled points, it mitigates the impact of network noise, leading to more accurate and stable surface point candidates. The effectiveness and robustness of DualMesh-UDF have been demonstrated through empirical evaluations on benchmarks including the MGN and ABC datasets. In conclusion, this dissertation contributes robust and efficient methodologies that advance the frontier of 3D shape fitting with neural implicit functions. These works demonstrate significant progress in enabling neural implicit functions to efficiently and accurately handle complex, diverse geometric features, and assist users in extracting high-quality explicit geometry from neural implicit functions.