Neural Vector Fields: Implicit Representation by Explicit Learning (2303.04341v2)

Published 8 Mar 2023 in cs.CV, cs.AI, and cs.GR

Abstract: Deep neural networks (DNNs) are widely applied for nowadays 3D surface reconstruction tasks and such methods can be further divided into two categories, which respectively warp templates explicitly by moving vertices or represent 3D surfaces implicitly as signed or unsigned distance functions. Taking advantage of both advanced explicit learning process and powerful representation ability of implicit functions, we propose a novel 3D representation method, Neural Vector Fields (NVF). It not only adopts the explicit learning process to manipulate meshes directly, but also leverages the implicit representation of unsigned distance functions (UDFs) to break the barriers in resolution and topology. Specifically, our method first predicts the displacements from queries towards the surface and models the shapes as \textit{Vector Fields}. Rather than relying on network differentiation to obtain direction fields as most existing UDF-based methods, the produced vector fields encode the distance and direction fields both and mitigate the ambiguity at "ridge" points, such that the calculation of direction fields is straightforward and differentiation-free. The differentiation-free characteristic enables us to further learn a shape codebook via Vector Quantization, which encodes the cross-object priors, accelerates the training procedure, and boosts model generalization on cross-category reconstruction. The extensive experiments on surface reconstruction benchmarks indicate that our method outperforms those state-of-the-art methods in different evaluation scenarios including watertight vs non-watertight shapes, category-specific vs category-agnostic reconstruction, category-unseen reconstruction, and cross-domain reconstruction. Our code is released at https://github.com/Wi-sc/NVF.

Authors (4)

Xianghui Yang (17 papers)
Guosheng Lin (157 papers)
Zhenghao Chen (30 papers)
Luping Zhou (72 papers)

Citations (16)

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Summary

Neural Vector Fields: Implicit Representation by Explicit Learning

The paper "Neural Vector Fields: Implicit Representation by Explicit Learning" introduces a novel approach to 3D shape representation called Neural Vector Fields (NVF). This method synergizes the advantages of explicit and implicit 3D representations to improve the computational efficiency and generalization capabilities in surface reconstruction tasks.

Overview of Methodology

The NVF approach leverages both explicit learning for manipulating mesh vertices and the implicit power of unsigned distance functions (UDFs). Traditional methods of 3D surface reconstruction can be broadly categorized into explicit methods, such as meshes and voxels, which often struggle with issues of resolution and topology, and implicit methods, like those that utilize signed distance functions, which require cumbersome pre-processing for non-watertight meshes.

NVF overcomes these limitations by modeling 3D shapes directly as vector fields, predicting the displacements from queries to surfaces without relying on differentiation to compute gradient directions. This distinction is crucial in avoiding complex inference procedures that are typically involved in extracting surfaces from UDFs.

Technical Insights

The proposed framework consists of three core modules: Feature Extraction, a Multi-head Codebook, and Field Prediction. Each query point's displacement vector is computed based on the point's relative positioning and its surrounding features, identified from a point cloud. Differentiation-free vector prediction significantly minimizes the computational burden, a key contribution outlined in the experimentation sections.

Moreover, NVF implements a shape codebook using vector quantization techniques, allowing it to learn and encode cross-object priors. This innovative step facilitates model generalization and accelerates training, optimally leveraging non-differentiable components within the feature space.

Empirical Evaluations

The experimental results on ShapeNet and MGN datasets highlight NVF's exceptional ability to outperform existing state-of-the-art benchmarks in several scenarios, particularly in handling non-watertight shapes. The framework demonstrates superior performance across category-specific, agnostic, unseen, and cross-domain reconstruction challenges.

Significantly, NVF proves its efficacy in cross-domain applications, validating reconstructed non-trained objects directly on real-world data. Compared to methods like NDF and GIFS, NVF achieves remarkable reductions in Chamfer Distance (CD) and Earth Mover's Distance (EMD), and improved F-scores, reaffirming its robustness and efficacy in varied topological conditions.

Complexity and Practical Implications

The NVF framework significantly reduces inference times and memory footprints due to its differentiation-free approach. The computational efficiency unlocks potential applications where real-time performance is crucial, such as virtual reality, robotics, and interactive 3D modeling.

The implementation of a multi-head codebook not only enhances the model's representational capacity but also serves as a form of regularization, expediting convergence during training. The flexibility in model design heralded by non-differentiable elements opens avenues for further explorations in network architectures for 3D reconstructions.

Future Directions

This research sheds light on the ongoing evolution in balancing explicit and implicit methodologies for 3D representation. Future work can explore the integration of NVF with other neural architectures to imbue them with enhanced scalability and efficiency. Furthermore, the conceptual innovations within NVF could inspire adaptations across different modalities, such as texture synthesis and dynamic object modeling, expanding its applicability in broader contexts beyond static surface reconstruction.

In conclusion, the introduction of Neural Vector Fields represents a compelling development in 3D surface modeling, promising enhanced computational efficacy and broad generalization capabilities across diverse 3D reconstruction tasks.

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