Neural Subdivision (2005.01819v1)

Abstract: This paper introduces Neural Subdivision, a novel framework for data-driven coarse-to-fine geometry modeling. During inference, our method takes a coarse triangle mesh as input and recursively subdivides it to a finer geometry by applying the fixed topological updates of Loop Subdivision, but predicting vertex positions using a neural network conditioned on the local geometry of a patch. This approach enables us to learn complex non-linear subdivision schemes, beyond simple linear averaging used in classical techniques. One of our key contributions is a novel self-supervised training setup that only requires a set of high-resolution meshes for learning network weights. For any training shape, we stochastically generate diverse low-resolution discretizations of coarse counterparts, while maintaining a bijective mapping that prescribes the exact target position of every new vertex during the subdivision process. This leads to a very efficient and accurate loss function for conditional mesh generation, and enables us to train a method that generalizes across discretizations and favors preserving the manifold structure of the output. During training we optimize for the same set of network weights across all local mesh patches, thus providing an architecture that is not constrained to a specific input mesh, fixed genus, or category. Our network encodes patch geometry in a local frame in a rotation- and translation-invariant manner. Jointly, these design choices enable our method to generalize well, and we demonstrate that even when trained on a single high-resolution mesh our method generates reasonable subdivisions for novel shapes.

• The paper presents a novel neural subdivision method that integrates self-supervised learning to dynamically adjust vertex positions in triangle meshes.
• The approach leverages recursive mesh refinement with invariant local geometry features to outperform traditional Loop subdivision methods.
• Quantitative evaluations show enhanced accuracy and generalization across diverse meshes, promising improved workflows in interactive 3D design and modeling.

An Expert Review of "Neural Subdivision"

The paper, "Neural Subdivision", presents a novel framework for geometry modeling by leveraging machine learning techniques to enhance classical subdivision methodologies. Focusing on triangle meshes, the authors introduce a neural network-driven approach to dynamically adjust vertex positions during mesh refinement, conditioned on local geometric features. This marks a departure from traditional methods, which rely solely on static linear averaging for vertex repositioning.

Core Contributions

One of the standout contributions of this work is the self-supervised training setup, which circumvents the need for paired high-resolution and low-resolution mesh data. Instead, high-resolution meshes are algorithms generated to create diverse low-resolution variations while maintaining bijective correspondences. This clever design enables the learning framework to extrapolate complex non-linear subdivision schemes that go beyond established linear techniques like those in Loop Subdivision.

Methodology and Network Architecture

The paper meticulously details a recursive mesh subdivision process. This involves initially applying established topological updates attendant to Loop Subdivision while positioning vertices informed by the neural network's predictions. The network architecture reflects this hierarchical mesh processing approach, leveraging local geometry patches to maintain robustness across various mesh discretizations and manifold structures.

Notably, the neural modules involved share weights across meshes and subdivision levels. This ensures the neural assembly has an invariant interpretation of local mesh features, encoded in rotation- and translation-invariant frames. Such a design ensures adaptability to novel shapes, including those wildly differing from training data.

Evaluation and Results

Qualitative and quantitative experiments showcase the network's ability to generalize significantly better across different mesh configurations than conventional methods. The model consistently outperforms classical approaches, including Loop and modified butterfly subdivisions, when measured against traditional metrics like Hausdorff and mean surface distances. Importantly, the neural subdivision framework exhibits the ability to maintain fidelity in both organic and mechanical object domains, demonstrating flexibility often demanded in practical settings.

Future Prospects and Challenges

The findings of this paper have several practical implications for applications in mesh upscaling and 3D modeling, particularly in interactive design platforms where real-time feedback is crucial. The approach could streamline workflows in art design, engineering, and game development by reducing the need for manual intervention during the mesh refinement processes.

Looking forward, potential areas of exploration include extending the methodology to meshes other than triangles, like quad meshes, and enhancing the network to support surfaces with boundaries. There is also the intriguing problem of establishing the convergence of this nonlinear subdivision approach toward a limit surface, akin to classic subdivision methods. Moreover, integrating semantic understanding into the network to craft higher-level feature content could significantly enhance stylization and detail extrapolation capabilities.

Overall, this paper is a robust entry into the landscape of computational graphics, setting a precedent for more intelligent, data-aware techniques in mesh processing.