Implicit Geometric Regularization for Learning Shapes

Abstract

Representing shapes as level sets of neural networks has been recently proved to be useful for different shape analysis and reconstruction tasks. So far, such representations were computed using either: (i) pre-computed implicit shape representations; or (ii) loss functions explicitly defined over the neural level sets. In this paper we offer a new paradigm for computing high fidelity implicit neural representations directly from raw data (i.e., point clouds, with or without normal information). We observe that a rather simple loss function, encouraging the neural network to vanish on the input point cloud and to have a unit norm gradient, possesses an implicit geometric regularization property that favors smooth and natural zero level set surfaces, avoiding bad zero-loss solutions. We provide a theoretical analysis of this property for the linear case, and show that, in practice, our method leads to state of the art implicit neural representations with higher level-of-details and fidelity compared to previous methods.

arXiv comment37th International Conference on Machine Learning, Vienna, Austria, 2020

References in corpus (9)

• DGM: A deep learning algorithm for solving partial differential equations
• Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling
• Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
• Perspective Transformer Nets: Learning Single-View 3D Object Reconstruction without 3D Supervision
• Gradient Descent Converges to Minimizers
• Implicit Regularization in Deep Learning
• Controlling Neural Level Sets
• Deep Level Sets: Implicit Surface Representations for 3D Shape Inference
• SDFDiff: Differentiable Rendering of Signed Distance Fields for 3D Shape Optimization

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• Riemannian Denoising Diffusion Probabilistic Models
• Moser Flow: Divergence-based Generative Modeling on Manifolds
• Normal-guided Detail-Preserving Neural Implicit Function for High-Fidelity 3D Surface Reconstruction
• Omni-GAN: On the Secrets of cGANs and Beyond