Implicit Geometric Regularization for Learning Shapes

By Amos Gropp, Lior Yariv, Niv Haim, Matan Atzmon, Yaron Lipman. International Conference on Machine Learning, 2020

1,034 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/4ad2a20794a802b8acedb059a8aea7a864e3851e

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In Computer Vision and Pattern Recognition

Citations in the corpus

Shape As Points: A Differentiable Poisson Solver (2021, methodology): “Optimization-based 3D reconstruction: We use the ofﬁcial implementation of IGR 6 [19] and Point2Mesh 7 [23].”
Efficient Geometry-aware 3D Generative Adversarial Networks (2021, neutral): “Emerging neural scene representations use differentiable 3D-aware representations [1, 3, 6, 8, 13, 17, 43, 44, 52, 65] that can be optimized using 2D multi-view images via neural rendering [15, 20, 24, 30, 34–37, 40, 45, 46, 50, 51, 54, 62, 63, 70– 72].”
pi-GAN: Periodic Implicit Generative Adversarial Networks for 3D-Aware Image Synthesis (2020, background): “These can be supervised with 3D data, such as point clouds, and optimized as either signed distance functions [46, 38, 1, 16, 57, 20, 47, 55, 27] or occupancy networks [37, 6].”
Neuralangelo: High-Fidelity Neural Surface Reconstruction (2023, methodology): “First, using numerical gradients to compute higher-order derivatives, such as surface normals for the eikonal regularization [8, 12, 20, 42], is critical to stabilizing the optimization.”
3D Neural Field Generation Using Triplane Diffusion (2022, neutral): “They either solely learn geometry [1,4,5,10,11,15,21,23,45, 47, 48, 57, 65, 73] or use posed images to jointly optimize geometry and appearance [6,7,18,25,29,33,36–39,44,49,50,54, 55,59,67,72,82–84].”
Moser Flow: Divergence-based Generative Modeling on Manifolds (2021, methodology): “First, the sphere, represented with the SDF f ( x ) = (cid:107) x (cid:107) − 1 , and second, the Stanford Bunny surface, representing a general curved surface and represented with an SDF learned with (Gropp et al., 2020) from point cloud data.”
PlenOctrees for Real-time Rendering of Neural Radiance Fields (2021, methodology): “These networks have been used to predict occupancy [28, 4, 34, 40, 31, 20], signed distance ﬁelds [32, 10, 61, 62], and radiance [30].”
I M Avatar: Implicit Morphable Head Avatars from Videos (2021, methodology): “For this reason, we also eliminated the Eikonal loss [9] in IDR [16], and reconstruct an occupancy field instead of an SDF field.”
AutoInt: Automatic Integration for Fast Neural Volume Rendering (2020, background): “Such representations have been explored for modeling shape parts [16, 17], objects [3, 6, 10, 19, 25, 27, 30, 34, 35, 40, 42, 43, 49, 53, 60], or scenes [14, 21, 29, 37, 45, 51].”
NeuS2: Fast Learning of Neural Implicit Surfaces for Multi-view Reconstruction (2022, methodology): “We also employ an Eikonal term [14] to regularize the learned signed distance field leading to our final loss where and R is the Huber loss [17].”
Geo-Neus: Geometry-Consistent Neural Implicit Surfaces Learning for Multi-view Reconstruction (2022, positive): “During rendering colors from a speciﬁc view, our total loss is: L color is the difference between the ground truth colors and the rendered colors: And L reg is an eikonal term [10] to regularize the gradients of SDF network: In our experiments, we choose α , β and γ as 0.3, 1.0 and 0.5 respectively.”
RegNeRF: Regularizing Neural Radiance Fields for View Synthesis from Sparse Inputs (2021, background): “…coordinate-based neural representations [7, 33, 34, 44] have become a popular representation for various tasks such as 3D reconstruction [1,7,13,14,33,39,42,44,45,48,51,55,57], 3D-aware generative modelling [5, 9, 15, 16, 32, 37, 38, 41, 49, 64], and novel-view synthesis [2, 3, 12, 22, 24, 27,…”
MetaSDF: Meta-learning Signed Distance Functions (2020, background): “This is noteworthy, as inferring an SDF from only the zero-level set points amounts to solving a boundary value problem defined by a particular Eikonal equation, see [14].”
Learning Smooth Neural Functions via Lipschitz Regularization (2022, methodology): “Previous works also introduced other geometric regularizations for encouraging different properties, such as [Gropp et al. 2020; Williams et al. 2021].”
FoundationPose: Unified 6D Pose Estimation and Tracking of Novel Objects (2023, methodology): “We also apply eikonal regularization [12] to the near-surface SDF: where x denotes a sampled 3D point along the rays in the divided space; d x and d D are the distance from ray origin to the sample point and the observed depth point, respectively.”
Multiview Neural Surface Reconstruction by Disentangling Geometry and Appearance (2020, methodology): “Lastly, we enforce f to be approximately a signed distance function with Implicit Geometric Regularization (IGR) [11], i.e., incorporating the Eikonal regularization: ) where x is distributed uniformly in a bounding box of the scene.”
NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction (2021, methodology): “We also studied the effect of Eikonal regularization [10] and geometric initialization [1].”