DeepMesh: Differentiable Iso-Surface Extraction

Guillard, Benoît; Remelli, Edoardo; Lukoianov, Artem; Richter, Stephan R.; Bagautdinov, Timur; Baqué, Pierre; Fua, Pascal

doi:10.48550/arxiv.2106.11795

Cited by 3 publications

(4 citation statements)

References 40 publications

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“…[50] model the problem of triangulation locally by predicting a logarithmic map which allows triangulation in 2D using non-differentiable Delaunay triangulation. Finally, some recent work focus on using the neural implicit representation as the core representation for differentiable meshing or learning [16,48,26]. Neural Marching Cubes [16] implements a data-driven approach to improve the mesh quality at sharp edges by defining a learnable representation to differentiate between the topological configurations of marching cubes.…”

Section: Related Workmentioning

confidence: 99%

“…In contrast, our method operates in continuous space and therefore on arbitrary resolutions. DeepMesh [26] uses a trick, i.e., an additional forward pass on all mesh vertex locations for computing gradients with respect to an underlying implicit representation without the need to make the meshing differentiable. They use a non-differentiable marching cubes algorithm to generate the output and define loss functions directly on the obtained mesh.…”

Section: Related Workmentioning

confidence: 99%

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NeuralMeshing: Differentiable Meshing of Implicit Neural Representations

Vetsch

Lombardi

Pollefeys

et al. 2022

Lecture Notes in Computer Science

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The generation of triangle meshes from point clouds, i.e. meshing, is a core task in computer graphics and computer vision. Traditional techniques directly construct a surface mesh using local decision heuristics, while some recent methods based on neural implicit representations try to leverage data-driven approaches for this meshing process. However, it is challenging to define a learnable representation for triangle meshes of unknown topology and size and for this reason, neural implicit representations rely on non-differentiable post-processing in order to extract the final triangle mesh. In this work, we propose a novel differentiable meshing algorithm for extracting surface meshes from neural implicit representations. Our method produces the mesh in an iterative fashion, which makes it applicable to shapes of various scales and adaptive to the local curvature of the shape. Furthermore, our method produces meshes with regular tessellation patterns and fewer triangle faces compared to existing methods. Experiments demonstrate the comparable reconstruction performance and favorable mesh properties over baselines.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

NeuralMeshing: Differentiable Meshing of Implicit Neural Representations

Vetsch

Lombardi

Pollefeys

et al. 2022

Lecture Notes in Computer Science

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show abstract

“…Thus they differ markedly from the present work which uses the latent surface representation as a prior. The work [25] has used the latent representation to solve shape optimization problems, but the forward problem is modeled with a neural network. This makes heavy regularization crucial, and thus the optimized shape can only differ from the initial guess slightly.…”

Section: Introductionmentioning

confidence: 99%

Solving inverse obstacle scattering problem with latent surface representations

Chen,

Jin,

Liu

2024

Inverse Problems

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We propose a novel iterative numerical method to solve the three-dimensional inverse obstacle scattering problem of recovering the shape of the obstacle from far-field measurements. To address the inherent ill-posed nature of the inverse problem, we advocate the use of a trained latent representation of surfaces as the generative prior. This prior enjoys excellent expressivity within the given class of shapes, and meanwhile, the latent dimensionality is low, which greatly facilitates the computation. Thus, the admissible manifold of surfaces is realistic and the resulting optimization problem is less ill-posed. We employ the shape derivative to evolve the latent surface representation, by minimizing the loss, and we provide a local convergence analysis of a gradient descent type algorithm to a stationary point of the loss. We present several numerical examples, including also backscattered and phaseless data, to showcase the effectiveness of the proposed algorithm.

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“…It allows us to represent various shapes with the number of parameters smaller than the number of grid points of interest. Contrary to the deep learning shape optimization frameworks, such as [20], [21], where the Marching Cubes algorithm [22], [23] extracts the surface from the neural SDF on some prede-Fig. 2.…”

Section: Introductionmentioning

confidence: 99%

Implicit Neural Representation for Mesh-Free Inverse Obstacle Scattering

Vlašić¹,

Nguyen²

2022

Preprint

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Implicit representation of shapes as level sets of multilayer perceptrons has recently flourished in different shape analysis, compression, and reconstruction tasks. In this paper, we introduce an implicit neural representation-based framework for solving the inverse obstacle scattering problem in a meshfree fashion. We efficiently express the obstacle shape as the zero-level set of a signed distance function which is implicitly determined by a small number of network parameters. To solve the direct scattering problem, we implement the implicit boundary integral method. It uses projections of the grid points in the tubular neighborhood onto the boundary to compute the PDE solution instead of a grid-size-dependent extraction method of surface points such as Marching Cubes. The implicit representation conveniently handles the shape perturbation in the optimization process. To update the shape, we use PyTorch's automatic differentiation to backpropagate the loss function w.r.t. the network parameters, allowing us to avoid complex and error-prone manual derivation of the shape derivative. The proposed framework makes the inverse scattering problem more tractable with fewer parameters to optimize in comparison to the memory-inefficient grid-based approaches and outputs highquality reconstruction results.

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DeepMesh: Differentiable Iso-Surface Extraction

Cited by 3 publications

References 40 publications

NeuralMeshing: Differentiable Meshing of Implicit Neural Representations

NeuralMeshing: Differentiable Meshing of Implicit Neural Representations

Solving inverse obstacle scattering problem with latent surface representations

Implicit Neural Representation for Mesh-Free Inverse Obstacle Scattering

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