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Parameterization and reconstruction from 3D scattered points based on neural network and PDE techniques

J. Barhak, A. Fischer
2001 IEEE Transactions on Visualization and Computer Graphics  
The parameterization method described in this paper is based on two stages: 1) 2D initial parameterization and 2) 3D adaptive parameterization.  ...  Neural network SOM parameterization creates a grid where all the sampled points, not only the boundary points, affect the grid, leading to a uniform and smooth surface.  ...  The approach outlined in this paper is based on the following stages: 1) reconstructing a parametric base surface based on neural network SOM or PDE methods; 2) adaptively calculating the parameterization  ... 
doi:10.1109/2945.910817 fatcat:4yhrvqf3wjajjkrujnifl5i57m

Neural Fields in Visual Computing and Beyond [article]

Yiheng Xie, Towaki Takikawa, Shunsuke Saito, Or Litany, Shiqin Yan, Numair Khan, Federico Tombari, James Tompkin, Vincent Sitzmann, Srinath Sridhar
2022 arXiv   pre-print
These methods, which we call neural fields, have seen successful application in the synthesis of 3D shapes and image, animation of human bodies, 3D reconstruction, and pose estimation.  ...  In Part I, we focus on techniques in neural fields by identifying common components of neural field methods, including different representations, architectures, forward mapping, and generalization methods  ...  We would like to thank Sunny Li for their help in designing the website, and Alexander Rush and Hendrik Strobelt of the Mini-Conf project.  ... 
arXiv:2111.11426v4 fatcat:yteqzbu6gvgdzobnfzuqohix2e

Hybrid Functional-Neural Approach for Surface Reconstruction

Andrés Iglesias, Akemi Gálvez
2014 Mathematical Problems in Engineering  
Our approach is based on the combination of two powerful artificial intelligence paradigms: on one hand, we apply the popular Kohonen neural network to address the data parameterization problem.  ...  These neural and functional networks are applied in an iterative fashion for further surface refinement.  ...  Special thanks are owed to the editor and the four anonymous reviewers for their useful comments and suggestions that allowed us to improve the final version of this paper.  ... 
doi:10.1155/2014/351648 fatcat:lbgi7iyfrnc6lmozotxrqqd67q

Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next [article]

Salvatore Cuomo, Vincenzo Schiano di Cola, Fabio Giampaolo, Gianluigi Rozza, Maziar Raissi, Francesco Piccialli
2022 arXiv   pre-print
The study indicates that most research has focused on customizing the PINN through different activation functions, gradient optimization techniques, neural network structures, and loss function structures  ...  Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself.  ...  Modern methods, based on NN techniques, take advantage of optimization frameworks and auto-differentiation, like Berg and Nyström (2018) that suggested a unified deep neural network technique for estimating  ... 
arXiv:2201.05624v3 fatcat:elmdoax7ongblim3cbvkj2pdxi

GMLS-Nets: A framework for learning from unstructured data [article]

Nathaniel Trask, Ravi G.Patel, Ben J. Gross, Paul J. Atzberger
2019 arXiv   pre-print
For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and invariances.  ...  We generalize CNNs by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares (GMLS).  ...  For data sampled on regular grids, Convolutional Neural Networks (CNNs) are widely used to exploit translation invariance and hierarchical structure to extract features from data.  ... 
arXiv:1909.05371v2 fatcat:4qwq3u3rx5axnf5qyrdrje2lb4

Extending Neural Networks for B-Spline Surface Reconstruction [chapter]

G. Echevarría, A. Iglesias, A. Gálvez
2002 Lecture Notes in Computer Science  
This approach has been successfully applied to the reconstruction of a surface from a given set of 3D data points assumed to lie on unknown Bézier [17] and B-spline tensor-product surfaces [18] .  ...  Recently, a new extension of the standard neural networks, the so-called functional networks, has been described [5] .  ...  Finally, a very recent work using a combination of neural networks and PDE techniques for the parameterization and reconstruction of surfaces from 3D scattered points can be found in [2] .  ... 
doi:10.1007/3-540-46080-2_32 fatcat:skcjl7xurbggrh7hho53qhxiay

Shape As Points: A Differentiable Poisson Solver [article]

Songyou Peng, Chiyu "Max" Jiang, Yiyi Liao, Michael Niemeyer, Marc Pollefeys, Andreas Geiger
2021 arXiv   pre-print
We demonstrate the effectiveness of SAP on the task of surface reconstruction from unoriented point clouds and learning-based reconstruction.  ...  In recent years, neural implicit representations gained popularity in 3D reconstruction due to their expressiveness and flexibility.  ...  Acknowledgement: Andreas Geiger was supported by the ERC Starting Grant LEGO-3D (850533) and the DFG EXC number 2064/1 -project number 390727645.  ... 
arXiv:2106.03452v2 fatcat:guf3qerjkzgtnh5evwadetcncm

SSNO: Spatio-spectral Neural Operator for Functional Space Learning of Partial Differential Equations

Muhammad Rafiq, Ghazala Rafiq, Ho-Youl Jung, Gyu Sang Choi
2022 IEEE Access  
Our proposed solution achieves superior accuracy to the current level of research on learning-based solvers and Fourier neural operators.  ...  Recent research to solve the parametric partial differential equations shifted the focus of conventional neural networks from finite-dimensional Euclidean space to generalized functional spaces.  ...  operator (MGNO), low-rank neural operator (LNO), DeepONet, and neural network based on principle component analysis (PCANN).  ... 
doi:10.1109/access.2022.3148401 fatcat:maxl6opdnvgnhmsu5ow2m4vlpi

Learning nonlocal constitutive models with neural networks [article]

Xu-Hui Zhou, Jiequn Han, Heng Xiao
2021 arXiv   pre-print
The range of nonlocal dependence and the convolution structure are derived from the formal solution to transport equations. The neural network-based nonlocal constitutive model is trained with data.  ...  Inspired by the structure of the exact solutions to linear transport PDEs, we propose a neural network representing a region-to-point mapping to describe such nonlocal constitutive models.  ...  [42] [43] [44] in some inverse problems like tomographic reconstruction and wave scattering inversion.  ... 
arXiv:2010.10491v2 fatcat:swao7yb4czcfxp5bwoswortnee

Neural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networks [article]

Francis Williams, Matthew Trager, Joan Bruna, Denis Zorin
2021 arXiv   pre-print
We present Neural Splines, a technique for 3D surface reconstruction that is based on random feature kernels arising from infinitely-wide shallow ReLU networks.  ...  Our method achieves state-of-the-art results, outperforming recent neural network-based techniques and widely used Poisson Surface Reconstruction (which, as we demonstrate, can also be viewed as a type  ...  Sloan Foundation, NSF RI-1816753, NSF CA-REER CIF 1845360, NSF CHS-1901091, and Samsung Electronics.  ... 
arXiv:2006.13782v3 fatcat:lpqv6xm7hje3neors6nl2sy7za

Conditionally Parameterized, Discretization-Aware Neural Networks for Mesh-Based Modeling of Physical Systems [article]

Jiayang Xu, Aniruddhe Pradhan, Karthik Duraisamy
2021 arXiv   pre-print
While neural networks have recently been explored for surrogate and reduced order modeling of PDE solutions, they often ignore interactions or hierarchical relations between input features, and process  ...  We generalize the idea of conditional parameterization -- using trainable functions of input parameters to generate the weights of a neural network, and extend them in a flexible way to encode critical  ...  We thank Alvaro Sanchez and Peter Battaglia for valuable advice on training noise injection for robust prediction.  ... 
arXiv:2109.09510v3 fatcat:a3tmnn22pndhva3x4rx6xzuipu

Solving the acoustic VTI wave equation using physics-informed neural networks [article]

Chao Song and Tariq Alkhalifah and Umair bin Waheed
2020 arXiv   pre-print
Additional tests on a modified 3D Overthrust model and a model with irregular topography also show the effectiveness of the proposed method.  ...  After training a deep neural network (NN), we can evaluate the wavefield at any point in space instantly using this trained NN.  ...  Thuwal, Saudi Arabia, and we are grateful for that. We thank Bin She, from the University of electronic science and technology, for sharing the 3D plot tool.  ... 
arXiv:2008.01865v1 fatcat:dkzz5b5te5eoxprc6cqkmx6gce

Functional networks for B-spline surface reconstruction

A. Iglesias, G. Echevarría, A. Gálvez
2004 Future generations computer systems  
This approach has been successfully applied to the reconstruction of a surface from a given set of 3D data points assumed to lie on unknown Bézier [A. Iglesias, A.  ...  Recently, a new extension of the standard neural networks, the so-called functional networks, has been described [E. Castillo, Functional networks, Neural Process. Lett. 7 (1998) 151-159].  ...  Finally, a very recent work using a combination of neural networks and Partial Differential Equation (PDE) techniques for the parameterization and reconstruction of surfaces from 3D scattered points can  ... 
doi:10.1016/j.future.2004.05.025 fatcat:4k4ljfwxjvf63gf4hkq2hnunu4

Cuckoo Search Algorithm with Lévy Flights for Global-Support Parametric Surface Approximation in Reverse Engineering

Andrés Iglesias, Akemi Gálvez, Patricia Suárez, Mikio Shinya, Norimasa Yoshida, César Otero, Cristina Manchado, Valentin Gomez-Jauregui
2018 Symmetry  
In this paper we address the general problem of global-support parametric surface approximation from clouds of data points for reverse engineering applications.  ...  We also take advantage of the symmetric structure of the tensor-product surfaces, where the parametric variables u and v play a symmetric role in shape reconstruction.  ...  Acknowledgments: This research work has received funding from the project PDE-GIR (Partial Differential Equations for Geometric modelling, Image processing, and shape Reconstruction) of the European Union's  ... 
doi:10.3390/sym10030058 fatcat:yermdvu3i5hhdnqvvxvozuyc6i

Photometric stereo for strong specular highlights

Maryam Khanian, Ali Sharifi Boroujerdi, Michael Breuß
2018 Computational Visual Media  
It uses several input images of a static scene taken from one and the same camera position but under varying illumination.  ...  Experiments are performed on both synthetic and real world images; the latter do not benefit from laboratory conditions.  ...  She is mainly interested in computer vision, 3D reconstruction, deep learning, machine learning, neural networks, and data analysis.  ... 
doi:10.1007/s41095-017-0101-9 fatcat:e6f6jgoeavglhdleqwe2t6h3wq
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