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Implicit Regularization and Convergence for Weight Normalization [article]

Xiaoxia Wu and Edgar Dobriban and Tongzheng Ren and Shanshan Wu and Zhiyuan Li and Suriya Gunasekar and Rachel Ward and Qiang Liu
2020 arXiv   pre-print
Normalization methods such as batch [Ioffe and Szegedy, 2015], weight [Salimansand Kingma, 2016], instance [Ulyanov et al., 2016], and layer normalization [Baet al., 2016] have been widely used in modern  ...  These methods adaptively regularize the weights and converge close to the minimum l2 norm solution, even for initializations far from zero.  ...  XW, SW, ED, SG, and RW thank the Simons Institute for their hospitality during the Summer 2019 program on the Foundations of Deep Learning.  ... 
arXiv:1911.07956v4 fatcat:aatlegsrkvaw3felgfw2dkeafe

A Multi-Scale Tikhonov Regularization Scheme for Implicit Surface Modelling

Jianke Zhu, Steven C.H. Hoi, Michael R. Lyu
2007 2007 IEEE Conference on Computer Vision and Pattern Recognition  
In this paper, we propose a fast solution for approximating implicit surfaces based on a multi-scale Tikhonov regularization scheme.  ...  The optimization of our scheme is formulated into a sparse linear equation system, which can be efficiently solved by factorization methods.  ...  The normal information is of-ten engaged in traditional methods which usually generate two off-surface points along each normal vector of the surface.  ... 
doi:10.1109/cvpr.2007.383022 dblp:conf/cvpr/ZhuHL07 fatcat:kfks2yuv4ng3pko2426zy4tcaq

GPU-based polygonization and optimization for implicit surfaces

Junjie Chen, Xiaogang Jin, Zhigang Deng
2014 The Visual Computer  
Despite the popularity of polygonization of implicit surfaces in graphics applications, an efficient solution to both polygonize and optimize meshes from implicit surfaces on modern GPUs has not been developed  ...  than or comparable to other GPU iso-surface extraction methods.  ...  HPDC_10 (left); TVCG_12 (mid- dle); ours (right) Table 4 4 Maximum and average errors of position, normal and regularity of polygonized implicit surfaces before and after optimizationTable 5Quality  ... 
doi:10.1007/s00371-014-0924-7 fatcat:rporq6y4pncupmawux3kws5luu

Vectorfield isosurface-based reconstruction from oriented points

Peter G. Sibley, Gabriel Taubin
2005 ACM SIGGRAPH 2005 Sketches on - SIGGRAPH '05  
We present a new and much simpler formulation for the problem of reconstructing an implicit surface from an oriented point cloud acquired by a range scanner or a stereo vision system.  ...  Function discretizations associated with regular grids automatically produce Iso-surface polygon meshes.  ...  In the area of geometry processing, the notion of decoupling the filtering of normal fields and geometry has emerged as a powerful method for denoising [Tasdizen et al. 2003 ].  ... 
doi:10.1145/1187112.1187146 dblp:conf/siggraph/SibleyT05 fatcat:5c4sb35xljhmfggckhmgu7f244

Regularity Normalization: Neuroscience-Inspired Unsupervised Attention across Neural Network Layers [article]

Baihan Lin
2021 arXiv   pre-print
Inspired by the adaptation phenomenon of neuronal firing, we propose the regularity normalization (RN) as an unsupervised attention mechanism (UAM) which computes the statistical regularity in the implicit  ...  Treating the neural network optimization process as a partially observable model selection problem, the regularity normalization constrains the implicit space by a normalization factor, the universal code  ...  Our proposed method adopt a similar definition of implicit space, but consider the implicit space as datadependent encoding statistical regularities.  ... 
arXiv:1902.10658v13 fatcat:bb7helcugrehddai22n3zwtfgu

Hermite Interpolation of Implicit Surfaces with Radial Basis Functions

Ives Macêdo, João Paulo Gois, Luiz Velho
2009 2009 XXII Brazilian Symposium on Computer Graphics and Image Processing  
normals).  ...  Intrinsic properties of this method allow the computation of implicit surfaces rich in details, with irregularly spaced points even in the presence of close sheets.  ...  of both methods by ensuring well-posedness of a promising combined interpolation/regularization approach which we haven't explored yet.  ... 
doi:10.1109/sibgrapi.2009.11 dblp:conf/sibgrapi/MacedoGV09 fatcat:n5wefq342zds3lgehy6asukf7u

Hierarchically Partitioned Implicit Surfaces for Interpolating Large Point Set Models [chapter]

David T. Chen, Bryan S. Morse, Bradley C. Lowekamp, Terry S. Yoo
2006 Lecture Notes in Computer Science  
We present a hierarchical spatial partitioning method for creating interpolating implicit surfaces using compactly supported radial basis functions (RBFs) from scattered surface data.  ...  From this hierarchy of functions we create a range of models from coarse to fine, where a coarse model approximates and a fine model interpolates all the surface points.  ...  17,485,117 tree nodes 799 tree height 5 build time (minutes) 127.35 Averages regular constraints 961.77 per phantom constraints 202.00 evaluation number of nodes 6.59 avg. implicit error  ... 
doi:10.1007/11802914_40 fatcat:ll3krpoquzgyrd4zslq4pygmi4

Feature Surface Extraction and Reconstruction from Industrial Components Using Multistep Segmentation and Optimization

Yuan Wang, Jiajing Wang, Xiuwan Chen, Tianxing Chu, Maolin Liu, Ting Yang
2018 Remote Sensing  
The method analyzes the normal vector distribution matrix to segment feature points from a 3D point cloud.  ...  Method The proposed method uses PCA based on the normal vector distribution matrix to classify feature points as surface, edge, or corner points.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/rs10071073 fatcat:vn4doco3qfanncamrdjcqjuv34

A Transition-Aware Method for the Simulation of Compliant Contact with Regularized Friction [article]

Alejandro M. Castro, Ante Qu, Naveen Kuppuswamy, Alex Alspach, and Michael Sherman
2019 arXiv   pre-print
We find that TALS works best with semi-implicit integration, but that the explicit treatment of normal compliance can be problematic.  ...  Unfortunately, regularized friction introduces high-frequency stiff dynamics and even implicit methods struggle with these systems, especially during slip-stick transitions.  ...  To describe our method, we make a brief overview of the implicit Euler method, though TALS can be used with other implicit integrators.  ... 
arXiv:1909.05700v2 fatcat:rdst3ysvqveijirsz6wepeyzhy

Iso-Points: Optimizing Neural Implicit Surfaces with Hybrid Representations [article]

Wang Yifan, Shihao Wu, Cengiz Oztireli, Olga Sorkine-Hornung
2021 arXiv   pre-print
We demonstrate that our method can be adopted to improve state-of-the-art techniques for reconstructing neural implicit surfaces from multi-view images or point clouds.  ...  In this work, we develop a hybrid neural surface representation that allows us to impose geometry-aware sampling and regularization, which significantly improves the fidelity of reconstructions.  ...  None of these methods exploit an explicit sampling of the implicit function to improve the optimization. Poursaeed et al.  ... 
arXiv:2012.06434v2 fatcat:guysfuk2b5cnjpljmb4hslezyu

Learning to Infer Implicit Surfaces without 3D Supervision [article]

Shichen Liu, Shunsuke Saito, Weikai Chen, Hao Li
2019 arXiv   pre-print
To this end, we propose a novel ray-based field probing technique for efficient image-to-field supervision, as well as a general geometric regularizer for implicit surfaces, which provides natural shape  ...  We address the fundamental problem of learning implicit surfaces for shape inference without the need of 3D supervision.  ...  While geometric regularization for implicit fields is largely unexplored, we propose a new method for constraining geometric properties of an implicit surface using the approximated derivatives of the  ... 
arXiv:1911.00767v1 fatcat:vq33mtgfvvc7llzkigbvpljo4i

Surface Reconstruction from Point Clouds without Normals by Parametrizing the Gauss Formula

Siyou Lin, Dong Xiao, Zuoqiang Shi, Bin Wang
2022 ACM Transactions on Graphics  
Our method bypasses the need for accurate input normals as required by most existing non-data-driven methods, while also exhibiting superiority over data-driven methods since no training is needed.  ...  By viewing surface normals and surface element areas as unknown parameters, the Gauss formula interprets the indicator as a member of some parametric function spaces.  ...  ACKNOWLEDGMENTS This work is supported by the National Key R&D Program of China (2020YFB1708900) and the NSFC project 12071244. Zuoqiang Shi and Bin Wang are the corresponding authors of this work.  ... 
doi:10.1145/3554730 fatcat:ge45oxd3rjbd5brh3gtictulqi

Detailed Facial Geometry Recovery from Multi-View Images by Learning an Implicit Function [article]

Yunze Xiao, Hao Zhu, Haotian Yang, Zhengyu Diao, Xiangju Lu, Xun Cao
2022 arXiv   pre-print
Unlike previous learning-based methods that regularize the cost volume via 3D CNN, we propose to learn an implicit function for regressing the matching cost.  ...  Traditional multi-view stereo (MVS) methods adopt an optimization-based scheme to regularize the matching cost.  ...  Different from all the above methods, our method is the first to learn an implicit function for cost regularization in the learning-based framework. Face-specific MVS.  ... 
arXiv:2201.01016v2 fatcat:r75cjigl65ao3dxckihuydzi4u

Implicit Geometric Regularization for Learning Shapes [article]

Amos Gropp, Lior Yariv, Niv Haim, Matan Atzmon, Yaron Lipman
2020 arXiv   pre-print
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  ...  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).  ...  Implicit geometrical regularization.  ... 
arXiv:2002.10099v2 fatcat:6bkz2kbu7zcc5eqwwgnaj3e3me

Implicit Surface Modeling from Imprecise Point Clouds

E. Funk, L. S. Dooley, A. Boerner
2013 The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences  
This paper presents a robust scene reconstruction method which is predicated upon the observation that most objects contain only a small set of primitives.  ...  The resulting scene surface models are defined as implicit functions and may be processed using conventional rendering algorithms such as marching cubes, to deliver polygonal models of arbitrary resolution  ...  The inputs (3D points + normals) in a local neighbourhood are used to estimate the parameters of a larger planar patch, the surfels, which model the implicit function. methods relies on the search of an  ... 
doi:10.5194/isprsarchives-xl-4-w4-7-2013 fatcat:ai4cp22p7jg3dhwk4teeiydiga
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