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Sampling and Reconstruction of Surfaces and Higher Dimensional Manifolds
2007
Journal of Mathematical Imaging and Vision
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We present new sampling theorems for surfaces and higher dimensional manifolds. The core of the proofs resides in triangulation results for manifolds with boundary, not necessarily bounded. ...
The method is based upon geometric considerations that are further augmented for 2-dimensional manifolds (i.e surfaces). ...
Lorentz for his careful reading of the manuscript and his many helpful comments and suggestions. ...
doi:10.1007/s10851-007-0048-z
fatcat:lns62pnkinakfmafnuyfyief5a
Sampling and Reconstruction of Surfaces and Higher Dimensional Manifolds
2008
Journal of Mathematical Imaging and Vision
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We present new sampling theorems for surfaces and higher dimensional manifolds. The core of the proofs resides in triangulation results for manifolds with boundary, not necessarily bounded. ...
The method is based upon geometric considerations that are further augmented for 2-dimensional manifolds (i.e surfaces). ...
Lorentz for his careful reading of the manuscript and his many helpful comments and suggestions. ...
doi:10.1007/s10851-008-0103-4
fatcat:7syqgml3b5hpxgpyehbsiiimju
Generalized Ricci curvature based sampling and reconstruction of images
2015
2015 23rd European Signal Processing Conference (EUSIPCO)
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We introduce a novel method of image sampling based on viewing grayscale images as manifolds with density, and sampling them according to the generalized Ricci curvature introduced by Bakry, Emery and ...
A variation of this approach, due to Morgan and his students is also considered. This new paradigm generalizes ideas and results that are by now common in Imaging and Graphics. ...
(This is a generalization of the similar sampling criterion using Gaussian/sectional curvature for surfaces [5] and higher dimensional manifolds [14] .) ...
doi:10.1109/eusipco.2015.7362454
dblp:conf/eusipco/LinLZS15
fatcat:unvw2b7fhbbxnd56m24b2h6hou
Geodesic-HOF: 3D Reconstruction Without Cutting Corners
[article]
2020
arXiv
pre-print
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Our results show that taking advantage of these learned lifted coordinates yields better performance for estimating surface normals and generating surfaces than using point cloud reconstructions alone. ...
To address this issue, we propose learning an image-conditioned mapping function from a canonical sampling domain to a high dimensional space where the Euclidean distance is equal to the geodesic distance ...
The key insight of our approach is to embed points sampled from the surface of a 3-dimensional object into a higher-dimensional space such that geodesic distances on the surface of the object can be computed ...
arXiv:2006.07981v1
fatcat:msyxgquzkjbx7fv77vawjkvaey
Curvature Based Clustering for DNA Microarray Data Analysis
[chapter]
2005
Lecture Notes in Computer Science
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Zeevi, Journal of Fourier Analysis and Applications, Special Issue -"Analysis on the Sphere II" 13(6), 2007, 711-727. (10) Sampling and Reconstruction of Surfaces and Higher Dimensional Manifolds, with ...
( 1 ) 1 Sampling and Reconstruction of Surfaces and Higher Dimensional Manifolds, with Eli Appleboim and Yehoshua Y. Zeevi, Technion CCIT Report #591, June 2006 (EE PUB #1543 June 2006). ...
doi:10.1007/11492542_50
fatcat:lney3vpjbzggza4cgcnqfbqheu
Dimensionality reduction and principal surfaces via Kernel Map Manifolds
2009
2009 IEEE 12th International Conference on Computer Vision
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The manifold is represented as a parametrized surface represented by a set of parameters that are defined on the input samples. ...
The representation also provides a natural mapping from high to low dimensional space, and a concatenation of these two mappings induces a projection operator onto the manifold. ...
This work was supported by the NIH/NCBC grant U54-EB005149 and the NSF grant CCF-073222. ...
doi:10.1109/iccv.2009.5459193
dblp:conf/iccv/GerberTW09
fatcat:a7xsk7wjjbh3xlzmnzrfw7m5oa
Jeffrey's prior sampling of deep sigmoidal networks
[article]
2017
arXiv
pre-print
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In connection with the results we present, we discuss problems of sampling high-dimensional manifolds as well as recent work [M. Transtrum, G. Hart, and P. ...
Neural networks have been shown to have a remarkable ability to uncover low dimensional structure in data: the space of possible reconstructed images form a reduced model manifold in image space. ...
For the DBN and SdA, the reconstructed manifold is 30 dimensional and the factor is a meager 1.03. ...
arXiv:1705.10589v1
fatcat:pzsnvtcxincshnbm4vq7dx6pk4
Shape Dimension and Approximation from Samples
2003
Discrete & Computational Geometry
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There are many scientific and engineering applications where an automatic detection of shape dimension from sample data is necessary. ...
We present a Voronoi based dimension detection algorithm that assigns a dimension to a sample point which is the topological dimension of the manifold it belongs to. ...
The first author thanks Marshall Bern for suggesting the problem of dimension detection from sample points and for his insightful comments. ...
doi:10.1007/s00454-002-2838-9
fatcat:dhbbswabszeb5eoraerot2ebjy
High-veracity functional imaging in scanning probe microscopy via Graph-Bootstrapping
2018
Nature Communications
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To meet this challenge, we present a data-driven approach, Graph-Bootstrapping, based on low-dimensional manifold learning of the full SPM spectra and demonstrate its successes for high-veracity mechanical ...
The key objective of scanning probe microscopy (SPM) techniques is the optimal representation of the nanoscale surface structure and functionality inferred from the dynamics of the cantilever. ...
Department of Energy, Office of Science User Facility at Oak Ridge National Laboratory. ...
doi:10.1038/s41467-018-04887-1
pmid:29930246
pmcid:PMC6013493
fatcat:irlqbqp53zbgjfn5h6xhoierna
Spectral sampling of manifolds
2010
ACM SIGGRAPH Asia 2010 papers on - SIGGRAPH ASIA '10
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We propose a new method to solve this problem based on spectral analysis of manifolds which results in faithful reconstructions and high quality isotropic samplings, is efficient, out-of-core, feature ...
Although our main focus is on sampling surfaces, the analysis and algorithms are general and can be applied for simplifying and resampling point clouds lying near a manifold of arbitrary dimension. ...
The models used in the paper are courtesy of AIM@SHAPE Shape Repository, Stanford University Computer Graphics Laboratory, Cyberware, SensAble, MIT CSAIL, INRIA, IMATI and Clemson University. ...
doi:10.1145/1882262.1866190
fatcat:e5jkdty2avgw5mryo6h6w53p2i
Spectral sampling of manifolds
2010
ACM Transactions on Graphics
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We propose a new method to solve this problem based on spectral analysis of manifolds which results in faithful reconstructions and high quality isotropic samplings, is efficient, out-of-core, feature ...
Although our main focus is on sampling surfaces, the analysis and algorithms are general and can be applied for simplifying and resampling point clouds lying near a manifold of arbitrary dimension. ...
The models used in the paper are courtesy of AIM@SHAPE Shape Repository, Stanford University Computer Graphics Laboratory, Cyberware, SensAble, MIT CSAIL, INRIA, IMATI and Clemson University. ...
doi:10.1145/1882261.1866190
fatcat:cuziwmjmejhhzplgs3wojklv6e
Spectral sampling of manifolds
2010
ACM SIGGRAPH Asia 2010 papers on - SIGGRAPH ASIA '10
Preserved Fulltext
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We propose a new method to solve this problem based on spectral analysis of manifolds which results in faithful reconstructions and high quality isotropic samplings, is efficient, out-of-core, feature ...
Although our main focus is on sampling surfaces, the analysis and algorithms are general and can be applied for simplifying and resampling point clouds lying near a manifold of arbitrary dimension. ...
The models used in the paper are courtesy of AIM@SHAPE Shape Repository, Stanford University Computer Graphics Laboratory, Cyberware, SensAble, MIT CSAIL, INRIA, IMATI and Clemson University. ...
doi:10.1145/1866158.1866190
fatcat:wf6jzidycva5tapfumn3vqbv2y
Prediction of high-dimensional states subject to respiratory motion: a manifold learning approach
2016
Physics in Medicine and Biology
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We evaluated and compared the proposed method with PCA-based approach on level-set surfaces reconstructed from point clouds captured by a 3D photogrammetry system. ...
In this study, we extend such rationale to a more general manifold and propose a framework for high-dimensional motion prediction with manifold learning, which allows to learn more descriptive features ...
We also acknowledge the support from UCLA dissertation year fellowship and Vision RT. ...
doi:10.1088/0031-9155/61/13/4989
pmid:27299958
pmcid:PMC4975535
fatcat:aayz2e6fkrflhjiw3vjarkyqkq
Geometric Understanding of Deep Learning
[article]
2018
arXiv
pre-print
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data concentrates close to a low-dimensional manifold, deep learning learns the manifold and the probability distribution on it. ...
We further introduce the concepts of rectified linear complexity for deep neural network measuring its learning capability, rectified linear complexity of an embedding manifold describing the difficulty ...
We uniformly sample the surface, there are 235, 771 samples in total. The number of cells in the cell decomposition induced by the reconstruction map is 230051. ...
arXiv:1805.10451v2
fatcat:d2dbdlkqqnavxg5ajqtxalxa6q
Manifold bootstrapping for SVBRDF capture
2010
ACM Transactions on Graphics
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The first acquires representatives of high angular dimension but sampled sparsely over the surface, while the second acquires keys of low angular dimension but sampled densely over the surface. ...
Abstract Manifold bootstrapping is a new method for data-driven modeling of real-world, spatially-varying reflectance, based on the idea that reflectance over a given material sample forms a low-dimensional ...
Wang et al. [2006] reconstruct the BRDF manifold from samples over the surface and from these predict reflectance variation over time. ...
doi:10.1145/1778765.1778835
fatcat:vqmiumhxbrhtji6lxmecdxxbwy
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