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Pre-image as Karcher Mean Using Diffusion Maps: Application to Shape and Image Denoising
[chapter]
2009
Lecture Notes in Computer Science
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We propose to model the underlying manifold as the set of Karcher means of close sample points. This non-linear interpolation is particularly well-adapted to the case of shapes and images. ...
A set of shapes or images being known through given samples, we capture its structure thanks to the diffusion maps method. ...
We then define the pre-image s = Ψ −1 |M (φ) as a Karcher mean that minimizes the mean-squared criterion: s = arg min z∈S Ψ (z) − φ 2 (6)
Shape interpolation using Karcher means Given a set of neighboring ...
doi:10.1007/978-3-642-02256-2_60
fatcat:fhpyaqlbbrhsrf22gobys547me
Rapid Precision Functional Mapping of Individuals Using Multi-Echo fMRI
2020
Cell Reports
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Resting-state functional magnetic resonance imaging (fMRI) is widely used in cognitive and clinical neuroscience, but long-duration scans are currently needed to reliably characterize individual differences ...
Together, these findings establish the potential utility of multi-echo fMRI for rapid precision mapping using experimentally and clinically tractable scan times and will facilitate longitudinal neuroimaging ...
Evan Gordon shared templates used to assign known functional brain network identities to InfoMap communities and code for creating the appearance of stripes on the surface and in the volume. Dr. ...
doi:10.1016/j.celrep.2020.108540
pmid:33357444
pmcid:PMC7792478
fatcat:sggl6tmj2zeejpj6r4wroumn64
Mathematical morphology on the sphere
1990
Visual Communications and Image Processing '90: Fifth in a Series
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It is necessary therefore a pre-filtering stage in order to denoise as well as possible, but preserving also the structures of the image (targets, changes in clutter, etc.). ...
using a gradient descent method as proposed by Karcher [13] . ...
doi:10.1117/12.24213
fatcat:c3vxrvzhnnfuno5zklccnm4e2u
A novel manifold learning denoising method on bearing vibration signals
2016
Journal of Vibroengineering
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Furthermore, this method can be used in other fault detection fields, such as engine, suspension device, and vehicle structures. ...
According to keeping the computing time acceptable, a novel manifold learning denoising method is put forward combining data compression and reconstruct operations. ...
Pre-Image as Karcher Mean using Diffusion Maps:
Application to Shape and Image Denoising. Scale Space and Variational Methods in Computer Vision. ...
doaj:3f51874750ec401086c8ec9edd36bb8e
fatcat:2c44twrfdvd53bydk355pnt4iu
Fiber Direction Estimation, Smoothing and Tracking in Diffusion MRI
[article]
2015
arXiv
pre-print
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Diffusion magnetic resonance imaging is an imaging technology designed to probe anatomical architectures of biological samples in an in vivo and non-invasive manner through measuring water diffusion. ...
First it proposes a new method to identify and estimate multiple diffusion directions within a voxel through a new and identifiable parametrization of the widely used multi-tensor model. ...
Hoffman-La Roche, Schering-Plough, Synarc, Inc., as well as non-profit partners the Alzheimer's Association and Alzheimer's Drug Discovery Foundation, with participation from the U.S. ...
arXiv:1406.0581v2
fatcat:3p75a55ptbh2dfeeaf75siicma
Intrinsic wavelet regression for curves of Hermitian positive definite matrices
[article]
2019
arXiv
pre-print
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The finite-sample performance of intrinsic wavelet thresholding is assessed by means of simulated data and compared to several benchmark estimators in the Riemannian manifold. ...
Intrinsic wavelet transforms and wavelet estimation methods are introduced for curves in the non-Euclidean space of Hermitian positive definite matrices, with in mind the application to Fourier spectral ...
Emad Eskandar (Massachussetts General Hospital) for the local field potential data to illustrate the methodology and the anonymous referees for their suggestions that helped improving the presentation ...
arXiv:1701.03314v6
fatcat:ub56futy5zc2ngqjrqsei7wwaa
The Human Connectome Project: A Retrospective
2021
NeuroImage
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We discuss several scientific advances using HCP data, including improved cortical parcellations, analyses of connectivity based on functional and diffusion MRI, and analyses of brain-behavior relationships ...
To date, more than 27 Petabytes of data have been shared, and 1538 papers acknowledging HCP data use have been published. ...
Supported by NIH grants U54MH091657 ( HCP-YA: Mapping the Human Connectome: Structure, Function, and Heritability), U01MH109589 ( HCP-D: Mapping the Human Connectome During Typical Development), U01AG052564 ...
doi:10.1016/j.neuroimage.2021.118543
pmid:34508893
fatcat:qzxs43vy7reavhdqkn2f5yhw6u
Geodesic Methods in Computer Vision and Graphics
2009
Foundations and Trends in Computer Graphics and Vision
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Using this local tensor field, the geodesic distance is used to solve many problems of practical interest such as segmentation using geodesic balls and Voronoi regions, sampling points at regular geodesic ...
We show several applications of the numerical computation of geodesic distances and shortest paths to problems in surface and shape processing, in particular segmentation, sampling, meshing and comparison ...
Such an efficient triangulation is likely to be also efficient for applications to image compression and denoising, because it captures well the geometry of the image. ...
doi:10.1561/0600000029
fatcat:oe2kxm2lofff7gsqn4f7yraa4i
ÉCole De Physique Des Houches
[chapter]
2007
Les Houches
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The Mont Blanc is the highest mountain in the Alps, Western Europe and the European Union. ...
It rises 4,810.45 m above sea level and is ranked 11th in the world in topographic prominence. ecole de Physique des houches la côte des chavants 74310 les houches, france +33 (0)4 50 54 40 69 ...
., and Schmittbuhl, M. (2008)
correlaTive analysis of recurrenT MulTicolor fluorescence iMaGes To characTerize in vivo The effecT of anTiveGf druGs on GlioBlasToMa TuMor develoPMenT Rodriguez, T. ...
doi:10.1016/s0924-8099(13)60020-7
fatcat:jydcwidbbnf3nppqp4x3pyu6ga
École de Physique des Houches
[chapter]
2008
Les Houches
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The Mont Blanc is the highest mountain in the Alps, Western Europe and the European Union. ...
It rises 4,810.45 m above sea level and is ranked 11th in the world in topographic prominence. ecole de Physique des houches la côte des chavants 74310 les houches, france +33 (0)4 50 54 40 69 ...
., and Schmittbuhl, M. (2008)
correlaTive analysis of recurrenT MulTicolor fluorescence iMaGes To characTerize in vivo The effecT of anTiveGf druGs on GlioBlasToMa TuMor develoPMenT Rodriguez, T. ...
doi:10.1016/s0924-8099(13)60004-9
fatcat:nxiezedqabbbtnfqonvw6c3doi
École de Physique des Houches
[chapter]
2006
Les Houches
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
The Mont Blanc is the highest mountain in the Alps, Western Europe and the European Union. ...
It rises 4,810.45 m above sea level and is ranked 11th in the world in topographic prominence. ecole de Physique des houches la côte des chavants 74310 les houches, france +33 (0)4 50 54 40 69 ...
., and Schmittbuhl, M. (2008)
correlaTive analysis of recurrenT MulTicolor fluorescence iMaGes To characTerize in vivo The effecT of anTiveGf druGs on GlioBlasToMa TuMor develoPMenT Rodriguez, T. ...
doi:10.1016/s0924-8099(06)80084-3
fatcat:6w7diik2k5af7cpowh4xz3nsky
Understanding Human-Centric Images: From Geometry to Fashion
[article]
2015
arXiv
pre-print
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Along these lines, we have proposed two low-level keypoint descriptors: one based on the theory of the heat diffusion on images, and the other that uses a convolutional neural network to learn discriminative ...
In order to build these high level models it is paramount to have a battery of robust and reliable low and mid level cues. ...
Acknowledgements I would like to firstly thank both my advisors Francesc and Carme, to whom I owe this opportunity. ...
arXiv:1604.08164v1
fatcat:rq43466do5b2rpkrkbqlvdudqi
SAGA: sparse and geometry-aware non-negative matrix factorization through non-linear local embedding
2014
Machine Learning
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It operates by coding the data with respect to local neighbors with non-linear weights. This locality is obtained as a consequence of the simultaneous sparsity and convexity constraints. ...
structure of the manifold embedding the data; (2) provides an optimal representation with a controllable level of sparsity; (3) has an overall linear complexity allowing handling in tractable time large and ...
work was partially supported by the ANR fundings ANR-10-INBS-08 (ProFI project, "Infrastructures Nationales en Biologie et Santé", "Investissements d'Avenir"), ANR-13-JS02-0005-01 (Asterix project). and ...
doi:10.1007/s10994-014-5463-y
fatcat:djud7urtbzdafcubootv3dw6zu
Riemannian geometry for EEG-based brain-computer interfaces; a primer and a review
2017
Brain-Computer Interfaces
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radar data processing, image processing, computer vision, shape analysis, medical imaging (especially diffusion magnetic resonance imaging and, indeed, BCI), sensor networks, elasticity, mechanics, optimization ...
useful in applications. ...
doi:10.1080/2326263x.2017.1297192
fatcat:zxlvqa7eh5cttnclne6pgcbyqy
Statistical inference for intrinsic wavelet estimators of SPD matrices in a log-Euclidean manifold
[article]
2022
arXiv
pre-print
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This estimator preserves positive-definiteness and enjoys permutation-equivariance, which is particularly relevant for covariance matrices. ...
Our second-generation wavelet estimator is based on average-interpolation and allows the same powerful properties, including fast algorithms, known from nonparametric curve estimation with wavelets in ...
Johannes Krebs gratefully acknowledges the support of the Deutsche Forschungsgemeinschaft (grants KR-4977/1-1, KR-4977/2-1) and the hospitality of ISBA/LIDAM (UCLouvain). ...
arXiv:2202.07010v1
fatcat:ngzvtqfpwzf53jmzob3twjip3e
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