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Pre-image as Karcher Mean Using Diffusion Maps: Application to Shape and Image Denoising [chapter]

Nicolas Thorstensen, Florent Segonne, Renaud Keriven
2009 Lecture Notes in Computer Science  
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

Charles J. Lynch, Jonathan D. Power, Matthew A. Scult, Marc Dubin, Faith M. Gunning, Conor Liston
2020 Cell Reports  
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

Jos B. Roerdink, Murat Kunt
1990 Visual Communications and Image Processing '90: Fifth in a Series  
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

Jingwei Gao, Ruichen Wang, Lei Hu, Rui Zhang
2016 Journal of Vibroengineering  
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]

Raymond K. W. Wong, Thomas C. M. Lee, Debashis Paul, Jie Peng, the Alzheimer's Disease Neuroimaging Initiative
2015 arXiv   pre-print
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]

Joris Chau, Rainer von Sachs
2019 arXiv   pre-print
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

Jennifer Stine Elam, Matthew F. Glasser, Michael P. Harms, Stamatios N. Sotiropoulos, Jesper L.R. Andersson, Gregory C. Burgess, Sandra W. Curtiss, Robert Oostenveld, Linda J. Larson-Prior, Jan-Mathijs Schoffelen, Michael R. Hodge, Eileen A. Cler (+6 others)
2021 NeuroImage  
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

Gabriel Peyré
2009 Foundations and Trends in Computer Graphics and Vision  
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  
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  
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  
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]

Edgar Simo-Serra
2015 arXiv   pre-print
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

Nicolas Courty, Xing Gong, Jimmy Vandel, Thomas Burger
2014 Machine Learning  
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

Marco Congedo, Alexandre Barachant, Rajendra Bhatia
2017 Brain-Computer Interfaces  
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]

Johannes Krebs, Daniel Rademacher, Rainer von Sachs
2022 arXiv   pre-print
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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