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Time sequence diffeomorphic metric mapping and parallel transport track time-dependent shape changes

Anqi Qiu, Marilyn Albert, Laurent Younes, Michael I. Miller
2009 NeuroImage  
To track anatomical shape changes in serial images, we introduce new point-based time sequence large deformation diffeomorphic metric mapping (TS-LDDMM) to infer the time flow of within-subject geometric  ...  The time-dependent momentum obtained from the TS-LDDMM encodes within-subject shape changes.  ...  Ying Sun at National University of Singapore for providing the cardiac MRI data and the segmented contours of the endocardium and epicardium.  ... 
doi:10.1016/j.neuroimage.2008.10.039 pmid:19041947 pmcid:PMC2718697 fatcat:mket4p3p2rggxe6humsfx3dxki

Discrete Ladders for Parallel Transport in Transformation Groups with an Affine Connection Structure [chapter]

Marco Lorenzi, Xavier Pennec
2014 Signals and Communication Technology  
This framework enables to transport diffeomorphic deformations of point supported and image data, and it was applied to study the hippocampal shape changes in Alzheimer's disease [35, 34] .  ...  Thus, in the Riemannian setting the covariant derivative is uniquely defined by the metric, and the parallel transport thus depends from the path γ and from the local expression of the metric tensor g  ... 
doi:10.1007/978-3-319-05317-2_9 fatcat:q3othyog4ncs5evlxtyxzasb3y

Parallel Transport of Surface Deformations from Pole Ladder to Symmetrical Extension [chapter]

Shuman Jia, Nicolas Duchateau, Pamela Moceri, Maxime Sermesant, Xavier Pennec
2018 Lecture Notes in Computer Science  
In this study, we encode inter-subject shape variations and temporal deformations in a common space of diffeomorphic registration. They are parameterized by stationary velocity fields.  ...  Previous normalization algorithms applied in medical imaging were first order approximations of parallel transport.  ...  To apply it to cardiac sequences, we need to: -Parameterize the temporal deformations Φ ti from the subject-specific shape S at baseline to its shape S ti at time t i by SVF v ti ; this step amounts to  ... 
doi:10.1007/978-3-030-04747-4_11 fatcat:kmsxvgozyjfhtkyp2vok26nseq

The emerging discipline of Computational Functional Anatomy

Michael I. Miller, Anqi Qiu
2009 NeuroImage  
For this we focus on two things: (i) the construction of bijections (via diffeomorphisms) between the coordinatized manifolds of human anatomy, and (ii) the transfer (group action and parallel transport  ...  We examine the transfer via these bijections of functional response variables into anatomical coordinates via group action on scalars and matrices in DTI as well as parallel transport of metric information  ...  HL52307) and NSF (DMS-0456253).  ... 
doi:10.1016/j.neuroimage.2008.10.044 pmid:19103297 pmcid:PMC2839904 fatcat:xv4fognxc5e6ziu3sedwc37p6u

A New Geometric Metric in the Space of Curves, and Applications to Tracking Deforming Objects by Prediction and Filtering

Ganesh Sundaramoorthi, Andrea Mennucci, Stefano Soatto, Anthony Yezzi
2011 SIAM Journal of Imaging Sciences  
According to this metric centroid translations, scale changes and deformations are orthogonal, and the metric is also invariant with respect to reparameterizations of the curve.  ...  the best shape according to a criterion; examples include image segmentation and object tracking; andshape analysis, where we study families of shapes for purposes of statistics, (automatic) cataloging  ...  His corrections, comments, and many valuable suggestions are greatly appreciated.  ... 
doi:10.1137/090781139 fatcat:tmryfdgs5vhvznyglfnvymgja4

The TPS Direct Transport: A New Method for Transporting Deformations in the Size-and-Shape Space

Valerio Varano, Stefano Gabriele, Luciano Teresi, Ian L. Dryden, Paolo E. Puddu, Concetta Torromeo, Paolo Piras
2017 International Journal of Computer Vision  
Modern shape analysis allows the fine com  ...  Zastrow and Antonio Di-Carlo for hints and advices; their helpful discussions stimulated us to go far beyond our initial intuitions.  ...  L.T., V.V. and S.G acknowledge the National Group of Mathematical Physics (GNFM-INdAM), Italy, for support.  ... 
doi:10.1007/s11263-017-1031-9 fatcat:3xzkenig7zdq5h7j5fsurvikiu

Transporting Deformations of Face Emotions in the Shape Spaces: A Comparison of Different Approaches

Paolo Piras, Valerio Varano, Maxime Louis, Antonio Profico, Stanley Durrleman, Benjamin Charlier, Franco Milicchio, Luciano Teresi
2021 Journal of Mathematical Imaging and Vision  
We used the large diffeomorphic deformation metric mapping and thin plate spline, in order to estimate deformations in a deformational trajectory of a human face experiencing different emotions.  ...  We found DT, LS and FS very effective in recovering the original deformation while NT fails under several aspects in transporting the shape change.  ...  Large Deformation Diffeomorphic Metric Mapping (LDDMM) The LDDMM framework [28, 51] proposes to compare shapes via the action of diffeomorphisms φ : E m → E m of the ambient space.  ... 
doi:10.1007/s10851-021-01030-6 fatcat:7jcna7vu4vf3rlygmuyjzil7mm

Tracking deforming objects by filtering and prediction in the space of curves

Ganesh Sundaramoorthi, Andrea Mennucci, Stefano Soatto, Anthony Yezzi
2009 Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference  
We propose a dynamical model-based approach for tracking the shape and deformation of highly deforming objects from time-varying imagery.  ...  We then derive an associated nonlinear filter that estimates and predicts the shape and deformation of a object from image measurements.  ...  Therefore, in this metric, centroid translations, scale changes and deformations of the shape are orthogonal.  ... 
doi:10.1109/cdc.2009.5400786 dblp:conf/cdc/SundaramoorthiMSY09 fatcat:yuy6kbryf5aorc4fflmusdv4gm

A new geodesic-based feature for characterization of 3D shapes: application to soft tissue organ temporal deformations [article]

Karim Makki, Amine Bohi, Augustin C. Ogier, Marc-Emmanuel Bellemare
2020 arXiv   pre-print
frame are tracked throughout a long dynamic MRI sequence using a Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework.  ...  In this paper, we propose a method for characterizing 3D shapes from point clouds and we show a direct application on a study of organ temporal deformations.  ...  Bone et al. have detailed a scheme for parallel transport on a high-dimensional manifold of diffeomorphisms based on the LDDMM [4] , in the context of shape analysis.  ... 
arXiv:2003.08332v1 fatcat:nqhegnrwb5cypbp7soiwg7fkoq

Quantification of local changes in myocardial motion by diffeomorphic registration via currents: Application to paced hypertrophic obstructive cardiomyopathy in 2D echocardiographic sequences

Nicolas Duchateau, Geneviève Giraldeau, Luigi Gabrielli, Juan Fernández-Armenta, Diego Penela, Reinder Evertz, Lluis Mont, Josep Brugada, Antonio Berruezo, Marta Sitges, Bart H. Bijnens
2015 Medical Image Analysis  
Time-to-peak measurements and single-parameter observations are cumbersome and often confusing for quantifying local changes in myocardial function.  ...  Non-rigid registration (diffeomorphic registration via currents) is used to match pairs of patterns, and pattern changes are inferred from the registration output.  ...  First, it builds upon shape warping and fitting via continuous diffeomorphic transformations from the large deformation diffeomorphic metric mapping (LDDMM) framework (Beg et al., 2005; Miller et al.,  ... 
doi:10.1016/ pmid:25461338 fatcat:jky4r7knrvenvef5cw7dcg6y5e

Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms

M. Faisal Beg, Michael I. Miller, Alain Trouvé, Laurent Younes
2005 International Journal of Computer Vision  
This paper examine the Euler-Lagrange equations for the solution of the large deformation diffeomorphic metric mapping problem studied in Dupuis et al. (1998) and Trouvé (1995) in which two images I 0  ...  , I 1 are given and connected via the diffeomorphic change of coordinates I 0 • ϕ −1 = I 1 where ϕ = φ 1 is the end point at Beg et al.  ...  John Csernansky and David Van Essen of Washington University for providing the data on hippocampal and Macaque shapes, and Dr.  ... 
doi:10.1023/b:visi.0000043755.93987.aa fatcat:qzmpveitrnewbc6yvrytyuacki

A spatio-temporal atlas and statistical model of the tongue during speech from cine-MRI

Jonghye Woo, Fangxu Xing, Junghoon Lee, Maureen Stone, Jerry L. Prince
2016 Computer Methods in Biomechanics and Biomedical Engineering Imaging & Visualization  
Finally, the spatio-temporal atlas is created by time-warping each subject, generating new mean images at each time, and producing shape statistics around these mean images using principal component analysis  ...  In order to study the variability of tongue shape and motion in populations, a consistent integration and characterization of inter-subject variability is needed.  ...  For the mean of magnitude of deformation fields, let ψ m (x; t): Ω×t → Ω (m=2,···, 26), be the diffeomorphic mapping between the reference time frame and the remaining time frames.  ... 
doi:10.1080/21681163.2016.1169220 pmid:30034953 pmcid:PMC6051546 fatcat:6a7idepcmzhhnjdklnzpkmryja

Geometry of Image Registration: The Diffeomorphism Group and Momentum Maps [article]

Martins Bruveris, Darryl D. Holm
2013 arXiv   pre-print
These lecture notes explain the geometry and discuss some of the analytical questions underlying image registration within the framework of large deformation diffeomorphic metric mapping (LDDMM) used in  ...  Parallel transport was used in [59] as the transport method to compare deformations of the hippocampus in subjects with early AD and healthy controls across a time span of two years.  ...  We shall concentrate on the definition used in the large deformation diffeomorphic metric mapping (LDDMM) approach [10, 49, 50, 67] , which generates the transformation ϕ = ϕ 1 as the flow of a time-dependent  ... 
arXiv:1306.6854v2 fatcat:gvw3lcvugjdbhl6e5tmg2xkghm

Contour Manifolds and Optimal Transport [article]

Bernhard Schmitzer, Christoph Schnörr
2013 arXiv   pre-print
A discussion of the metric induced by optimal transport and the corresponding geodesic equation is given.  ...  In particular we show that the pseudo-Riemannian structure of optimal transport, when restricted to the set of shape measures, yields a manifold which is diffeomorphic to the manifold of closed contours  ...  Since ϕ t is a C ∞ -diffeomorphism it preserves simple connectedness and C ∞ -smoothness of the boundary of spt(µ 0 ). Therefore µ t must be a shape measure at all times.  ... 
arXiv:1309.2240v1 fatcat:e3xnla5tlbbztkojaiy5mw3ixm

Learning a Generative Motion Model from Image Sequences based on a Latent Motion Matrix [article]

Julian Krebs, Hervé Delingette, Nicholas Ayache, Tommaso Mansi
2021 arXiv   pre-print
This unsupervised generative model follows a novel multivariate Gaussian process prior and is applied within a temporal convolutional network which leads to a diffeomorphic motion model.  ...  Besides, we demonstrate the model's applicability for motion analysis, simulation and super-resolution by an improved motion reconstruction from sequences with missing frames compared to linear and cubic  ...  We have shown that such a space allows for accurate diffeomorphic tracking, temporal interpolation, motion simulation and motion transport.  ... 
arXiv:2011.01741v2 fatcat:fvtbu7y3ejfo3ieb5ji7oaclke
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