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An Elasticity-Based Covariance Analysis of Shapes

Martin Rumpf, Benedikt Wirth
2010 International Journal of Computer Vision  
Shape contours are approximated by single well phase fields, which enables an extension of the method to a covariance analysis of image morphologies.  ...  Based on the notion of nonlinear elastic deformations from one shape to another, a suitable linearization of geometric shape variations is introduced.  ...  Acknowledgements The authors thank Guillermo Sapiro for pointing them to the issue of an elastic principal component analysis.  ... 
doi:10.1007/s11263-010-0358-2 fatcat:swiwog3skbfd3ebmo7rhhl7uxu

An Elasticity Approach to Principal Modes of Shape Variation [chapter]

Martin Rumpf, Benedikt Wirth
2009 Lecture Notes in Computer Science  
Concepts from elasticity are applied to analyze modes of variation on shapes in two and three dimensions.  ...  To compute a shape average, all input shapes are elastically deformed into the same configuration.  ...  The authors thank Guillermo Sapiro for pointing them to the issue of an elastic principal component analysis.  ... 
doi:10.1007/978-3-642-02256-2_59 fatcat:mvfptvugqzbqdf7apd4ncub7jq

Elastic Full Procrustes Analysis of Plane Curves via Hermitian Covariance Smoothing [article]

Almond Stöcker, Manuel Pfeuffer, Lisa Steyer, Sonja Greven
2022 arXiv   pre-print
We propose an elastic full Procrustes mean of shapes of (oriented) plane curves, which are considered equivalence classes of parameterized curves with respect to translation, rotation, scale, and re-parameterization  ...  Identifying the real plane with the complex numbers, we establish a connection to covariance estimation in irregular/sparse functional data analysis and propose Hermitian covariance smoothing for (in)elastic  ...  of the tongue muscle to adjust its shape (elastic analysis).  ... 
arXiv:2203.10522v1 fatcat:vvyqbavjmnbbteqftiyb4cgebm

Bayes Reconstruction of Missing Teeth

Jon Sporring, Katrine Hommelhoff Jensen
2008 Journal of Mathematical Imaging and Vision  
, using the eigenstructure of the covariance matrix, also known as Principle Component Analysis (PCA).  ...  Sporring gratefully acknowledges Technical Finally we use Bayes method to propose the reconstruction of missing data, for e.g. finding the most probable shape of a missing tooth based on the best match  ...  Conclusion We have presented a system for reconstructing teeth based on an extension of the Principal Component Analysis on shape models containing selected teeth in the human bite.  ... 
doi:10.1007/s10851-008-0081-6 fatcat:qrc6xmbcwzgj3ju7fei2ikmmzu

Radiologic image-based statistical shape analysis of brain tumours

Karthik Bharath, Sebastian Kurtek, Arvind Rao, Veerabhadran Baladandayuthapani
2018 Journal of the Royal Statistical Society, Series C: Applied Statistics  
on the space of tumor shapes, and (3) allows for a rich class of continuous deformations of a tumor shape.  ...  A key component of the framework is a suitable metric that (1) enables comparisons of tumor shapes, (2) provides tools for computing descriptive statistics and implementing principal component analysis  ...  Shape-based principal component analysis We explore dominant directions of variation in a sample of tumor shapes with an efficient basis for T [q] (S) using traditional PCA (also referred to as tangent  ... 
doi:10.1111/rssc.12272 pmid:30420787 pmcid:PMC6225782 fatcat:roxrsvo7tvdlvixcgbylyb4qf4

Radiologic Image-based Statistical Shape Analysis of Brain Tumors [article]

Karthik Bharath, Sebastian Kurtek, Arvind Rao, Veerabhadran Baladandayuthapani
2017 arXiv   pre-print
We propose a curve-based Riemannian-geometric approach for general shape-based statistical analyses of tumors obtained from radiologic images.  ...  A key component of the framework is a suitable metric that (1) enables comparisons of tumor shapes, (2) provides tools for computing descriptive statistics and implementing principal component analysis  ...  Shape-based principal component analysis We explore dominant directions of variation in a sample of tumor shapes with an efficient basis for T [q] (S) using traditional PCA as follows.  ... 
arXiv:1702.01191v1 fatcat:hlypfjjwizhi3ezzlbgazahdia

Shell PCA: Statistical Shape Modelling in Shell Space

Chao Zhang, Behrend Heeren, Martin Rumpf, William A. P. Smith
2015 2015 IEEE International Conference on Computer Vision (ICCV)  
It is in this setting that we show how to perform statistical analysis of a set of shapes (meshes in dense correspondence), providing a hybrid between physical and statistical shape modelling.  ...  Thin shells, or their discrete counterparts, can be considered to reside in a shell space in which the notion of distance is given by the elastic energy required to deform one shape into another.  ...  This motivates our idea of performing statistical shape analysis in shell space. We define a notion of covariance based on the Hessian of an elastic energy term.  ... 
doi:10.1109/iccv.2015.195 dblp:conf/iccv/ZhangHRS15 fatcat:zbni6imlpvb2hgb6ffi5nvtgpu

Comparison between HEMNMA-3D and Traditional Classification Techniques for Analyzing Biomolecular Continuous Shape Variability in Cryo Electron Subtomograms

Mohamad Harastani, Slavica Jonic
2021 2021 4th International Conference on Bio-Engineering for Smart Technologies (BioSMART)  
Recently, HEMNMA-3D was introduced for cryo-ET continuous shape variability analysis, based on elastic and rigid-body 3D registration between simulated shapes and cryo-ET data using normal mode analysis  ...  Other shape variability analysis techniques simplify the problem by considering discrete rather than continuous conformational changes of complexes.  ...  HEMNMA-3D is based on elastic and rigid-body 3D registration between simulated shapes and cryo-ET data based on normal mode analysis (NMA) and fast rotational matching (FRM) with missing wedge compensation  ... 
doi:10.1109/biosmart54244.2021.9677643 fatcat:hnisylqvebcg7p2gtgdjqq64ci

Affine-invariant, elastic shape analysis of planar contours

D. Bryner, A. Srivastava, E. Klassen
2012 2012 IEEE Conference on Computer Vision and Pattern Recognition  
The removal of the rotation and the re-parameterization groups results in a quotient space, termed affine elastic shape space, and the resulting geodesic paths exhibit an improved matching of features  ...  These geodesics are used for shape comparison, retrieval, and statistical modeling of given curves.  ...  The authors would also like to acknowledge the NSWC PCD ILIR Program and the support of Dr. Kerry Commander and Dr. Quyen Huynh.  ... 
doi:10.1109/cvpr.2012.6247700 dblp:conf/cvpr/BrynerSK12 fatcat:zp25f7xss5celg5rxufmoczraq

Bayesian Active Contours with Affine-Invariant Elastic Shape Prior [chapter]

Darshan Bryner, Anuj Srivastava
2015 Current Trends in Bayesian Methodology with Applications  
However, most contour methods use shape priors based on similarity-shape analysis, i.e. analysis that is invariant to rotation, translation, and scale.  ...  Using an elastic, affine-invariant shape modeling of planar curves, we propose an active contour algorithm in which the training and test shapes can be at arbitrary affine transformations, and the resulting  ...  The authors would also like to acknowledge the NSWC PCD ILIR Program and the support of Dr. Quyen Huynh.  ... 
doi:10.1201/b18502-8 fatcat:voaqm376ibbpdgd7u525vfmszi

Bayesian Active Contours with Affine-Invariant, Elastic Shape Prior

Darshan Bryner, Anuj Srivastava
2014 2014 IEEE Conference on Computer Vision and Pattern Recognition  
However, most contour methods use shape priors based on similarity-shape analysis, i.e. analysis that is invariant to rotation, translation, and scale.  ...  Using an elastic, affine-invariant shape modeling of planar curves, we propose an active contour algorithm in which the training and test shapes can be at arbitrary affine transformations, and the resulting  ...  The authors would also like to acknowledge the NSWC PCD ILIR Program and the support of Dr. Quyen Huynh.  ... 
doi:10.1109/cvpr.2014.47 dblp:conf/cvpr/BrynerS14 fatcat:gpapueiyczfttn7ihbcmxsuruu

A Mathematical Framework for Protein Structure Comparison

Wei Liu, Anuj Srivastava, Jinfeng Zhang, Roland L. Dunbrack
2011 PLoS Computational Biology  
With curves representing protein structures, the matching is performed using elastic shape analysis of curves, which can effectively model conformational changes and insertions/deletions.  ...  Using an elastic Riemannian metric on spaces of curves, geodesic distance, a proper distance on spaces of curves, can be computed for any two protein structures.  ...  Contributed reagents/ materials/analysis tools: WL. Wrote the paper: AS JZ.  ... 
doi:10.1371/journal.pcbi.1001075 pmid:21304929 pmcid:PMC3033361 fatcat:6vg4jylihjgr7halcensxdai3y

Characterization of the energy-dependent uncertainty and correlation in silicon neutron displacement damage metrics

Patrick Griffin, Dimitri Rochman, Arjan Koning, A. Plompen, F.-J. Hambsch, P. Schillebeeckx, W. Mondelaers, J. Heyse, S. Kopecky, P. Siegler, S. Oberstedt
2017 EPJ Web of Conferences  
An energy-dependent covariance matrix is used to characterize the resulting uncertainty.  ...  A strong correlation between different reaction channels is observed in the high energy neutron contributions to the displacement damage metrics which supports the necessity of using a Monte Carlo based  ...  An analysis was made, using a subset of 297-element random TENDL-2015 nuclear evaluations, to separate the effect of the variation in the magnitude of the cross section from the shape of the recoil spectrum  ... 
doi:10.1051/epjconf/201714602008 fatcat:nqydh5veijfpleeayha3pcfgda

Variational Methods in Shape Analysis [chapter]

Martin Rumpf, Benedikt Wirth
2015 Handbook of Mathematical Methods in Imaging  
. has been developed in cooperation with Leah Bar and Guillermo Sapiro from the University of Minnesota. Benedikt Wirth has been funded by the Bonn International Graduate School in Mathematics.  ...  Furthermore, the work was supported by the Deutsche Forschungsgemeinschaft, SPP  "Optimization with Partial Differential Equations. " Part of > Figs. ---, and > --- have been taken from  ...  analysis on shapes as two exemplary applications of the state-based elastic shape space.  ... 
doi:10.1007/978-1-4939-0790-8_56 fatcat:cd7zghqpzrcdzdfezryhyztxz4

Statistical shape analysis of tap roots: a methodological case study on laser scanned sugar beets

Behrend Heeren, Stefan Paulus, Heiner Goldbach, Heiner Kuhlmann, Anne-Katrin Mahlein, Martin Rumpf, Benedikt Wirth
2020 BMC Bioinformatics  
The shape based PCA was used for a statistical analysis of 140 sugar beet roots of different cultivars.  ...  The computation of a shape based principal component analysis (PCA) built on concepts from continuum mechanics has proven to be an effective tool for a qualitative and quantitative shape examination.  ...  Using the physical model of 3D elasticity Rumpf and Wirth compute shape averages [33] and describe a covariance analysis [34, 35] of shapes represented as boundary contours of elastic objects.  ... 
doi:10.1186/s12859-020-03654-8 pmid:32727350 fatcat:u7xujopu65fivkswvsfmolkkim
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