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Deformation with enforced metrics on length, area and volume

Shuo Jin, Yunbo Zhang, Charlie C.L. Wang
2014 Computer graphics forum (Print)  
In this paper, we present an effective framework to deform mesh models by enforcing demanded metrics on length, area and volume.  ...  Figure 1 : Our framework for generating deformation with enforced metrics provides a user-friendly tool for designers to accurately control the metrics in a deformation while well preserving the shape  ...  However, it is not clear how to further extend their work to generate deformation results with accurate values on length, area and volume.  ... 
doi:10.1111/cgf.12331 fatcat:44m3wmytzffmpcooh34wjyxuym

Area and Volume Restoration in Elastically Deformable Solids

Micky Kelager, Anders Fleron, Kenny Erleben
2005 ELCVIA Electronic Letters on Computer Vision and Image Analysis  
Within the original framework of the classical model a complete restoration of area and volume is introduced.  ...  The improved model is suitable for interactive simulation and can recover from volumetric collapsing, in particular upon large deformation.  ...  Implosions With the improved area and volume restorations we can restore the shape of the discrete grid cubes after deformation.  ... 
doi:10.5565/rev/elcvia.104 fatcat:u5dtdmojqre7raqjb2rizufp3e

AREA AND VOLUME RESTORATION IN ELASTICALLY DEFORMABLE SOLIDS [chapter]

Micky Kelager, Anders Fleron, Kenny Erleben
2009 Series in Machine Perception and Artificial Intelligence  
Within the original framework of the classical model a complete restoration of area and volume is introduced.  ...  The improved model is suitable for interactive simulation and can recover from volumetric collapsing, in particular upon large deformation.  ...  Implosions With the improved area and volume restorations we can restore the shape of the discrete grid cubes after deformation.  ... 
doi:10.1142/9789812834461_0021 dblp:series/smpai/KelagerFE09 fatcat:qsoqfvcoonf4znn37bq66bqp5i

Generalized Metric Energies for Continuous Shape Deformation [chapter]

Janick Martinez Esturo, Christian Rössl, Holger Theisel
2014 Lecture Notes in Computer Science  
In this work we derive a generalized metric energy for deformation vector fields that has close-to-isometric AKVFs as a special case and additionally supports close-to-length-preserving, close-to-conformal  ...  We compare our approach to AKVF-based deformations for the planar case and demonstrate the effectiveness of our method for the 2d and 3d case.  ...  Deformations based on the Akvf energy show better angle preservation compared to Metr, but they also show greater errors in length and area variation.  ... 
doi:10.1007/978-3-642-54382-1_8 fatcat:eznj2y2hjba3jjov2z7a2hwrza

Geodesics in Shape Space via Variational Time Discretization [chapter]

Benedikt Wirth, Leah Bar, Martin Rumpf, Guillermo Sapiro
2009 Lecture Notes in Computer Science  
For decreasing time step size, the proposed model leads to the minimization of the actual geodesic length, where the Hessian of the pairwise matching energy reflects the chosen Riemannian metric on the  ...  The proposed framework is based on the time discretization of a geodesic path as a sequence of pairwise matching problems, which is strictly invariant with respect to rigid body motions and ensures a 1  ...  Furthermore, the authors thank Sergio Conti for valuable hints on the physical model.  ... 
doi:10.1007/978-3-642-03641-5_22 fatcat:tqvp7pqtkzcenenvmgjlakuegq

Viscous regularization and r-adaptive remeshing for finite element analysis of lipid membrane mechanics

Lin Ma, William S. Klug
2008 Journal of Computational Physics  
The Augmented Lagrangian method is used to enforce global constraints on area and volume during membrane deformations.  ...  In particular, a viscous regularization method is proposed to stabilize tangential mesh deformations and improve the convergence rate of nonlinear solvers.  ...  of global constraints on area and volume.  ... 
doi:10.1016/j.jcp.2008.02.019 fatcat:lznp37ipc5dbblq2gmn2ntlzsm

Simultaneous Registration and Parcellation of Bilateral Hippocampal Surface Pairs for Local Asymmetry Quantification

N.A. Lord, J. Ho, B.C. Vemuri, S. Eisenschenk
2007 IEEE Transactions on Medical Imaging  
We propose a novel variational formulation for segmenting asymmetric regions from surface pairs based on the minimization of a functional of both the deformation map and the segmentation boundary, which  ...  The functional minimization is achieved via a quasi-simultaneous evolution of the map and the segmenting curve, conducted on and between two-dimensional surface parametric domains.  ...  The one modification present in our case is that length and area computations respect the distances between grid points by using the appropriate Riemannian metric at each point (as opposed to the uniform  ... 
doi:10.1109/tmi.2007.892502 pmid:17427734 pmcid:PMC2913155 fatcat:45qifpeidze37belakjpngdumy

All-Hex Mesh Generation via Volumetric PolyCube Deformation

James Gregson, Alla Sheffer, Eugene Zhang
2011 Computer graphics forum (Print)  
Our work introduces a new method for computing low-distortion volumetric PolyCube deformations of general shapes and for subsequent all-hex remeshing.  ...  For a given input model, our method simultaneously generates an appropriate PolyCube structure and mapping between the input model and the PolyCube.  ...  Alla Sheffer and James Gregson are funded by NSERC, MI-TACS and DISCOVERY. Eugene Zhang is partially supported by NSF awards IIS-0546881 and CCF-0830808.  ... 
doi:10.1111/j.1467-8659.2011.02015.x fatcat:6hx7jgiblraujko2fq6gac76ni

On 3D shape synthesis [chapter]

Heung-Yeung Shum, Martial Hebert, Katsushi Ikeuchi
1996 Lecture Notes in Computer Science  
Furthermore, with regularity constraints on the mesh, the inverse mapping from curvature space to shape space always exists and can be recovered using an iterative method.  ...  A curved or polyhedral 3D object of genus zero is represented by a curvature distribution on a spherical mesh that has nearly uniform distribution with known connectivity among mesh nodes.  ...  Because the shape reconstruction is only up to an unknown rigid transformation (rotation and translation) and an unknown scale factor, constant area or constant volume [2] can be enforced during the  ... 
doi:10.1007/3-540-61750-7_26 fatcat:mqbgrt545jeztgc2w3nymri4ya

Automated manifold surgery: constructing geometrically accurate and topologically correct models of the human cerebral cortex

B. Fischl, A. Liu, A.M. Dale
2001 IEEE Transactions on Medical Imaging  
Surface deformation techniques can guarantee the topological correctness of a model, but are time-consuming and may result in geometrically inaccurate models.  ...  a surface that is both geometrically accurate and topologically correct.  ...  Glessner and D. Salat for extensive testing of the proposed algorithms.  ... 
doi:10.1109/42.906426 pmid:11293693 fatcat:trwgz6d45javdlpd362jzjmvmi

Non-parametric Discrete Registration with Convex Optimisation [chapter]

Mattias P. Heinrich, Bartlomiej W. Papież, Julia A. Schnabel, Heinz Handels
2014 Lecture Notes in Computer Science  
To deal with this, previous work has focussed on parametric transformation models.  ...  We show improvements on current state-of-the-art performance both in terms of accuracy and computation time.  ...  B.W.P. and J.A.S. would like to acknowledge funding from the CRUK/ EPSRC Cancer Imaging Centre at Oxford.  ... 
doi:10.1007/978-3-319-08554-8_6 fatcat:juxmwzrg7jgizllozelhdrgsru

Conformal invariants for multiply connected surfaces: Application to landmark curve-based brain morphometry analysis

Jie Shi, Wen Zhang, Miao Tang, Richard J. Caselli, Yalin Wang
2017 Medical Image Analysis  
Although the lengths of the landmarks in Euclidean space, cortical surface area, and volume features did not differ between the two groups, our conformal invariant based shape indices revealed significant  ...  Such shape indices may be used to identify which surfaces are conformally equivalent and further quantitatively measure surface deformation.  ...  ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: Alzheimer's Association; Alzheimer's  ... 
doi:10.1016/j.media.2016.09.001 pmid:27639215 pmcid:PMC5099092 fatcat:qczplwszpzdppanhoom5wiwvaa

A geometric approach to Hu-Washizu variational principle in nonlinear elasticity [article]

Bensingh Dhas, Debasish Roy
2020 arXiv   pre-print
With the mathematical machinery provided by differentiable manifolds, we rewrite the deformation gradient and Cauchy-Green deformation tensor in terms of frame and co-frame fields.  ...  The mainstay of the present approach is to treat quantities defined on the co-tangent bundles of reference and deformed configurations as primal.  ...  Stokes theorem can be written as, C dα = ∂C α (6) We now assume that the manifold M is equipped with a metric g and dV denotes the volume form generated by the metric.  ... 
arXiv:2009.00275v1 fatcat:ee7bf6ckjfhrlpo7z3iwyi2bsi

Deformation similarity measurement in quasi-conformal shape space

Vahid Taimouri, Jing Hua
2014 Graphical Models  
The shapes with similar deformation patterns follow a similar deformation curve in shape space.  ...  A new quasi-conformal metric is introduced which measures the curvature changes at each vertex of each pose during the deformation.  ...  Wong Education Foundation, Hong Kong, and the National Science Foundation under the grants NSF IIS-0915933, NSF IIS-0937586 and NSF IIS-0713315.  ... 
doi:10.1016/j.gmod.2013.12.001 fatcat:5xgxag4d6fa4nlmdm52o4xcsdu

Type-Specific Analysis of Morphometry of Dendrite Spines of Mice

E. Ceyhan, L. Fong, T. N. Tasky, M. K. Hurdal, M. F. Beg, M. E. Martone, J. T. Ratnanather
2007 Image and Signal Processing and Analysis  
The morphometric measures we consider include the metric distance, volume, surface area, and length of dendrite spines of mice.  ...  The question of interest is how these morphometric measures differ by condition of mice; and how the metric distance relates to volume, surface area, length, and condition of mice.  ...  A previous version of this data (with fewer dendrite spines) was analyzed in ([1]) wherein a linear model was fit on metric distances versus other variables such as volume, surface area, and length values  ... 
doi:10.1109/ispa.2007.4383655 fatcat:qybeb3k5nnhnra5ac463mcxt3u
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