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A fast modal space transform for robust nonrigid shape retrieval

Jianbo Ye, Yizhou Yu
2015 The Visual Computer  
Retrieval of such objects in large databases based on shape similarity is still a challenging problem.  ...  In this paper, we take advantages of functional operators as characterizations of shape deformation, and further propose a framework to design novel shape signatures for encoding nonrigid geometries.  ...  Acknowledgments The authors would like to thank Maks Ovsjanikov and Dirk Smeets for sharing their software implementations.  ... 
doi:10.1007/s00371-015-1071-5 fatcat:mcw22plna5di5fdqghuyth2qe4

Self Functional Maps [article]

Oshri Halimi, Ron Kimmel
2018 arXiv   pre-print
Using this representation, geometric shape similarity is converted into algebraic distances between matrices.  ...  A classical approach for surface classification is to find a compact algebraic representation for each surface that would be similar for objects within the same class and preserve dissimilarities between  ...  The rapid growth of the amount of geometric data requires the design of efficient content-based shape retrieval engines, that could perform similar tasks to those of existing search engines for textual  ... 
arXiv:1804.08080v2 fatcat:l4g2ywhvejc5jnnclgrywdw37u

Foundations [chapter]

2011 Methods of Geometry  
. • Corollary 4. φσ ε φ' ι = σ φ[ι:] for any isometry φ and any plane ε. Proof.  ...  But the intuitive representation will never be used essentially in the logical development of geometry. That will be based solely on the axioms.  ...  For these matrices A and vectors Β verify that the equation X'=AX+B defines an isometry or similarity φ: X-+X', and classify it.  ... 
doi:10.1002/9781118032787.ch2 fatcat:6ft5vaghbratrgvyxj6mhppppu

Symmetry in 3D Geometry: Extraction and Applications

Niloy J. Mitra, Mark Pauly, Michael Wand, Duygu Ceylan
2013 Computer graphics forum (Print)  
We focus on elucidating the key similarities and differences between existing methods to gain a better understanding of a fundamental problem in digital geometry processing and shape understanding in general  ...  We discuss a variety of applications in computer graphics and geometry processing that benefit from symmetry information for more effective processing.  ...  The authors thank Hao (Richard) Zhang and the anonymous reviewers for their comments on various versions of this manuscript.  ... 
doi:10.1111/cgf.12010 fatcat:mbgf3fe7qjajlkkoiiucqfkoaa

Cusp shapes of Hilbert-Blumenthal surfaces [article]

Joseph Quinn, Alberto Verjovsky
2019 arXiv   pre-print
We include computer generated images and data illustrating various examples.  ...  We introduce a new fundamental domain for the cusp stabilizer of a Hilbert modular group over a real quadratic field K=Q(sqrt n).  ...  for their detailed comments and corrections; and to Dennis Ryan and Simon Woods for help with creating the computer generated images.  ... 
arXiv:1711.02418v5 fatcat:ktjkos7vl5esjlt2tkcppwf3pi

Symmetry in 3D Geometry: Extraction and Applications [article]

Niloy J. Mitra, Mark Pauly, Michael Wand, Duygu Ceylan
2012 Eurographics State of the Art Reports  
We focus on elucidating the similarities and differences between existing methods to gain a better understanding of a fundamental problem in digital geometry processing and shape understanding in general  ...  We discuss a variety of applications in computer graphics and geometry that benefit from symmetry information for more effective processing.  ...  Intuitively this can be thought to be a level of symmetry representation, similar to frequency band representations for images.  ... 
doi:10.2312/conf/eg2012/stars/029-051 fatcat:mw7cbmy5mrhhfhv2qrynrcmegq

Algorithms to Improve the Reparameterization of Spherical Mappings of Brain Surface Meshes

Rachel A. Yotter, Paul M. Thompson, Christian Gaser
2011 Journal of Neuroimaging  
A spherical map of a cortical surface is often used for improved brain registration, for advanced morphometric analysis (eg, of brain shape), and for surface-based analysis of functional signals recorded  ...  Furthermore, for intersubject analysis, it is usually necessary to reparameterize the surface mesh into a common coordinate system.  ...  The 3D distance error may be important in the field of morphometry, because if the original surface is not accurately approximated during reparameterization, some statistical power may be lost for shape  ... 
doi:10.1111/j.1552-6569.2010.00484.x pmid:20412393 fatcat:eoshmpzjhfhfpgehsnfo6ka5bq

The Geometric Theory of the Fundamental Germ [article]

T.M. Gendron
2005 arXiv   pre-print
The fundamental germ is a generalization of π_1, first defined for laminations which arise through group actions in math.DG/0506270.  ...  The mother germ is used to give a proof of a Nielsen theorem for the algebraic universal cover of a closed surface of hyperbolic type.  ...  Indeed, such a product would have the shape (4) γ α Θ α η α ∆ α ω α , for {∆ α } another sequence of rotations based at x with angle going to 0 and {ω α } another f-diophantine approximation.  ... 
arXiv:math/0506275v2 fatcat:bjs5f5sqn5ce7n3mdv6dmmsrdu

Local versus Global in Quasi-Conformal Mapping for Medical Imaging

Emil Saucan, Eli Appleboim, Efrat Barak-Shimron, Ronen Lev, Yehoshua Y. Zeevi
2008 Journal of Mathematical Imaging and Vision  
A method and algorithm of flattening of folded surfaces for two-dimensional representation and analysis of medical images are presented.  ...  Further applications of the algorithm, for image processing in general are also considered.  ...  [35] ), and since planar quasiisometries almost preserve shape when strain is under the critical value ( [11] ), the application of quasi-isometries in higher-dimensional image processing and related  ... 
doi:10.1007/s10851-008-0101-6 fatcat:g325yyjoyrh2ffqvz6foivkbsy

A Novel Method for Invariant Image Reconstruction

Mirosław Pawlak, Gurmukh Singh Panesar, Marcin Korytkowski
2021 Journal of Artificial Intelligence and Soft Computing Research  
We make use of Zernike radial moments to represent an image due to their invariance properties to isometry transformations and the ability to uniquely represent the salient features of the image.  ...  AbstractIn this paper we propose a novel method for invariant image reconstruction with the properly selected degree of symmetry.  ...  Let us assume the observation model Y kl = f (x k , y l ) + ε kl , (25) for 1 ≤ k, l ≤ n and {ε kl } is the zero-mean noise process.  ... 
doi:10.2478/jaiscr-2021-0005 fatcat:lyjfysyd5jcd5eps47k2v34xqe

Riemann-Roch isometries in the non-compact orbifold setting [article]

Gerard Freixas i Montplet, Anna von Pippich
2016 arXiv   pre-print
We generalize work of Deligne and Gillet-Soulé on a Riemann-Roch type isometry, to the case of the trivial sheaf on cusp compactifications of Riemann surfaces ΓH, for Γ⊂ PSL_2(R) a fuchsian group of the  ...  We make use of surgery techniques through Mayer-Vietoris formulae for determinants of laplacians, in order to reduce to explicit evaluations of such for model hyperbolic cusps and cones.  ...  However, we still need to evaluate det ∆ V ε/2 ,hyp,ε . This is the content of the following lemma. as ε → 0. 54 Proof.  ... 
arXiv:1604.00284v2 fatcat:qgrwe3stxvbkzapgj6mkg7p7w4

Dilatation structures I. Fundamentals [article]

Marius Buliga
2007 arXiv   pre-print
For this space, the dilatation based at x, of coefficient ε > 0, is the function δ x ε : R n → R n δ x ε y = x + ε(−x + y) For fixed x the dilatations based at x form a one parameter group which contracts  ...  Therefore a metric profile gives two types of information: • a distance estimate like (3.2) from point 4, • an "approximate shape" estimate, like in the points 1-3, where we see that two sets, namely the  ...  Then, for any x ∈ X, ε ∈ Γ, ν(ε) < 1, we have (a) For any u ∈ U (x), Σ x ε (x, u) = u. (b) For any u ∈ U (x) the functions Σ x ε (u, ·) and ∆ x ε (u, ·) are inverse one to another.  ... 
arXiv:math/0608536v4 fatcat:eh35urq4cjgjpfqme6wp4sue3i

Dilatation structures I. Fundamentals

Marius Buliga
2007 Journal of Generalized Lie Theory and Applications  
For this space, the dilatation based at x, of coefficient ε > 0, is the function δ x ε : R n → R n δ x ε y = x + ε(−x + y) For fixed x the dilatations based at x form a one parameter group which contracts  ...  Therefore a metric profile gives two types of information: • a distance estimate like (3.2) from point 4, • an "approximate shape" estimate, like in the points 1-3, where we see that two sets, namely the  ...  Then, for any x ∈ X, ε ∈ Γ, ν(ε) < 1, we have (a) For any u ∈ U (x), Σ x ε (x, u) = u. (b) For any u ∈ U (x) the functions Σ x ε (u, ·) and ∆ x ε (u, ·) are inverse one to another.  ... 
doi:10.4303/jglta/s070201 fatcat:6ifxx3fjtfacjgi7m4yhjiul2i

Dilatation structures I. Fundamentals

Marius BULIGA
2007 Journal of Generalized Lie Theory and Applications  
For this space, the dilatation based at x, of coefficient ε > 0, is the function δ x ε : R n → R n δ x ε y = x + ε(−x + y) For fixed x the dilatations based at x form a one parameter group which contracts  ...  Therefore a metric profile gives two types of information: • a distance estimate like (3.2) from point 4, • an "approximate shape" estimate, like in the points 1-3, where we see that two sets, namely the  ...  Then, for any x ∈ X, ε ∈ Γ, ν(ε) < 1, we have (a) For any u ∈ U (x), Σ x ε (x, u) = u. (b) For any u ∈ U (x) the functions Σ x ε (u, ·) and ∆ x ε (u, ·) are inverse one to another.  ... 
doi:10.4172/1736-4337.1000106 fatcat:v3cntdcaqvgp7ggvmushowvc2m

Sketches of a platypus: persistent homology and its algebraic foundations [article]

Mikael Vejdemo-Johansson
2013 arXiv   pre-print
Once we can accomodate quiver-based shapes, as in zigzag persistence, alongside both continuous and discrete shapes, as with the difference between (R, ≤)-modules and kQ-modules for an A e -quiver Q, the  ...  Shapes of theories, future directions A dichotomy such as the one we have seen above cries out for a unifying theory -everyone start out with the same underlying problem, and believe they do approximately  ... 
arXiv:1212.5398v2 fatcat:owk4wvddwbhl5maxim4cgdbgby
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