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A fast modal space transform for robust nonrigid shape retrieval

2015
*
The Visual Computer
*

Retrieval of such objects in large databases

doi:10.1007/s00371-015-1071-5
fatcat:mcw22plna5di5fdqghuyth2qe4
*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. ...##
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Self Functional Maps
[article]

2018
*
arXiv
*
pre-print

Using this

arXiv:1804.08080v2
fatcat:l4g2ywhvejc5jnnclgrywdw37u
*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 ...##
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Foundations
[chapter]

2011
*
Methods of Geometry
*

. • Corollary 4. φσ

doi:10.1002/9781118032787.ch2
fatcat:6ft5vaghbratrgvyxj6mhppppu
*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. ...##
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Symmetry in 3D Geometry: Extraction and Applications

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

doi:10.1111/cgf.12010
fatcat:mbgf3fe7qjajlkkoiiucqfkoaa
*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. ...##
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Cusp shapes of Hilbert-Blumenthal surfaces
[article]

2019
*
arXiv
*
pre-print

We include computer generated

arXiv:1711.02418v5
fatcat:ktjkos7vl5esjlt2tkcppwf3pi
*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*. ...##
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Symmetry in 3D Geometry: Extraction and Applications
[article]

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

doi:10.2312/conf/eg2012/stars/029-051
fatcat:mw7cbmy5mrhhfhv2qrynrcmegq
*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*. ...##
###
Algorithms to Improve the Reparameterization of Spherical Mappings of Brain Surface Meshes

2011
*
Journal of Neuroimaging
*

A spherical map of a cortical surface is often used

doi:10.1111/j.1552-6569.2010.00484.x
pmid:20412393
fatcat:eoshmpzjhfhfpgehsnfo6ka5bq
*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*...##
###
The Geometric Theory of the Fundamental Germ
[article]

2005
*
arXiv
*
pre-print

The fundamental germ is a generalization of π_1, first defined

arXiv:math/0506275v2
fatcat:bjs5f5sqn5ce7n3mdv6dmmsrdu
*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*. ...##
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Local versus Global in Quasi-Conformal Mapping for Medical Imaging

2008
*
Journal of Mathematical Imaging and Vision
*

A method and algorithm of flattening of folded surfaces

doi:10.1007/s10851-008-0101-6
fatcat:g325yyjoyrh2ffqvz6foivkbsy
*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 ...##
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A Novel Method for Invariant Image Reconstruction

2021
*
Journal of Artificial Intelligence and Soft Computing Research
*

We make use of Zernike radial moments to represent an

doi:10.2478/jaiscr-2021-0005
fatcat:lyjfysyd5jcd5eps47k2v34xqe
*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. ...##
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Riemann-Roch isometries in the non-compact orbifold setting
[article]

2016
*
arXiv
*
pre-print

We generalize work of Deligne and Gillet-Soulé on a Riemann-Roch type

arXiv:1604.00284v2
fatcat:qgrwe3stxvbkzapgj6mkg7p7w4
*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. ...##
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Dilatation structures I. Fundamentals
[article]

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. ...

##
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Dilatation structures I. Fundamentals

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. ...

##
###
Dilatation structures I. Fundamentals

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. ...

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

2013
*
arXiv
*
pre-print

Once we can accomodate quiver-

arXiv:1212.5398v2
fatcat:owk4wvddwbhl5maxim4cgdbgby
*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*...
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