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Affine invariant points

2015
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Israel Journal of Mathematics
*

We answer in the negative a question by Grünbaum who asked if there exists a finite basis of

doi:10.1007/s11856-015-1196-2
fatcat:i4qocivdb5grnld4qyfgzuk7ly
*affine**invariant*points. ... We give a positive answer to another question by Grünbaum about the "size" of the set of all*affine**invariant*points. ... Remark (i) provides examples of non-proper*affine**invariant*points: once there are two different*affine**invariant*points, there are*affine**invariant*points p(K) / ∈ K, i.e. nonproper*affine**invariant*points ...##
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Affine invariant points
[article]

2013
*
arXiv
*
pre-print

We answer in the negative a question by Gruenbaum who asked if there exists a finite basis of

arXiv:1301.2606v1
fatcat:7v3vrm2s5bgahnzzor63hk5fpe
*affine**invariant*points. ... Crucial to establish these results, are new*affine**invariant*points, not previously considered in the literature. ... Remark (i) provides examples of non-proper*affine**invariant*points: once there are two different*affine**invariant*points, there are*affine**invariant*points p(K) / ∈ K, i.e. nonproper*affine**invariant*points ...##
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Affine invariant triangulations
[article]

2020
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arXiv
*
pre-print

Springer, 1993] that uses the inverse of the covariance matrix of S to define an

arXiv:2011.02197v1
fatcat:e3itntpbirbetdfxygpuevnvmy
*affine**invariant*norm, denoted A_S, and an*affine**invariant*triangulation, denoted DT_A_S[S]. ... In addition, we provide different*affine**invariant*sorting methods of a point set S and of the vertices of a polygon P that can be combined with known algorithms to obtain other*affine**invariant*triangulation ...*affine**invariant*sorting methods. ...##
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Extended affinization of Invariant Affine Reflection Algebras
[article]

2011
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arXiv
*
pre-print

*Invariant*

*affine*reflection algebras are the last and the most general known extension of

*affine*Kac-Moody Lie algebras, introduced in recent years. ... , and applying the so called "loop construction", we obtain again an

*invariant*

*affine*reflection algebra. ... To be more precise, we note that the main difference of the class of

*invariant*

*affine*reflection algebras with extended

*affine*Lie algebras or locally extended

*affine*Lie algebras, is that in the latter ...

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Some Affine Invariants Revisited
[chapter]

2013
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Fields Institute Communications
*

We present several sharp inequalities for the SL(n)

doi:10.1007/978-1-4614-6406-8_16
fatcat:do7s37hkbnazrn5dlmzxc3fna4
*invariant*Ω 2,n (K) introduced in our earlier work on centro-*affine**invariants*for smooth convex bodies containing the origin. ... The technique employed prompts us to conjecture that any SL(n)*invariant*of convex bodies with continuous and positive centro-*affine*curvature function can be obtained as a limit of normalized p-*affine*... Inequalities for a second order centro-*affine**invariant*In [34] , we introduced a class of SL(n)*invariants*for smooth convex bodies in R n . ...##
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Cutting Affine Moment Invariants

2012
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Mathematical Problems in Engineering
*

The traditional

doi:10.1155/2012/928161
fatcat:fuu2yyoa4jfytk34tmirtori4i
*affine*moment*invariants*(AMIs) method is applied to the new image. Consequently, cutting*affine*moment*invariants*(CAMIs) are derived. ... The extraction of*affine**invariant*features plays an important role in many fields of image processing. ... More*affine**invariant*features, cutting*affine*moment*invariants*CAMIs , are extracted. Furthermore, we combine CAMIs with the original AMIs we call the obtained*affine**invariants*as CCAMIs . ...##
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Dual Affine invariant points
[article]

2013
*
arXiv
*
pre-print

An

arXiv:1310.0128v1
fatcat:kv7fcebpobfgva7rq4wr7iy554
*affine**invariant*point on the class of convex bodies in R^n, endowed with the Hausdorff metric, is a continuous map p which is*invariant*under one-to-one*affine*transformations A on R^n, that is, p( ... We define a product on the set of*affine**invariant*points, in relation with duality. Finally, examples are given which exhibit the rich structure of the set of*affine**invariant*points. ... Now we recall the definitions of*affine**invariant*points and of*affine**invariant*sets [3, 13] . Definition 1. ...##
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Robust Affine Invariant Descriptors

2011
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Mathematical Problems in Engineering
*

An approach is developed for the extraction of

doi:10.1155/2011/185303
fatcat:tfibvnnjf5dqravf5xsdebarae
*affine**invariant*descriptors by cutting object into slices. ... Gray values associated with every pixel in each slice are summed up to construct*affine**invariant*descriptors. As a result, these descriptors are very robust to additive noise. ...*Affine**Invariant**Affine*maps parallel lines onto parallel lines, intersecting lines into intersecting lines. ...##
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Dual Affine invariant points

2015
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Indiana University Mathematics Journal
*

An

doi:10.1512/iumj.2015.64.5514
fatcat:5i5fegbgubfmzox7kaj7rpkp5u
*affine**invariant*point on the class of convex bodies Kn in R n , endowed with the Hausdorff metric, is a continuous map from Kn to R n which is*invariant*under one-to-one*affine*transformations A on ... Now we recall the definitions of*affine**invariant*points and of*affine**invariant*sets [3, 13] . Definition 1. ... Let p be a proper*affine**invariant*point. ...##
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Some Affine Invariants Revisited
[article]

2012
*
arXiv
*
pre-print

We present several sharp inequalities for the SL(n)

arXiv:1208.0783v1
fatcat:4uabanb7qfck3exb7jsbxn6sti
*invariant*Ω_2,n(K) introduced in our earlier work on centro-*affine**invariants*for smooth convex bodies containing the origin. ... The technique employed prompts us to conjecture that any SL(n)*invariant*of convex bodies with continuous and positive centro-*affine*curvature function can be obtained as a limit of normalized p-*affine*... Inequalities for a second order centro-*affine**invariant*In [32] , we introduced a class of SL(n)*invariants*for smooth convex bodies in R n . ...##
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Affine-Invariant Midrange Statistics
[chapter]

2019
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Lecture Notes in Computer Science
*

We formulate and discuss the

doi:10.1007/978-3-030-26980-7_51
fatcat:u2gn5tfh2jb6zcg73kxs3h325u
*affine*-*invariant*matrix midrange problem on the cone of n× n positive definite Hermitian matrices ℙ(n), which is based on the Thompson metric. ...*Affine*-*invariant*Finsler metrics on P(n) Consider the family of*affine*-*invariant*metric distances d Φ on P(n) defined as d Φ (A, B) = log A −1/2 BA −1/2 Φ , (1) where • Φ is any unitarily*invariant*norm ... In Subsection 1.2, we define the*affine*-*invariant*midrange problem for a collection of N points. ...##
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Affine invariants of annuli

2012
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Annales Universitatis Mariae Curie-Sklodowska. Sectio A. Mathematica
*

*Affine*

*invariants*of annuli are introduced. 2000 Mathematics Subject Classification. 53A04. ...

*Invariants*of annuli. We note that Theorem 2.1. Let an annulus CD belongs to CΛ. ... The number c o (CD) given by the formula (2.1) c o (CD) = exp − 2π 0 |ż(t)| λ (t) dt = exp − 2π 0 R (t) λ (t) dt does not depend on parametrizations of C, D and

*affine*transformations. ...

##
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Affine Invariant Image Segmentation

2004
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Procedings of the British Machine Vision Conference 2004
*

with a set of

doi:10.5244/c.18.18
dblp:conf/bmvc/BhaleraoW04
fatcat:7po5zmqo2rh7xasdc7ckhjfw7u
*affine*transformation coefficients. ... An appropriate set of prototype blocks is determined for a given an image by clustering in a feature subspace of discrete samples from an*affine*symmetry group. ... Results based on 1 or more chosen prototypes using*affine**invariant*block based texture model. ...##
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Dual affine moment invariants
[article]

2019
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arXiv
*
pre-print

In this paper, we propose a general framework to derive moment

arXiv:1911.08233v1
fatcat:f3juqt4pqbdqhorg6oery3xwqu
*invariants*under DAT for objects in M-dimensional space with N channels, which can be called dual-*affine*moment*invariants*(DAMI). ... And*affine*transformations often occur in both shape and color space simultaneously, which can be termed as Dual-*Affine*Transformation (DAT). ...*Invariant*(M, N, P, Q, O S , O C ) is*invariant*under DAT in the M-D space with N channels, which can be called Dual-*Affine*Moment*Invariants*(DAMI(M, N)). ...##
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Affine-invariant scene categorization

2014
*
2014 IEEE International Conference on Image Processing (ICIP)
*

This paper presents a scene categorization method that is

doi:10.1109/icip.2014.7025205
dblp:conf/icip/WeiPB14
fatcat:oupimxe42ncjxhk5rja4igphei
*invariant*to*affine*transformations. ... ABSTRACT This paper presents a scene categorization method that is*invariant*to*affine*transformations. ... The existing approaches to*affine**invariance*can be divided into three categories:*invariance*by training,*invariance*by image normalization, and*invariance*by feature extraction. ...
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