Works (35)

Updated: May 29th, 2024 13:09

2024 journal article

Euclidean and affine curve reconstruction

INVOLVE, A JOURNAL OF MATHEMATICS, 17(1).

By: J. Agudelo, B. Dippold, I. Klein, A. Kokot, E. Geiger & I. Kogan

author keywords: planar curves; Euclidean and affine transformations; Euclidean and affine curvatures; curve reconstruction; Picard iterations; distances
Source: Web Of Science
Added: May 28, 2024

2023 article

Invariants: Computation and Applications

PROCEEDINGS OF THE INTERNATIONAL SYMPOSIUM ON SYMBOLIC & ALGEBRAIC COMPUTATION, ISSAC 2023, pp. 40–49.

By: I. Kogan n

author keywords: group actions; algebraic and differential invariants; moving frames; equivalence; signatures
TL;DR: This work shows how an algebraic adaptation of the moving frame method from differential geometry leads to a practical algorithm for computing a generating set of rational invariants and discusses the notion of differential invariant signature. (via Semantic Scholar)
UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: July 6, 2023

2021 journal article

Non-congruent non-degenerate curves with identical signatures

JOURNAL OF MATHEMATICAL IMAGING AND VISION, 63(5), 601–625.

By: E. Geiger n & I. Kogan n

author keywords: Closed curves; Euclidean transformations; Signature curves; Signature graphs (quivers); Object recognition
TL;DR: It is shown that while the claim by Hickman holds for simple, closed curves with simple signatures, it fails for curves with non-simple signatures, and congruence criteria for non-degenerate, closed, simple planar curves is formulated. (via Semantic Scholar)
UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: February 10, 2021

2021 article

Non-congruent non-degenerate curves with identical signatures (Feb, 1007/s10851-020-01015-x, 2021)

JOURNAL OF MATHEMATICAL IMAGING AND VISION, Vol. 63, pp. 776–776.

By: E. Geiger n & I. Kogan n

Sources: ORCID, Web Of Science, NC State University Libraries
Added: April 8, 2021

2020 journal article

A mixed boundary value problem for u(xy) = f (x , y, u, u(x), u(y))

JOURNAL OF DIFFERENTIAL EQUATIONS, 268(12), 7535–7560.

By: H. Jenssen* & I. Kogan n

Contributors: H. Jenssen* & I. Kogan n

author keywords: Second order hyperbolic partial differential equations; Mixed problems; Non-uniqueness
Sources: Web Of Science, NC State University Libraries, ORCID
Added: April 6, 2020

2020 journal article

Differential Signatures of Algebraic Curves

SIAM Journal on Applied Algebra and Geometry.

By: I. Kogan*, M. Ruddy & C. Vinzant

author keywords: algebraic curves; projective action; affine action; Euclidean action; equivalence classes of curves; differential invariants; classifying invariants; signatures; Fermat curves
TL;DR: The differential signature construction is adapted to the equivalence problem for complex plane algebraic curves under the actions of the projective group and its subgroups and it is proved that for any $G$-action, there exists a pair of rational differential invariants, called classifying invariant, that can be used to construct signatures. (via Semantic Scholar)
UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Source: ORCID
Added: March 11, 2020

2019 journal article

Jacobians with prescribed eigenvectors

Differential Geometry and Its Applications, 65, 108–146.

By: M. Benfield, H. Jenssen* & I. Kogan n

Contributors: M. Benfield, H. Jenssen* & I. Kogan n

Sources: Web Of Science, Crossref, NC State University Libraries, ORCID
Added: July 1, 2019

2018 journal article

A Generalization of an Integrability Theorem of Darboux

The Journal of Geometric Analysis, 29(4), 3470–3493.

By: M. Benfield, H. Jenssen* & I. Kogan n

Contributors: M. Benfield, H. Jenssen* & I. Kogan n

author keywords: Overdetermined systems of PDEs; Integrability theorems; Systems of first order PDEs; Local existence; Picard iteration
Sources: ORCID, Crossref, NC State University Libraries
Added: July 20, 2019

2017 journal article

Algorithm for computing mu-bases of univariate polynomials

JOURNAL OF SYMBOLIC COMPUTATION, 80, 844–874.

By: H. Hong n, Z. Hough n & I. Kogan n

Contributors: H. Hong n, Z. Hough n & I. Kogan n

author keywords: mu-basis; Syzygy module; Polynomial vectors; Rational curves
TL;DR: A new algorithm for computing a $\mu$-basis of the syzygy module of $n$ polynomials in one variable over an arbitrary field $\mathbb{K}$, based on standard linear algebra and completely self-contained is presented. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: August 6, 2018

2017 article

Degree-optimal moving frames for rational curves

(2017, March 8).

Irina Kogan

Source: ORCID
Added: September 16, 2020

2017 article

On Two Theorems of Darboux

(2017, September 21).

Irina Kogan

Source: ORCID
Added: September 16, 2020

2015 journal article

Invariants of objects and their images under surjective maps

Lobachevskii Journal of Mathematics, 36(3), 260–285.

By: I. Kogan n & P. Olver*

Contributors: I. Kogan n & P. Olver*

author keywords: invariant; surjective map; curve; centro-affine; affine; projective actions; image processing
UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Sources: Crossref, NC State University Libraries, ORCID
Added: July 20, 2019

2013 journal article

Object-Image Correspondence for Algebraic Curves under Projections

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 9.

By: J. Burdis*, I. Kogan n & H. Hong n

Contributors: J. Burdis*, I. Kogan n & H. Hong n

author keywords: central and parallel projections; finite and affine cameras; camera decomposition; curves; classifying differential invariants; projective and affine transformations; signatures; machine vision
UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: August 6, 2018

2012 journal article

Extensions for Systems of Conservation Laws

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 37(6), 1096–1140.

By: H. Jenssen* & I. Kogan n

Contributors: H. Jenssen* & I. Kogan n

author keywords: Eigenvector fields; Entropies; Extensions; Frame bundles; Hessian metric; Hyperbolic systems of conservation laws; Integrability; Rich systems
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: August 6, 2018

2012 conference paper

Object-image correspondence for curves under central and parallel projections

Proceedings of the 2012 symposuim on Computational Geometry - SoCG '12, 373–382.

By: J. Burdis n & I. Kogan n

Contributors: J. Burdis n & I. Kogan n

Event: the 2012 symposuim

TL;DR: A novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters, based on projection criteria that reduce the projection problem to a certain modification of the equivalence problem of planar curves under affine and projective transformations. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries, ORCID
Added: July 20, 2019

2010 journal article

Classification of Curves in 2D and 3D via Affine Integral Signatures

ACTA APPLICANDAE MATHEMATICAE, 109(3), 903–937.

By: S. Feng n, I. Kogan n & H. Krim n

Contributors: S. Feng n, I. Kogan n & H. Krim n

author keywords: Euclidean and affine transformations; Equivalence problem for curves; Integral invariants; Signatures; Image recognition
TL;DR: New robust classification algorithms for planar and spatial curves subjected to affine transformations based on integral invariants, which are significantly less sensitive to small perturbations of curves and noise than classically known differential invariants. (via Semantic Scholar)
UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: August 6, 2018

2010 journal article

SYSTEMS OF HYPERBOLIC CONSERVATION LAWS WITH PRESCRIBED EIGENCURVES

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 7(2), 211–254.

By: H. Jenssen* & I. Kogan n

Contributors: H. Jenssen* & I. Kogan n

author keywords: Hyperbolic systems of conservation laws; eigenvector fields; eigenvalues; rich systems; Frobenius, Darboux and Cartan-Kahler integrability theorems; connections on frame bundles
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: August 6, 2018

2009 other

Construction of conservative systems

By: H. Jenssen & I. Kogan*

Sources: Crossref, NC State University Libraries
Added: July 20, 2019

2007 conference paper

3D Face Recognition using Euclidean Integral Invariants Signature

2007 IEEE/SP 14th Workshop on Statistical Signal Processing, 156–160.

By: S. Feng n, H. Krim n & I. Kogan n

Contributors: S. Feng n, H. Krim n & I. Kogan n

Event: 2007 IEEE/SP 14th Workshop on Statistical Signal Processing

TL;DR: A novel 3D face representation and recognition approach based on comparing face feature in the invariant signature space is proposed and Substantiating examples are provided with an achieved classification accuracy of 95% for faces with various poses and facial expressions. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries, ORCID
Added: July 20, 2019

2007 conference paper

3D Mixed Invariant and its Application on Object Classification

2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07, 1.

By: S. Feng n, D. Aouada n, H. Krim n & I. Kogan n

Contributors: S. Feng n, D. Aouada n, H. Krim n & I. Kogan n

Event: 2007 IEEE International Conference on Acoustics, Speech, and Signal Processing

TL;DR: A new integro-differential invariant for curves in 3D transformed by affine group action is presented, and therefore this invariant is significantly less sensitive to noise than classical affine differential invariants. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, NC State University Libraries, ORCID
Added: July 20, 2019

2007 conference paper

College geometry students' uses of technology in the process of constructing arguments

In T. Lamberg (Ed.), Proceedings of the 29th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. (pp. 1153–1160).

By: R. Smith, K. Hollebrands, K. Iwancio & I. Kogan

Ed(s): T. Lamberg

Source: NC State University Libraries
Added: July 28, 2019

2007 conference paper

Integral invariants for 3D curves: an inductive approach

In C. W. Chen, D. Schonfeld, & J. Luo (Eds.), Visual Communications and Image Processing 2007 (Vol. 6508).

By: S. Feng n, I. Kogan n & H. Krim n

Contributors: S. Feng n, I. Kogan n & H. Krim n

Ed(s): C. Chen, D. Schonfeld & J. Luo

Event: Electronic Imaging 2007

author keywords: 3D affine and Euclidean transformations; integral affine invariants; moving frames; object classification
TL;DR: This paper obtains explicit formulae for integral invariants for curves in 3D with respect to the special and the full affine groups using an inductive approach and uses Euclidean integral invariant values to build the affine invariants. (via Semantic Scholar)
UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Sources: Crossref, NC State University Libraries, ORCID
Added: July 20, 2019

2007 article

Rational invariants of a group action. Construction and rewriting

JOURNAL OF SYMBOLIC COMPUTATION, Vol. 42, pp. 203–217.

By: E. Hubert* & I. Kogan n

Contributors: E. Hubert* & I. Kogan n

author keywords: rational invariants; algebraic group actions; cross-section; Grobner basis; differential invariants; moving frame
TL;DR: A new algorithm for computing rational invariants that allows any rational invariant to be expressed in terms of the generators of a finite generating set of invariants as the coefficients of a reduced Grobner basis. (via Semantic Scholar)
UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: August 6, 2018

2007 journal article

Smooth and algebraic invariants of a group action. Local and global constructions.

Foundations of Computational Math., 7(4), 345–383.

By: E. Hubert & I. Kogan

Source: NC State University Libraries
Added: July 28, 2019

2007 journal article

Smooth and algebraic invariants of a group action: Local and global constructions

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 7(4), 455–493.

By: E. Hubert* & I. Kogan n

Contributors: E. Hubert* & I. Kogan n

author keywords: rational and algebraic invariants; smooth and differential invariants; algebraic and Lie group actions; cross-section; moving frame method; Grobner basis
TL;DR: An algebraic formulation of the moving frame method for constructing local smooth invariants on a manifold under an action of a Lie group is provided, which gives rise to algorithms for constructing rational and replacement invariants. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: August 6, 2018

2007 conference paper

The effects of a dynamic program for geometry on college students' understandings of properties of quadrilaterals in the Poincare Disk model

Proceedings of the 9th International Conference on Mathematics Education in a Global Community, 613–618.

By: R. Smith, K. Hollebrands, K. Iwancio & I. Kogan

Source: NC State University Libraries
Added: July 10, 2019

2005 conference paper

3D object representation with topo-geometric shape models

Proceedings of European Signal Processing Conference (EUSIPCO), 2386–2389. http://www.scopus.com/inward/record.url?eid=2-s2.0-84863687976&partnerID=MN8TOARS

By: S. Baloch, H. Krim, I. Kogan & D. Zenkov

Contributors: S. Baloch, H. Krim, I. Kogan & D. Zenkov

Sources: NC State University Libraries, ORCID
Added: July 10, 2019

2005 conference paper

Rotation invariant topology coding of 2D and 3D objects using Morse theory

IEEE International Conference on Image Processing 2005, 3, 796–799.

By: S. Baloch n, H. Krim n, I. Kogan* & D. Zenkov

Contributors: S. Balocht, H. Krim n, I. Kogan* & D. Zenkov

Event: rnational Conference on Image Processing

TL;DR: A numerical algorithm based on capturing the topology of a modified Reeb graph by tracking the critical points of a distance function, which employs Morse theory in the study of translation, rotation, and scale invariant skeletal graphs. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019

2003 journal article

Invariant Euler-Lagrange equations and the invariant variational bicomplex

Acta Applicandae Mathematicae, 76(2), 137–193.

By: I. Kogan* & P. Olver*

Contributors: I. Kogan* & P. Olver*

author keywords: calculus of variations; Lie group; moving frame; differential invariant; Euler-Lagrange equation; variational bicomplex
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
Sources: ORCID, NC State University Libraries, NC State University Libraries
Added: July 28, 2019

2003 journal article

Two Algorithms for a Moving Frame Construction

Canadian Journal of Mathematics, 55(2), 266–291.

By: I. Kogan*

Contributors: I. Kogan*

UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
Sources: Crossref, NC State University Libraries, ORCID
Added: July 20, 2019

2002 conference paper

Computation of canonical forms for ternary cubics

Proceedings of the 2002 international symposium on Symbolic and algebraic computation - ISSAC '02, 151–160.

By: I. Kogan* & M. Maza*

Contributors: I. Kogan* & M. Maza*

Event: the 2002 international symposium

TL;DR: A computationally efficient algorithm is provided that matches an arbitrary ternary cubic with its canonical form and explicitly computes a corresponding linear change of coordinates. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries, ORCID
Added: July 28, 2019

2001 other

Inductive construction of moving frames

By: I. Kogan*

Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2001 other

The invariant variational bicomplex

By: I. Kogan* & P. Olver

Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2000 thesis

Inductive approach to Cartan's moving frame method with applications to classical invariant theory

https://www-proquest-com.prox.lib.ncsu.edu/docview/304612470/fulltextPDF/23BAF25E0A874972PQ/8?accountid=12725

Irina Kogan

Source: ORCID
Added: September 15, 2020

2000 journal article

Symmetries of Polynomials

Journal of Symbolic Computation, 29(4-5), 485–514.

By: I. Berchenko* & P. Olver*

TL;DR: New algorithms for determining discrete and continuous symmetries of polynomials — also known as binary forms in classical invariant theory — are presented, and implemented in Maple based on a new, comprehensive theory of moving frames that completely characterizes the equivalence and symmetry properties of submanifolds under general Lie group actions. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

Employment

Updated: September 15th, 2020 16:26

2003 - present

North Carolina State University Raleigh, North Carolina, US
Professor Mathematics

2000 - 2003

Yale University New Haven, Connecticut, US
Gibbs Instructor Mathematics

Education

Updated: September 15th, 2020 16:35

1994 - 2000

University of Minnesota Minneapolis, Minnesota, US
Ph.D. Mathematics

1986 - 1993

Gubkin Russian State University of Oil and Gas Moscow, RU
diploma (equivalent of MS) Applied Mathematics

Funding History

Funding history based on the linked ORCID record. Updated: September 15th, 2020 14:29

grant September 1, 2013 - August 31, 2017
AF: Small: Quantifier elimination by group analysis
Directorate for Computer & Information Science & Engineering
grant July 1, 2013 - June 30, 2017
Collaborative Research: Fundamental challenges in nonlinear hyperbolic PDEs
Directorate for Mathematical & Physical Sciences
grant September 15, 2007 - August 31, 2010
Symbolic Group-Invariant Computation
Directorate for Computer & Information Science & Engineering
grant September 15, 2007 - August 31, 2015
Noyce Mathematics Education Teaching Scholars at NC State University
Directorate for Education & Human Resources
grant September 15, 2005 - August 31, 2009
Scientific Computing Research Environments for the Mathematical Sciences (SCREMS): Parallel Computer Algebra
Directorate for Mathematical & Physical Sciences

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