Works (35)
Updated: June 3rd, 2024 08:14
2024 journal article
Euclidean and affine curve reconstruction
INVOLVE, A JOURNAL OF MATHEMATICS, 17(1).
author keywords: planar curves; Euclidean and affine transformations; Euclidean and affine curvatures; curve reconstruction; Picard iterations; distances
open access via arxiv.org (repository)
Sources: Web Of Science, NC State University Libraries
Added: May 28, 2024
2023 article
Invariants: Computation and Applications
PROCEEDINGS OF THE INTERNATIONAL SYMPOSIUM ON SYMBOLIC & ALGEBRAIC COMPUTATION, ISSAC 2023, pp. 40–49.
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.
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.
UN Sustainable Development Goal Categories
14. Life Below Water
(Web of Science)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: April 8, 2021
2020 journal article
Differential Signatures of Algebraic Curves
SIAM Journal on Applied Algebra and Geometry.
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
A mixed boundary value problem for u(xy) = f (x , y, u, u(x), u(y))
JOURNAL OF DIFFERENTIAL EQUATIONS, 268(12), 7535–7560.
Contributors: H. Jenssen* & 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
2019 journal article
Jacobians with prescribed eigenvectors
Differential Geometry and Its Applications, 65, 108–146.
Contributors: M. Benfield, H. Jenssen* & 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.
Contributors: M. Benfield, H. Jenssen * & 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 article
Degree-optimal moving frames for rational curves
(2017, March 8).
Source: ORCID
Added: September 16, 2020
2017 article
On Two Theorems of Darboux
(2017, September 21).
Source: ORCID
Added: September 16, 2020
2016 journal article
Algorithm for computing mu-bases of univariate polynomials
JOURNAL OF SYMBOLIC COMPUTATION, 80, 844–874.
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
2015 journal article
Invariants of objects and their images under surjective maps
Lobachevskii Journal of Mathematics, 36(3), 260–285.
Contributors: 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.
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.
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.
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
SYSTEMS OF HYPERBOLIC CONSERVATION LAWS WITH PRESCRIBED EIGENCURVES
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 7(2), 211–254.
Contributors: H. Jenssen * & 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
Sources: Crossref, NC State University Libraries
Added: July 20, 2019
2008 journal article
Classification of Curves in 2D and 3D via Affine Integral Signatures
ACTA APPLICANDAE MATHEMATICAE, 109(3), 903–937.
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
2007 conference paper
3D Face Recognition using Euclidean Integral Invariants Signature
2007 IEEE/SP 14th Workshop on Statistical Signal Processing, 156–160.
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.
Contributors: S. Feng n, D. Aouada n, H. Krim n & 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).
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).
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 journal article
Smooth and algebraic invariants of a group action. Local and global constructions.
Foundations of Computational Math., 7(4), 345–383.
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.
Contributors: E. Hubert * & 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)
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 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.
Source: NC State University Libraries
Added: July 10, 2019
2006 article
Rational invariants of a group action. Construction and rewriting
JOURNAL OF SYMBOLIC COMPUTATION, Vol. 42, pp. 203–217.
Contributors: E. Hubert * & 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
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
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.
Contributors: S. Balocht, H. Krim n, * & 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.
Contributors: * & 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.
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.
Contributors: * & 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
Sources: Crossref, NC State University Libraries
Added: July 28, 2019
2001 other
The invariant variational bicomplex
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
Source: ORCID
Added: September 15, 2020
2000 journal article
Symmetries of Polynomials
Journal of Symbolic Computation, 29(4-5), 485–514.
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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