Updated: May 29th, 2024 13:09

2024 journal article

Euclidean and affine curve reconstruction

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

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.

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

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}

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*.

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.

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}

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.

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).

Source: ORCID

Added: September 16, 2020

2017 article

On Two Theorems of Darboux

(2017, September 21).

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.

Contributors: ^{ n} & P. Olver ^{*}

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*.

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.

Contributors: H. Jenssen ^{*} & ^{ n}

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

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.

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.

Contributors: H. Jenssen ^{*} & ^{ n}

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

2007 conference paper

3D Face Recognition using Euclidean Integral Invariants Signature

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

Contributors: S. Feng ^{ n}, H. Krim ^{ n} & ^{ n}

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

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

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).

Contributors: S. Feng ^{ n}, ^{ 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.

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.

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.

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

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.

Event: rnational Conference on Image Processing

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 ^{*}

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

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.

Sources: Crossref, NC State University Libraries

Added: July 28, 2019

Updated: September 15th, 2020 16:26

2003 - present

2000 - 2003

Updated: September 15th, 2020 16:35

1994 - 2000

1986 - 1993

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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