math

Software (mostly free software) useful to researchers and teachers in maths
Higher Edu - Research dev card
Development from the higher education and research community
  • Creation or important update: 23/09/13
  • Minor correction: 23/09/13

gpu-openings : linear opening for GPU/CUDA

This software was developed (or is under development) within the higher education and research community. Its stability can vary (see fields below) and its working state is not guaranteed.
  • Web site
  • System:
  • Current version: 1.0 - janvier 2013
  • License(s): GPL
  • Status: stable release
  • Support: maintained, ongoing development
  • Designer(s): Pavel Karas, Thierry Grandpierre, Eva Dokladalova, Petr Dokladal
  • Contact designer(s): xkaras1@fi.muni.cz, thierry.grandpierre@esiee.fr, eva.dokladalova@esiee.fr, petr.dokladal@mines-paristech.fr
  • Laboratory, service:

 

General software features

This software implements a fast computing method for openings/closings by large linear morphological structuring element with an arbitrary angle. This method can be adapted to fast granulometry computations on the GPU and CPU. The results are obtained in stream with a single pass over the image, with a minimum of memory used. It is particularly suited to images of high resolution (HD).

Context in which the software is used

This software was used to obtain and validate the results published in the article [1].

Publications related to the software

[1] GPU Implementation of Linear Morphological Openings with Arbitrary Angle, Karas P., Morard V., Bartovsky J., Grandpierre T., Dokladalova E., Matula P., Dokládal P. Journal of Real-Time Image Processing In press, - (2012) - [hal-00680904 - version 1]

Higher Edu - Research dev card
Development from the higher education and research community
  • Creation or important update: 22/09/13
  • Minor correction: 22/09/13

K-VLD : virtual line descriptor and semi-local graph matching method

This software was developed (or is under development) within the higher education and research community. Its stability can vary (see fields below) and its working state is not guaranteed.
  • Web site
  • System:
  • Current version: 20130502 - 02/05/2013
  • License(s): BSD
  • Status: stable release
  • Support: maintained, no ongoing development
  • Designer(s): Zhe Liu
  • Contact designer(s): zhe.liu @ enpc.fr
  • Laboratory, service:

 

General software features

From matching interest points between two images, the algorithm finds a set of reliable correspondences using coherency. Virtual straight lines joining interest points in the same image are encoded by a descriptor invariant w.r.t. certain geometric and photometric deformations. This descriptor should be found in virtual lines between corresponding points in another image for ensuring the coherency of both correspondences.

The algorithm is used as a discrimination step between true/false correspondences in the process of rigid or deformable registration and of stereo reconstruction.

Context in which the software is used

Illustration of a research article.

Publications related to the software

Zhe Liu, Renaud MarletVirtual Line Descriptor and Semi-Local Matching Method for Reliable Feature Correspondence.
In 23rd British Machine Vision Conference (BMVC 2012), Surrey, England, September 2012.

Higher Edu - Research dev card
Development from the higher education and research community
  • Creation or important update: 22/09/13
  • Minor correction: 22/09/13

Imagine++ : C++ libraries for teaching, image processing and numerical computation

This software was developed (or is under development) within the higher education and research community. Its stability can vary (see fields below) and its working state is not guaranteed.
  • Web site
  • System:
  • Current version: 4.0.1 - Septembre 2012
  • License(s): not yet chosen
  • Status: stable release, under development
  • Support: maintained, ongoing development
  • Designer(s): R. Keriven, P. Monasse
  • Contact designer(s): monasse @ imagine.enpc.fr
  • Laboratory, service:

 

General software features

4 libraries are proposed:

  • Common: multi-dimensional arrays with shared memory for fast copy, static size vector and matrices.
  • LinAlg: linear algebra with dynamic size vectors and matrices, solution of linear systems, matrix decompositions (SVD, QR, Cholesky).
  • Graphics: windows with tabs, 2D graphics (elementary shapes, bitmaps) and 3D graphics (elementary volumes, triangulated meshes), animations, mouse and keyboard events.
  • Images: input/output in standard formats, geometric transformations, interpolation, standard filters.
Context in which the software is used

The focus is put on easy usage and efficiency. Display relies on Qt and OpenGL, linear algebra on Eigen.

  • Teaching programming: allows writing easily recreational software, with protection from classical errors that are critical for performance by using shallow copy for images and matrices.
  • Research in image processing and computer vision: additional modules for optimization, multi-view geometry and interest point dectection are used internally.
Publications related to the software
Higher Edu - Research dev card
Development from the higher education and research community
  • Creation or important update: 22/09/13
  • Minor correction: 22/09/13

OrsaHomography : automatic homographic registration of images

This software was developed (or is under development) within the higher education and research community. Its stability can vary (see fields below) and its working state is not guaranteed.
  • Web site
  • System:
  • Current version: 20130522 - 22/05/2013
  • License(s): LGPL
  • Status: stable release
  • Support: maintained, no ongoing development
  • Designer(s): Pierre Moulon, Pascal Monasse
  • Contact designer(s): pmo @ mikrosimage.eu
  • Laboratory, service:

 

General software features

This software registers two images by homography. This registration is meaningful in the two following situations:

  • no motion of optical center (only rotation and focal change), or
  • the observed scene is planar (painting, poster, aerial photo from high altitude...)

The software detects SIFT matching candidate points, then it sorts correct and outlier correspondences thanks to a variant of the robust estimation algorithm RANSAC. This variant uses the a contrario framework to estimate automatically the discrimination threshold.

As output, the user gets a list of matching interest points, the homography matrix, registered images, and a panorama built from the registered images by transparency.

Context in which the software is used

This software illustrates the algorithm ORSA, also known as AC-RANSAC, applied to the case of homography estimation.

Publications related to the software

Automatic Homographic Registration of a Pair of Images, with A Contrario Elimination of Outliers
Lionel Moisan, Pierre Moulon, Pascal Monasse
Image Processing On Line (IPOL), 2012.
http://dx.doi.org/10.5201/ipol.2012.mmm-oh

Higher Edu - Research dev card
Development from the higher education and research community
  • Creation or important update: 11/09/13
  • Minor correction: 11/09/13

Signal separation : generation and separation of digital signals

This software was developed (or is under development) within the higher education and research community. Its stability can vary (see fields below) and its working state is not guaranteed.
  • System:
  • Current version: 2012
  • License(s): Proprietary licence
  • Status: internal use
  • Support: not maintained, no ongoing development
  • Designer(s): Elena Florian, Antoine Chevreuil, Philippe Loubaton.
  • Contact designer(s): Philippe.Loubaton @ univ-mlv.fr
  • Laboratory, service:

 

General software features

This sofware generates various kinds of signals produced by standard digital communication systems, and simulates their propagation into a multi-channel multi-paths propagation channel. A number of blind source separation algorithms are also implemented.

Context in which the software is used

This software has been released for the industrial contract Aintercom, this software is not distributed otherwise.

Publications related to the software
  • Elena Florian, Antoine Chevreuil, Philippe Loubaton. Blind source separation of convolutive mixtures of non circular linearly modulated signals with unknown baud rates. Signal Processing, 2012, 92, pp. 715-726.

  • P. Jallon, Antoine Chevreuil, Philippe Loubaton. Separation of digital communication mixtures with the CMA: case of various unknown baud rates. Signal Processing, 2010, 90 (9), pp. 2633-2647.

Higher Edu - Research dev card
Development from the higher education and research community
  • Creation or important update: 08/09/13
  • Minor correction: 08/09/13

IntegerVectorsModPermutationGroup : enumeration up to the action of a permutation group

This software was developed (or is under development) within the higher education and research community. Its stability can vary (see fields below) and its working state is not guaranteed.
  • Web site
  • System:
  • License(s): GPL
  • Status: stable release
  • Support: maintained, ongoing development
  • Designer(s): Nicolas Borie
  • Contact designer(s): nicolas.borie@univ-mlv.fr
  • Laboratory, service:

 

General software features

IntegerVectorsModPermutationGroup is an enumeration engine of integer vectors up to the action of a permutation group.

Let n a positif integer and G a permutation group, subgroup of the symmetric group of order n. This Sage module IntegerVectorsModPermutationGroup allows to enumerate tuples of length n modulo the action by position of G. This problem generalizes the enumeration of unlabelled graphs up to an isomorphism. One can also add some constraints like the sum of the entries or their maximum size.

This module is completly integrated in Sage since the version 4.7.

Exemple

Exemple for the cyclic group over 4 elements:

sage: G = PermutationGroup([[(1,2,3,4)]]); G
Permutation Group with generators [(1,2,3,4)]
sage: G.cardinality()
4
sage: S = IntegerVectorsModPermutationGroup(G); S
Integer vectors of length 4 enumerated up to the action of Permutation Group with generators [(1,2,3,4)]
sage: S.cardinality()
+Infinity
sage: it = iter(S)
sage: for i in range(25): v = it.next(); print v, " : ", S.orbit(v)
....:
[0, 0, 0, 0]  :  set([[0, 0, 0, 0]])
[1, 0, 0, 0]  :  set([[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]])
[2, 0, 0, 0]  :  set([[2, 0, 0, 0], [0, 0, 2, 0], [0, 0, 0, 2], [0, 2, 0, 0]])
[1, 1, 0, 0]  :  set([[1, 0, 0, 1], [0, 0, 1, 1], [1, 1, 0, 0], [0, 1, 1, 0]])
[1, 0, 1, 0]  :  set([[0, 1, 0, 1], [1, 0, 1, 0]])
[3, 0, 0, 0]  :  set([[0, 0, 3, 0], [0, 3, 0, 0], [3, 0, 0, 0], [0, 0, 0, 3]])
[2, 1, 0, 0]  :  set([[0, 2, 1, 0], [0, 0, 2, 1], [1, 0, 0, 2], [2, 1, 0, 0]])
[2, 0, 1, 0]  :  set([[0, 1, 0, 2], [0, 2, 0, 1], [1, 0, 2, 0], [2, 0, 1, 0]])
[2, 0, 0, 1]  :  set([[2, 0, 0, 1], [0, 1, 2, 0], [1, 2, 0, 0], [0, 0, 1, 2]])
[1, 1, 1, 0]  :  set([[1, 1, 1, 0], [1, 1, 0, 1], [1, 0, 1, 1], [0, 1, 1, 1]])
[4, 0, 0, 0]  :  set([[4, 0, 0, 0], [0, 4, 0, 0], [0, 0, 4, 0], [0, 0, 0, 4]])
[3, 1, 0, 0]  :  set([[0, 0, 3, 1], [1, 0, 0, 3], [0, 3, 1, 0], [3, 1, 0, 0]])
[3, 0, 1, 0]  :  set([[0, 3, 0, 1], [0, 1, 0, 3], [3, 0, 1, 0], [1, 0, 3, 0]])
[3, 0, 0, 1]  :  set([[0, 0, 1, 3], [3, 0, 0, 1], [0, 1, 3, 0], [1, 3, 0, 0]])
[2, 2, 0, 0]  :  set([[0, 2, 2, 0], [2, 2, 0, 0], [2, 0, 0, 2], [0, 0, 2, 2]])
[2, 1, 1, 0]  :  set([[2, 1, 1, 0], [1, 0, 2, 1], [1, 1, 0, 2], [0, 2, 1, 1]])
[2, 1, 0, 1]  :  set([[0, 1, 2, 1], [1, 0, 1, 2], [2, 1, 0, 1], [1, 2, 1, 0]])
[2, 0, 2, 0]  :  set([[2, 0, 2, 0], [0, 2, 0, 2]])
[2, 0, 1, 1]  :  set([[1, 2, 0, 1], [2, 0, 1, 1], [0, 1, 1, 2], [1, 1, 2, 0]])
[1, 1, 1, 1]  :  set([[1, 1, 1, 1]])
[5, 0, 0, 0]  :  set([[0, 0, 0, 5], [5, 0, 0, 0], [0, 5, 0, 0], [0, 0, 5, 0]])
[4, 1, 0, 0]  :  set([[0, 0, 4, 1], [1, 0, 0, 4], [0, 4, 1, 0], [4, 1, 0, 0]])
[4, 0, 1, 0]  :  set([[0, 4, 0, 1], [1, 0, 4, 0], [0, 1, 0, 4], [4, 0, 1, 0]])
[4, 0, 0, 1]  :  set([[4, 0, 0, 1], [1, 4, 0, 0], [0, 0, 1, 4], [0, 1, 4, 0]])
[3, 2, 0, 0]  :  set([[3, 2, 0, 0], [0, 0, 3, 2], [2, 0, 0, 3], [0, 3, 2, 0]])

Context in which the software is used

The development of a such engine was necessary for the thesis work of the author. The thesis is about effective invariant theory. This module is also usefull in the following fields:

  • Effective invariant theory,
  • Effective Galois theory,
  • Structure Species theory.
Publications related to the software
Higher Edu - Research dev card
Development from the higher education and research community
  • Creation or important update: 17/05/13
  • Minor correction: 17/07/13

LSMM : Majorize-Minimize LineSearch for logarithmic barrier function optimization

This software was developed (or is under development) within the higher education and research community. Its stability can vary (see fields below) and its working state is not guaranteed.
  • Web site
  • System:
  • Current version: 1.0 - mars 2013
  • License(s): CeCILL-B
  • Status: stable release
  • Support: maintained, no ongoing development
  • Designer(s): Emilie Chouzenoux (LIGM), Saïd Moussaoui (IRCCyN)
  • Contact designer(s): emilie.chouzenoux @ univ-mlv.fr
  • Laboratory, service:

 

General software features

This toolbox allows to determine a suitable stepsize in iterative descent algorithms applied to the minimization of a criterion containing a logarithmic barrier function associated to linear constraints. A Majorization-Minimization (MM) scheme is adopted. It is based on the derivation of a log-quadratic majorant function well suited to approximate the criterion containing barrier terms. The convergence of classical descent algorithms when this linesearch strategy is employed is ensured.

A demo file illustrates the efficiency of the MM linesearch on the Newton minimization of the barrier criterion associated to a random quadratic programming (QP) test problem.

Context in which the software is used

Linearly constrained optimization.

Publications related to the software
  • E. Chouzenoux, S. Moussaoui and J. Idier. "Majorize-Minimize Linesearch for Inversion Methods Involving Barrier Function Optimization." Inverse Problems, Vol. 28, No. 6, 2012.

  • E. Chouzenoux, S. Moussaoui and J. Idier. "Efficiency of Line Search Strategies in Interior Point Methods for Linearly Constrained Optimization." In Proceedings of the IEEE Workshop on Statistical Signal Processing (SSP 2011), pages 101-104, Nice, France, 28-30 juin 2011.

  • E. Chouzenoux, S. Moussaoui and J. Idier. "A Majorize-Minimize Line Search Algorithm for Barrier Function Optimization." In Proceedings of the 17th European Signal Processing Conference (EUSIPCO 2009), pages 1379-1383, Glasgow, UK, 24-28 août 2009. EURASIP Press.

Higher Edu - Research dev card
Development from the higher education and research community
  • Creation or important update: 06/05/13
  • Minor correction: 06/05/13

RestoVMFB_Lab : Matlab toolbox for image restauration with the Variable Metric Forward-Backward algorithm

This software was developed (or is under development) within the higher education and research community. Its stability can vary (see fields below) and its working state is not guaranteed.
  • Web site
  • System:
  • Current version: 1.0 - avril 2013
  • License(s): CeCILL-B
  • Status: stable release
  • Support: maintained, no ongoing development
  • Designer(s): Audrey Repetti (LIGM), Emilie Chouzenoux (LIGM)
  • Contact designer(s): audrey.repetti @ univ-mlv.fr
  • Laboratory, service:

 

General software features

This Matlab toolbox allows to restore an image degraded by a linear operator and Gaussian Dependant noise with variance depending linearly on the image. The considered criterion is composed with the neg-log-likelihood of the noise distribution as data fidelity term, the indicator function allowing to constraint the dynamic range and the isotropic total variation favorizing piecewise constant images.

The restoration process uses the Majorize-Minimize Variable Metric Forward-Backward Algorithm.

Context in which the software is used

Image restauration

Publications related to the software

E. Chouzenoux, J.-C. Pesquet and A. Repetti. "Variable Metric Forward-Backward Algorithm for Minimizing the Sum of a Differentiable Function and a Convex Function" Submitted, 2013. Available online at http://www.optimization-online.org/DB_FILE/2013/01...

Higher Edu - Research dev card
Development from the higher education and research community
  • Creation or important update: 18/04/13
  • Minor correction: 18/04/13

PST-Cox : PSTricks library for drawing 2D-projections of regular complex polytopes

This software was developed (or is under development) within the higher education and research community. Its stability can vary (see fields below) and its working state is not guaranteed.
  • Web site
  • System:
  • Current version: 1.0 - février 2008
  • License(s): LGPL
  • Status: stable release
  • Support: maintained, no ongoing development
  • Designer(s): Jean-Gabriel Luque
  • Contact designer(s): Jean-Gabriel.Luque@univ-mlv.fr
  • Laboratory, service:

 

General software features

PST-Cox is a library of LaTeX macros allowing to draw 2D-projections of regular complex polytopes. Regular complex polytopes are hyperplane arrangements satisfying certain constraints, and whose automorphism graphs are generated by pseudo-reflections (complex reflections). These objects generalize the classical Platonic solids.

Context in which the software is used

This software is used to illustrate research results (see references).

Publications related to the software
  • Briand, J.-G. Luque, J.-Y. Thibon, and F. Verstraete. The moduli space of three qutrit states. Journal of Mathematical Physics. Vol. 45. 2004. pp. 4855-4867.
  • J.-G. Luque. Invariants des hypermatrices. Habilitation à diriger des recherches. I.G.M., Université de Marne-la-Vallée. 2007.
Higher Edu - Research dev card
Development from the higher education and research community
  • Creation or important update: 18/04/13
  • Minor correction: 12/09/13

Euclidean skeletons : methods for robust Euclidean skeletonization in 2D and 3D

This software was developed (or is under development) within the higher education and research community. Its stability can vary (see fields below) and its working state is not guaranteed.
  • Web site
  • System:
  • Current version: 1.0 - sept. 2010
  • License(s): CeCILL
  • Status: stable release
  • Support: maintained, ongoing development
  • Designer(s): Michel Couprie
  • Contact designer(s): coupriem @ esiee.fr
  • Laboratory, service:

 

General software features

Skeletons suffer from the lack of stability with respect to noise. This is why, in real applications, skeleton filtering is a
crucial issue. This software implements recently introduced methods for obtaining robust, filtered Euclidean skeletons in 2D and 3D discrete spaces.

Context in which the software is used

This software has been built for finding and validating the results of the related publications.

Publications related to the software

[CCT10] J. Chaussard, M. Couprie and H. Talbot: "Robust skeletonization using the discrete lambda-medial axis", Pattern Recognition Letters, Volume 32, Issue 9, 1 July 2011, Pages 1384–1394.

[SCL09] A. Vital Saúde, M. Couprie and R. Lotufo: "Discrete 2D and 3D Euclidean medial axis in higher resolution", Image and Vision Computing, Vol. 27, pp. 354--363, 2009.

[CCZ07] M. Couprie, D. Coeurjolly and R. Zrour: "Discrete bisector function and Euclidean skeleton in 2D and 3D", Image and Vision Computing, Vol. 25, pp. 1543-1556, 2007.

Other publications: http://www.esiee.fr/~coupriem/es/ES_biblio.html

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