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Journal Article

  1. [GIRA-21a]“Dual Hyperquaternion Poincaré Groups”, Advances in Applied Clifford Algebras, vol. 31, 2021.PDF icon Girard2020 AACA Dual Hyperquaternion Poincare Groups.pdf (319.43 KB)
  2. [GIRA-21b]“Hyperquaternion Conformal Groups”, Advances in Applied Clifford Algebras, 2021.PDF icon Girard2021 AACA Dual Hyperquaternion Conformal Groups_revised.pdf (449.89 KB)
  3. [GIRA-18]“Hyperquaternions: a New Tool for Physics”, Advances in Applied Clifford Algebras, vol. 28, 2018.PDF icon Girard2018 AACA Hyperquaternions new tool for physics (Research Gate).pdf (226.29 KB)
  4. [WANG-15a]“Analytic signal phase-based myocardial motion estimation in tagged MRI sequences by a bilinear model and motion compensation”, Medical Image Analysis, vol. 24, pp. 149-162, 2015.
  5. [MARI-10a]A. Marion, P. R. Girard, and Vray, D., “Quaternionic spatiotemporal filtering for dense motion field estimation in ultrasound imaging”, Eurasip JASP, vol. 2010, p. 11 pages, 2010.
  6. [GIRA-99]P. R. Girard, “Einstein's equations and Clifford Algebras”, Advances in Applied Clifford Algebras, vol. 9, pp. 225–230, 1999.

Conference Paper

  1. [GIRA-22]“Hyperquaternions and Physics”, in 34th International Colloquium on Group Theoretical Methods in Physics, Strasbourg, 18-22 July, 2022, pp. 1-8.PDF icon Girard-22_Proceedings G34.pdf (151.92 KB)
  2. [WANG-21]“3D Clifford Analytic Signal for 3D Envelope Detection on Ultrasound Volume”, in IEEE International Ultrasonics Symposium, 2021.
  3. [GIRA-19]“Hyperquaternions: An Efficient Mathematical Formalism for Geometry”, in 4th conference on Geometric Science of Information, 2019.PDF icon Girard-19 preprint GSI Hyperquaternions An Efficient Mathematical Formalism for Geometry.pdf (314.59 KB)
  4. [GIRA-17a]“Hyperquaternion Symmetry Groups”, in 11th International Conference on Clifford Algebras and Their Applications in Mathematical Physics, ICCA11, Ghent, Belgique, 2017.
  5. [GIRA-17b]“Hyperquaternions and Physics: Historical Outlook”, in 11th International Conference on Clifford Algebras and Their Applications in Mathematical Physics", ICCA11, Ghent, Belgique, 2017.
  6. [WANG-14a]L. Wang, Liu, Z., Clarysse, P., Croisille, P., P. R. Girard, Liu, W. Y., and Delachartre, P., “Myocardial Motion Estimation Using Optical Flow with Multiple Constraint Equations”, in IEEE International Conference on Signal Processing (ICSP14), HangZhou, 2014, pp. 1066-1071.PDF icon Liang-14_IEEE-ICSP_0211.pdf (1.04 MB)
  7. [GIRA-14]P. R. Girard, Clarysse, P., Pujol, R., Wang, L., and Delachartre, P., “Biquaternion Clifford Algebra and Grassmann Differential Geometry”, in 8th International Conference, Curves and Surfaces, Paris, France, 2014, pp. 216-242.
  8. [WANG-12b]L. Wang, Liu, Z., P. R. Girard, Clarysse, P., and Delachartre, P., “Extension of Analytic Signal conception on Dynamic Image Sequences”, in 9ème Manifestation des Jeunes Chercheurs en Sciences et Technologies de l’Information et de la Communication, Lille, France, 2012.
    http://hal.inria.fr/hal-00780356
  9. [WANG-12c]L. Wang, P. R. Girard, Bernard, A., Liu, Z., Clarysse, P., and Delachartre, P., “3-D biquaternionic analytic signal and application to envelope detection in 3-D ultrasound imaging”, in 3D Imaging (IC3D), 2012 International Conference on, Liège, Belgium, 2012.PDF icon 56.pdf (1.45 MB)
    http://dx.doi.org/10.1109/IC3D.2012.6615144
  10. [WANG-12a]L. Wang, P. R. Girard, Clarysse, P., and Delachartre, P., “Phase extraction of the Analytic Video Signal in Clifford Algebra”, in 5th conference on Applied Geometric Algebras in Computer Science and Engineering, La Rochelle, France, 2012.PDF icon Upload_Version -pdf CameraReady_Article_AGACSE_2012v2.2-modify21092012.pdf (561.29 KB)
    http://hal.archives-ouvertes.fr/hal-00839287
  11. [DELA-11]P. Delachartre, Clarysse, P., Goutte, R., and P. R. Girard, “Mise en œuvre du signal analytique dans les algèbres de Clifford”, in GRETSI, Bordeaux, France, 2011.
  12. [GIRA-11b]P. R. Girard, “Multiquaternion Grassmann-Hamilton-Clifford Algebras in Physics and Engineering: A Short Historical Perspective”, in 9th International Conference on Clifford Algebras and Their Applications in Mathematical Physics, Editor, K. Gürlebeck. , Weimar, Germany, 2011.
  13. [GIRA-11a]P. R. Girard, Pujol, R., Clarysse, P., Marion, A., Goutte, R., and Delachartre, P., “Analytic Video (2D+T) Signals by Clifford Fourier Transforms in Multiquaternion Grassmann-Hamilton-Clifford Algebras”, in 9th International Conference on Clifford Algebras and Their Applications in Mathematical Physics, Editor, K. Gürlebeck. , Weimar, Germany, 2011.
  14. [GIRA-10]P. R. Girard and Pujol, R., “Electromagnetic energy-momentum tensor via Noether theorem and the tetraquaternion Grassmann-Hamilton-Clifford algebra”, in Applied Geometric Algebras in Computer Science and Engineering, AGACSE 2010, Amsterdam, Netherland, 2010.
  15. [GIRA-09]P. R. Girard, “Quaternion Grassmann-Hamilton-Clifford algebras : new mathematical tools for classical and relativistic modeling”, in World Congress 2009, Medical Physics and Biomedical Engineering, Munich, Germany, 2009.
  16. [GIRA-05]P. R. Girard, “Relativistic Moving Frame and Physical Applications within Clifford Algebra”, in 7th International Conference on Clifford Algebras and Applications, Toulouse, 2005.
  17. [GIRA-02]P. R. Girard, in 6th International Conference on Clifford Algebras and Applications, Cookeville, 2002.
  18. [GIRA-01]P. R. Girard, in Applied Geometrical Algebras in Computer Science and Engineering, Cambridge University, 2001.

Book Chapter

  1. [GIRA-15]P. R. Girard, Clarysse, P., Pujol, R., Wang, L., and Delachartre, P., “Differential Geometry Revisited by Biquaternion Clifford Algebra”, in in J.-D. Boissonnat et al. (Eds), Curves and Surfaces, Springer, 2015, pp. 216-242.PDF icon Girard-15 draft ICCS Differential Geometry Revisited by Biquaternion.pdf (404.61 KB)
    http://dx.doi.org/10.1007/978-3-319-22804-4_17
  2. [GIRA-13]P. R. Girard, Pujol, R., Clarysse, P., Marion, A., Goutte, R., and Delachartre, P., “Analytic Video (2D+T) Signals by Clifford Fourier Transforms in Multiquaternion Grassmann-Hamilton-Clifford Algebras”, in Quaternion and Clifford Fourier transforms and Wavelets, TIM/Birkhauser., Springer, 2013, p. 350.
    http://www.springer.com/birkhauser/mathematics/book/978-3-0348-0602-2

Book

  1. [GIRA-07]P. R. Girard, Quaternions, Clifford Algebras and Relativistic Physics. 2007.
  2. [GIRA-04]P. R. Girard, Quaternions, algèbre de Clifford et physique relativiste. 2004.