Prof. Dr. Eduardo Bayro-Corrochano

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Research Profile

Dr. Bayro-Corrochano is a pioneer and an internationally visible scientist in geometric computing specifically in Geometric Cybernetics for applied mathematics and engineer´s applications.

The scientific profile of Dr. Bayro-Corrochano is sustained by his contributions in academics, education, basic research and engineering with an impressive diversity of works. His goal is to build intelligent machines using computational intelligence as machine learning, pattern recognition, computer vision, neuro-computing, control engineering and robotics, pioneering using the framework of Clifford geometric algebra. Since the field of intelligent machines is nourished by theory of physics, mathematics and cybernetics, he has successfully applied advanced geometric concepts of these areas in the area of computational intelligence, specifically geometric cybernetics.

He has developed the geometric MLP, Clifford Support Vector Machines, quaternion quantum neural networks and the novel quaternion spike neural networks for pattern recognition and neuro control. He is the pioneer author of the Quaternion Wavelet Transform for quaternion multiresolution analysis using the phase concept. He has developed the Quaternion Fourier Transform using space-time metric. Quaternion Fractional FFT and the Quaternion Quantum FFT for colour image processing and the novel Quaternion spike neural network for simultaneous system identification and neuro control for robots. He has developed the interpolation of geometric entities (lines, plane, circle, spheres and hyperplanes) using the motor algebra (SE(3)) and a Bessier approach in the Study manifold, this has been applied successfully in haptics and medical robotics for minimal invasive surgery of the kidney. Due to his efforts he became in 2006 an IAPR fellow “For contribution in geometric computing for perception and action systems”. 

Among his technological designs the most outstanding is his creation in 2012-17 of the Mexican humanoid "MEXONE"  unique in Latin America. In addition, between 2012-2016, in cooperation with the famous PAL firm from Barcelona, he built a second humanoid called CINVESROB of 165 cm and 28 DOF. Other products of high added value are the development of a lens to guide the blind and the construction of smart hands and feet for the disabled.


Editorial and Conference Organization 

Associate Editor :  Journal Robotica, Journal of Pattern Recognition,IEEE Transaction of Neural Networks and Learning Systems, ICRA’s conferences, IROS’s conferences ,Humanoids´s conferences  

Editor:  International Conference of Robotics and Automation (ICRA)

Editorial Board Member : Journal of Mathematical Imaging and Vision,  Journal of Theoretical And Numerical Approximation 

Conference General Chair:

  • Application of Geometric Algebra in Computer Science and Engineering AGACSE’2008, Leipizig, Germany.
  • 14 th Iberoamerican Conference on Pattern Recogntion, CIARP’2009, Guadalajara, Jalisco, Nov., Mexico
  • International Conference on Pattern Recognition, Cancun, ICPR’2016, Cancun, December 1-7, 2016
  • IEEE/RAS Humanoids’2016, Cancun, México, Nov. 2016.

Selection of Publications

Prof. Bayro has 266 publications: 23 Book chapters, 83 journal articles, 3 Technical Reports, 146 Conference papers, 7 books, 2 patents. His scientific contributions are especially well represented in three of his seven books:

  1. Geometric Computing. For Wavelet Transforms, Robot Vision, Learning Control and Action, Springer Verlag, 2010.
  2. Geometric Algebra Applications Vol. I: for Graphics, Vision and Neurocomputing, (Springer Verlag 2018)
  3. Geometric Algebra Applications Vol. II: Robot Modelling and Control, (Springer Verlag 2019). These books are excellent for graduate courses and a good source of inspiration for researchers in applied mathematics working in diverse fields of cybernetics

Selected articles in applied mathematics, the geometry in robotics, image processing and neurocomputing

  1. Bayro--Corrochano E., Daniilidis K. and Sommer G, [2000]. Motor algebra for 3D kinematics. The case of the hand—eye calibration. Journal of Mathematical Imaging and Vision, vol. 13, pag. 79-99.
  2. Bayro--Corrochano E. and Kähle D. [2000]. Motor Algebra Approach for Computing the Kinematics of Robot Manipulators. Journal of Robotic Systems, vol. 17(9), pp. 495-516.
  3. Bayro--Corrochano E. and Zang Y. [2000]. The motor extended Kalman filter a geometric approach for rigid motion estimation. Journal of Mathematical Imaging and Vision, vol. 13, pag. 205-228.4.
  4. Bayro-Corrochano E. [2006] Theory and use of the quaternion wavelet transform. Journal of Mathematical Imaging and Vision, 24, pp. 19-35.
  5. Bayro-Corrochano E., Reyes-Lozano L. and Zamora-Esquivel J. [2006] Conformal geometric algebra for robotic vision. Journal of Mathematical Imaging and Vision, 24, pp. 55-81.
  6. Ortegón-Aguilar J. and Bayro-Corrochano, E. . [2006]. Lie algebra and system identification techniques for 3D rigid motion and monocular tracking. Journal of Mathematical Imaging and Vision, 25, pp. 173-185.
  7. Bayro-Corrochano E., Trujillo N., and Naranjo M. [2007]. Quaternion Fourier Descriptors for the Preprocessing and Recognition of Spoken Words Using Images of Spatiotemporal Representations. Journal of Mathematical Imaging and Vision. Volume 28, Issue 2, June, pp. 179 -190.
  8. Bayro-Corrochano. E. and Jorge Rivera-Rovelo. [2009] The use of geometric algebra for 3D modeling and registration of medical data. Journal of Mathematical Imaging and Vision., 34:48-60.
  9. Bayro-Corrochano, E. [2010]. What can Hamilton, Grassmann, Clifford and Hestenes tell us about perception and action systems. Journal of Advances in Applied Clifford Algebras. 20, 217-240.
  10. Bayro-Corrochano, E. and Arana Daniel, N. [2010]. Clifford Support Vector Machines. For Classification, Regression and Recurrence. IEEE Transactions on Neural Networks. November pp. 1731-1746.
  11. Serna-Morales, A. F., F. Prieto, E. Bayro-Corrochano. [2012]. Acquisition of Three-Dimensional Information of Brain Structures Using Endoneurosonography. In ESWA: Expert Systems With Applications. Vol. 39 (2), February, Pages 1656-1670.
  12. Moya-Sánchez, E.U. and E. Bayro-Corrochano. [2013] Hilbert and Riesz Transforms Using Atomic Function for Quaternionic Phase Computation. Journal in Advances of. Applications of Clifford Algebras 23, 929–949.
  13. Raviv, D, and Bayro-Corrochano, E. and Raskar, R. . [2017]. LRA: Local Rigid Averaging of Stretchable Non-rigid Shapes. Journal of Computer Vision, Vol. 124, Issue 2, pp. 132- 144.
  14. E. Bayro-Corrochano, L.  Lechuga-Gutierrez,, M.A.  Garza-Burgos, Geometric techniques for robotics and HMI: Interpolation and haptics in conformal geometric algebra and control using quaternion spike neural networks. Robotics and Autonomous Systems 104 (2018) 72–84.
  15. Carlos A. Arellano-Muro, Guillermo Osuna-González, Bernardino Castillo-Toledo and Eduardo Bayro-Corrochano,  Newton–Euler Modeling and Control  of a Multi-copter Using Motor Algebra, G+ 3,0,1. Advances in applications of Clifford Algebra Adv. Appl. Clifford Algebras 30, 19 (2020).