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Department of Mathematics & Statistics

Faculty Profile


Dr Jacek Turski




Office: 714-S
Phone: 713-221-8401


Curriculum Vita





Jacek Turski was awarded his Ph.D. from McGill University. After holding postdoctoral positions at the University of Manitoba and the University of Houston, he joined the University of Houston-Downtown where he is now a full professor in the Department of Mathematics and Statistics. A few years ago Turski constructed projective Fourier analysis of the conformal camera in the framework of representation theory of semisimple Lie groups. Based on this Fourier analysis, he is currently developing a physiologically realistic model of robotic vision systems. His research has been supported by NSF and UHD grants and published in mathematics, computer science, and neuroscience journals. Turski was the recipient of the 2006 Scholarship/Creativity Award at UHD.


Ph.D. in Mathematics from the McGill University, Montreal, Canada in 1986.

M.S. in Mathematics from the University of University of Warsaw in 1976.

Work History

Professor, Department of Mathematics and Statistics, University of Houston-Downtown 2013 through Present.

Professor, Department of Computer and Mathematical Sciences, University of Houston-Downtown 1990 through 2013.

Postdoctoral Fellow , Department of Mathematics, University of Houston, 1989 through 1990.

Visiting Scholar, Department of Mechanical Engineering, University of Houston, 1988 through 1989.

Research Associate , Department of Applied Mathematics, University of Manitoba, 1987 through 1988.

Research Associate , Department of Civil Engineering, University of Manitoba, 1986 through 1987.

Honors and Awards

Faculty Award for Excellence in Scholarship and Creativity, University of Houston-Downtown, 2006.

J.W. McConnell Fellowship, Department of Mathematics, McGill University, 1981-1982.

Research Interests

Research Topic: Projective Fourier analysis of the conformal camera with the group SL(2,C) generating image projective transformations has been constructed in the framework of representation theory of semisimple Lie groups. This analysis provides the data model for efficient, perspectively-covariant digital image representation well adapted to the retino–cortical mapping of the brain oculomotor and visual pathways, integrating the head, eyes (conformal cameras) and visual cortex into a single computational system. Based on this integrated system, the ongoing research develops algorithms for processing visual information during the motion of a camera with silicon retina that resembles the saccadic eye movements.

The challenges in my research work: Although the saccades are needed to reposition the high acuity fovea successively on the salient objects in a scene in order to build up the understanding of the scene, they pose a major challenge in modeling humanoid robotic vision. In fact, humans make three saccades per second at the eyeball’s maximum speed of 700deg/sec, producing about 200,000 saccades per day! In spite of recent advances, how the brain compensates for these incessant interruptions such that we perceive continuous and stable world remains a

  1. J. Turski, 2009. Geometric Analysis of the Conformal Camera for  Intermediate-level Vision and Perisaccadic Perception, Submitted [PDF]
  2. J. Turski, 2008. Harmonic Analysis for Cognitive Vision: Perisaccadic Perception , SPIE proceedings: Human Vision and Electronic Imaging XIV, Vol. 7240, 2009 [PDF]
  3. J. Turski, 2006. Computational Harmonic Analysis for Human and Robotic Vision Systems, Neurocomputing, 69, 1277-1280, 2006 [PDF]
  4. J. Turski, 2005. Geometric Fourier Analysis for Computational Vision, JFAA 11, 1-23, 2005 [PDF]
  5. J. Turski, 2004. Geometric Fourier Analysis of the Conformal Camera for Active Vision, SIAM Review 46, 230-255, 2004 [PDF]
  6. J. Turski, 2000. Projective Fourier Analysis for Patterns, PATTERN RECOGNITION 33, 2033-2043, 2000 [PDF]
  7. J. Turski, Harmonic Analysis on SL(2,C)  and Projectively Adapted Pattern Representation, JFAA 4, 67-91, 1998 [PDF]
  8. J. Turski, 1997. Projective Fourier Analysis in Computer Vision: Theory and Computer Simulations, SPIE 3168, 124-135, 1997 [PDF]
  9. E. Barany, M. Golubitsky and J. Turski, 1992. Bifurcations with local gauge symmetries in the Ginzburg-Landau equations. Physica D. 56, 36-56, 1992[Abstract]

Conferences and Workshops

  1. J. Turski, Geometric Analysis of SL(2,C) and Biologically-Mediated Computational Vision, Keynote Talk, International Conference on Computational and Information Sciences, University of Houston-Downtown, Houston, TX, April 30-May 2, 2009 [Keynote Speakers]
  2. J. Turski, Harmonic analysis for cognitive vision: perisaccadic perception. SPIE Conference 7240: Human Vision and Electronic Imaging XIV, San Jose, CA, January 19-22, 2009
  3. J.Turski, Projective Fourier analysis and perisaccadic perception, OSA Vision Meeting, Rochester, NY, October 24-25, 2008[PDF]
  4. J. Turski, Harmonic Analysis on SL(2,C) with Applications in Cognitive Vision, The Special Semester on Modern Methods of Time-Frequency  Analysis : 4th Workshop on Noncommutative Computational Harmonic Analysis, at the E. Schrödinger International Institute of Mathematical Physics, Vienna, July 4-7, 2005 [PDF]
  5. J. Turski, Geometrical Fourier Analysis in Computational Vision: Biological and Mathematical Background, 9th Int. Conf. on Cognitive and Neural Systems, Boston University, May 18-21, 2005 [PDF]
  6. J. Turski, Projective Fourier Analysis in Computer Vision: Mathematics for  Silicon Retina Sensors of Active Vision, SIAM Conference: Mathematics for Industry—Challenges and Frontiers, Toronto, 2003, See the article: James Case, SIAM Conference Highlights Works in Progress on Problems of Lasting Interest to Industry,SIAM News, 36, 2003 [PDF]





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