Zygmunt Pizlo

    Mathematical and Computational Cognitive Science
    Department of Psychological Sciences
    School of Electrical and Computer Engineering (by courtesy)
    Purdue University
    West Lafayette, IN 47907-2081 >> city map
    email: zpizlo at purdue dot edu
    Tel. (765) 494 6930
    Fax: (765) 496 1264
    Room #: PRCE 194

    Zyg's Conjecture: veridical 3D vision is mathematically and computationally so difficult that there is only one way to do it.

    Once you accept this, it follows that all animals (including us) that see the 3D world veridically (or nearly so) use the same algorithm. A computer that can also see veridically, must be using the algorithm that is used by the human visual system. So, there is no longer any need to wonder about whether computer vision should emulate biological vision. It must.

    How Noether's theorem can be applied in the case of 3D vision to derive shape constancy as a psychophysical conservation law.

    Conclusions from the review of "Making a machine...", by Adele Diederich published in the Journal of Mathematical Psychology

    Read the entire review.

    "What role does symmetry play in the perception of 3D objects?" - see our blog on the Oxford University Press Web site.

    "Questions about symmetry and visual perception" - tumblr on the Oxford University Press Web site.

    When Gestaltists stated that "the whole is different from the sum of its parts" they meant that the visual system is not linear. Recall that in a linear system, the response to a linear combination of inputs is a linear combination of the responses to the individual inputs. This is not the case in vision. See the demo (courtesy of Prof. Tadamasa Sawada), which shows that the percept of a 2D hexagon and of a 2D "Y junction" cannot explain the percept of a 3D cube.

    My work is directed by exploring new ideas rather than following established views. In this approach, rational arguments are as important for me as experimental results. The emphasis on principled reasoning means that in my view, cognitive psychology is not a bag of tricks; Neither is my research. A list of my most important contributions is provided below (in chronological order):

    1992 - formulated perspective invariants thereby providing the first model-based invariants in vision

    1994 - proposed a new theory of shape constancy that is NOT based on "taking slant into account"

    1995 - developed a pyramid model explaining the speed-accuracy trade-off in vision

    1997 - explained the role of the calibrated camera model in shape perception

    1999 - demonstrated shape constancy for solid shapes and explained the apparent controversy between Rock's and Biederman's results

    2000 - developed a pyramid model that shows how human beings solve the Traveling Salesman Problem (TSP)

    2000 - contributed to the rediscovery of Wertheimer's phi motion

    2001 - published a theoretical paper on inverse problems in vision, making it clear that a priori constraints are at least as important as the information in the retinal image

    2001 - provided a new criterion for classifying illusions as important or unimportant

    2005 - discovered a new binocular phenomenon showing that a priori 3D shape constraints are more important than binocular disparity

    2006 - developed a TSP model that emulates human visual attention and eye movements

    2008 - published the first coherent treatment of the history of shape perception

    2009 - introduced a new theory of 3D shape perception based on symmetry, compactness and planarity constraints

    2011 - developed a new Bayesian theory of the veridical binocular perception of symmetrical shapes that emphasizes the role played by stereoacuity

    2011 - demonstrated that a priori constraints are more important in achieving reliable shape constancy than depth cues

    2011 - published psychophysical results on the transfer of skilled movement that suggested that the motor system has a pyramidal architecture, very much like the architecture of the visual system

    2012 - modeled the veridical recovery of 3D scenes and 3D figure-ground organization

    2013 - showed that symmetry is the sine qua non of shape

    2013 - developed a TSP model with a small human-like working memory

    2014 - published a new theory of 3D veridical vision

    2014 - contributed to the discovery of new model-based invariants for 3D, piecewise planar, symmetrical curves

    2015 - showed that a perceived closed curve is the shortest path in the log-polar representation (aka complex logarithmic map) present in the primary visual cortex (area V1) of primates

    2016 - explained how 3D visual perception can be a "hard science" because symmetry, the least-action principle and the conservation laws operate in 3D vision

    2016 - helped to explain 3D and 2D figure-ground organization by using 3D symmetry and gravity a priori constraints

    These milestones are described in a little more detail in the Research link. Links to open access papers are in Publications.

    You can see the demos for the newest book.

    To see how our robot solves figure-ground organization problem and performs simple navigations tasks go to Yunfeng's web site and to the VSS demo site. Check also demos on Tada's web site

Yll Haxhimusa. Created: August 18, 2008; Last change: April 25, 2015 | Disclaimer & Copyright Notice |