Professor

Mathematical
and Computational Cognitive Science

Department of
Psychological Sciences

School of
Electrical and Computer Engineering (by courtesy)

Purdue University

West Lafayette, IN 47907-2081
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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