Form Perception through Phase Relations of Retina Ganglion Cell
Firing and Extraocular Muscle Contractions!
Jonathan Butner, Kyle Gagnon, Michael Geuss, Tom Malloy, Michael Kramer & Jeanine Stefanucci!
The University of Utah, Department of Psychology!
Background!
We propose a way of understanding form perception
that emphasizes the changes in eye movements
relative to changes in firing on the retina; a critical
ratio is formed between the frequency of retina
ganglion cell firing and the frequency of extraocular
muscle contractions (i.e., the muscles controlling eye
movements).
Experiment 2!
Experiment 1!
Do changes in eye movement frequencies alter
perceived forms and their perceived movement?
We altered the critical ratio between eye movement
and retinal firing frequencies by altering the natural
movement of the eye (Ω). Spinning participants
around in a chair alters the natural movement of the
eye in the direction opposite of spinning direction
(Jacobson & Shepard, 2007).
Are all motions/forms equally stable?
24 FPS
These two multidimensional flows define both object
and motion through the phase relations based on cell
firing relative to eye motion.
• Ps then reported if the object/repeating pattern and
its motion had changed or stayed the same
Stability
• Ps were then spun either clockwise or
counterclockwise in the chair (Within Subjects; order
randomized)
3
Discussion!
4 (less)
•  Same Ps examined a different moving repeating
dot pattern
•  The dot pattern was presented with 9 different
frames per second (FPS) displays of the same dot
pattern (order randomized)
Results: Experiment 2!
•
Conducted a mixed model in SPSS 19
• Range (upper limit minus lower limit) treated as the
dependent variable
55 cm Display @ 1024 x 768
K (Kappa) is the coupling strength (Attention)
•  Ω (Omega) is the driving frequency (Natural Eye
Movement)
Results: Experiment 1!
Twenty-six out of twenty-seven participants reported
drastic changes in the image after being spun
• Stability (left side of Farey Tree), proximity to most
stable ratio (24 fps in our experiment), and a stability
by proximity interaction were predictors
As per the model the interaction between initial fps
and stability reached conventional significance, t(248)
=2.338, p=.02,
• As Stability decreased, so did the range
The possible phase locking ratios can be differentiated
between rational and irrational numbers where
coupling (K) then facilitates stabilization of the
irrational numbers to nearest rational ones. Form
perception is defined as the clustering of phase locked
flows with motion in object defined as the ratio relative
to the natural eye speed.
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• Clockwise and Counterclockwise both altered form
perception
• The change in image lasts for about 8 seconds and
then returns to original perception when eye
movement normalizes
Suggests eye movements is a part of form perception.
This is consistent with the phase relations model.
Ranges decrease as
stability decreases
The results revealed an increase in the stability of the
form perceived by participants as the stability of the
critical ratio also increased.
2
•  Ps altered the FPS to identify the upper and
lower limit at which the image/motion qualitatively
changed
This generates a modular equation known as the
circle map :
•  θ (Theta) is phase (so future phase as a function
of current phase) forming the critical ratio between
eye movement and retinal firing frequency
12 FPS
1 (more)
• 27 participants examined a moving repeating dot
pattern
• Ps were instructed to identify an object or repeating
pattern
48 FPS
We examined whether critical ratios varied in stability
for perceptions of form consistent with the circle map
equation. One byproduct of the circle map is known as
the Farey sequence which dictates the relative
stability of each ratio.
• 24 FPS (the Most Stable) had well defined borders
when focal, but also absorbed the nearby frequencies
when not
• 48 FPS had wide range by being the second Most
Stable and far from 24 FPS
Notably, scaling initial fps in raw metric (rather than
distance from 1:1) showed the same interaction
pattern, albeit weaker in effect, t(248)=2.049, p=.04.
Together, these experiments suggest that the
perception of form is related to the critical ratio
between retinal firing frequencies and extraocular
muscle contraction frequencies.
Form perception through phase relations:
• Is not subject to the correspondence problem (Malloy,
Butner, & Jensen, 2008)
• Integrates motion and form into a single model
• Integrates motion illusion perception with still image
perception
• Operationalizes the potential influence of attention
through K (kappa)
• Can be expanded to account for phase relations
other than the extraocular muscle contraction
References
Jacobson, G.P. & Shepard, N.T. (2007). Balance
function assessment and management. San Diego,
CA: Plural Publishing Inc.
Malloy, T.E., Butner, J., Jensen, G.C. (2008). The
emergence of dynamic form through phase relations
in dynamic systems. Nonlinear Dynamics in the
Psychological and Life Sciences, 12, 371-395.
Acknowledgements!
We would like to thank our colleagues at the
Department of Psychology, University of Utah for their
support.