The processing of compound radial frequency patterns
GunnarSchmidtmann#, FrederickA.A.Kingdom#,GunterLoffler†
#
McGillVisionResearch, Dept. of Ophthalmology, McGillUniversity
†
GlasgowCaledonian University, Dept. of LifeSciences
INTRODUCTION
• Radial Frequency patterns (RF) have been extensively used to study
intermediate stages of shape perception (Wilkinson et al., 1998; Loffler, 2008;
Schmidtmann et al., 2012).
• Combinations of RF patterns can be used to investigate natural shapes like
faces or fruits/vegetables.
• Previous studies showed evidence that different RF patterns are processed by
different independent narrowly-tuned RF shape channels (Bell & Badcock,
2009; Bell et al., 2007; 2009).
PREDICTIONS
Probability Summation (PS)
If the two compone nts were proc essed ind epende ntly by separ ate ch an ne ls, on e wou ld
expect only a slight increase in sensitivity for the compound compared to the components.
AIMS
w1=75% RF3
w2=25% RF5
Discrimination thresholds were measured:
1. for circles vs ‘pure’ RFs
2. for circles vs compound RFs
3. for various supra-threshold ‘pure’and
compound RFs (A = 0.05, ~ 10 x
detection threshold)
0.15
w1=50% RF3
w2=50% RF5
c
0.10
w1=25% RF3
w2=75% RF5
b
Thresholds for various shapes (references)
were measuredas the incremental
amplitude of a test (A in Eq.1) required to
discriminate them.
Thresholds were determined for weights
of 100%/0% (e.g. ‘pure’ RF3); 75%/25%;
50%/50%;25%/75%and 0%/100% (e.g.
‘pure’ RF5) (Figs. 1 & 2).
0.05
a
0.015
in phase
out of phase
intermediate phase
SEM
N=3
0.01
0.005
Amplitude
0.15
w2=100%
RF5
RF5
0
0.01
0
0.01
RF3
0
0.02
0
0.01
RF3
0.02
0.02
Data
PS Model
AS model
Data
PS Model
AS model
0.01
relative Amplitude
RF3
RF3
RF3 - RF8
RF8 - RF3
0.02
0.015
0
0.02
A=0
0
0.005
0.01
0.015
relative Amplitude
RF3
RF3
RF7
0.005
RF8
0
0.02
0
0.005
0
relative Amplitude
RF7
RF7
0.01
0.015
relativeRF3
Amplitude RF3
RF7 - RF4
RF4 - RF7
0.02
Fraction of theoretical shape space spanning RF3, RF5 and various morphs of them.
0.005
A=0
0.005
0
0
0.005
0.01
0.015
RF3
relative Amplitude
RF3
0.02
RF7 - RF4
RF4 - RF7 A = 0.05
0.005
0.01
0.015
relativeRF4
Amplitude RF4
0.02
0.01
0
This suggest that the shapes tested here are processed by a
broadly tuned mechanism.
Complex shapes are unlikely to be encoded by RF functions,
because RF patterns are not suited as universal shape
descriptors.
REFERENCES
0.005
0
0.02
DISCUSSION
0.015
0.01
0.01
RF4
Results show that summation of information from different RF
components is consistent with AS.
0.02
0.015
0
0.01
0
0.02
0.01
MODEL RESULTS
• PS only gave a better model fit in 3 out of 42 conditions
0.005
0
0
0
RF3
0.015
0.01
0.01
RF3 - RF8 A = 0.05
RF8 - RF3
0.02
0.015
data plots).
• The resulting shape depends on the phase
relationshipbetween its components.
• The phases of the two components (φ 1 , φ 2) were
fixed relative toeach other.
• Discrimination thresholds for RFs beingin-phase (first
row); out-of-phase for RF3-RF5( second row) andfor
intermediate phases (third row) were measured.
PROCEDURE
• Temporal 2AFC, Method of constant stimuli, pres.
time = 160 ms
• Thresholds expressedas Weber fraction (A/r me a n )
• Discrimination threshold: amplitude at which subjects
were correct on 75 % of the trials.
• To avoid cues: patterns were presentedwith random
orientations and positions.
0.01
0.005
relative Amplitude
RF7
RF7
0.10
0.01
0.01
0
Discrimination thresholds were measured
for morphs between RF3-RF5 (Fig.1 & 2),
0.05
Data
PS Model
AS model
0.02
0.015
‘pure’ RF5 RF3-RF8 and RF4-RF7 (See icons within
Circle (A=0)
Data
PS Model
AS model
RF3 - RF5 A = 0.05
RF5 - RF3
0.02
RESULTS
relative Amplitude
RF5
RF5
distance = 1.2 m)
• A = modulation amplitude (sharpness
of lobes)
• φ = phase, i.e. orientation
• w1 /w2 = relative weights of each RF
component in percent
‘pure’ RF3
Amplitude
• ω = radial frequency (number of lobes)
• rm e a n = mean radius = 0.5 deg (viewing
A=0
relative Amplitude
RF8
RF8
= rmean(1+w1• A • sin(ω1θ+φ1)+w2• A • sin(ω2θ+φ2))
relative Amplitude
RF5
RF5
RF shape: sinusoidal modulation of the radius of a closedcontour in polar coordinates (Wilkinson et al., 1998).
RF3 - RF5
RF5 - RF3
0.02
relative Amplitude
RF8
RF8
METHODS
w1=100%
• PS / AS model under Signa l Detect ion The ory for a 2-IFC task (Kingdom et al.,
2015)
• The m odel cal cul ates the proporti on c orrect (Pc) based on the PS of n signa ls
presented in n out of Q spatial l oc ations, with al l signal s havi ng t he sam e d', for a
M-IFC (M-AFC) task, under the assumptions of SDT and assumi ng an unbi ased
observer.
• Model comparison: Akaike Information Criterion (Akaike, 1974)
0.02
• To test the multiple RF shape channel hypothesis for a wide range of nearthreshold and supra-threshold (high modulation amplitude) shapes
• To model summation with a Signal Detection Theory (SDT) Additive and
Probability Summation Model (Kingdom et al., 2015)
r(θ)
MODEL
Additive Summation (AS)
If both RF compone nts were pr oc essed by a c omm on br oadba nd ch an ne l, one would e xpect
a substant ia l in crea se in s ens itiv ity as the i nformat ion from bot h compone nts wou ld be
summed within the same channel.
0
0.005
0.01
0.015
RF4
relative Amplitude
RF4
0.02
1.
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2.
3.
Loffler.; Vision Research, 2008
S chmidtmann, G., Kennedy, G.J., Orbach, H.S ., & Loffler, G.; Vision Research, 2012
4.
Bell, J., & Badcock, D.R. Vision Research; 2009
5.
Bell, Badcock, Wilson, & Wilkinson, Vision Research, 2007
6.
Bell, Wilkinson, Wilson, Loffler, & Badcock, Vision Research, 2009
7.
Kingdom, Baldwin & S chmidtmann, Journal of Vision, 2015
8.
A kaike, IEEE Transactions on Automatic Control, 1974
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