Detection of change as a measure of closure

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Detection of change as a measure of closure

• Joachim Vandekerckhove
• Sven Panis
• Johan Wagemans
• Laboratory for Experimental Psychology
• University of Leuven, Belgium

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What is closure?

• The state of being closed
• The property of being mathematically closed
• A Gestalt principle of organization holding that
  there is a tendency to perceive incomplete
  objects as complete and to close or fill gaps

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What is closure?
4
What is closure?
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What is closure?

• The state of being closed
• The property of being mathematically closed
• A Gestalt principle of organization holding that
  there is a tendency to perceive incomplete
  objects as complete and to close or fill gaps
• But how do we quantify it?

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What is closure?

• When does a stimulus cease to be a collection of
  line fragments, and start to be a figure?
• Relatability (Kellman Shipley, 1991)
• Weighted gap sizes (Elder Zucker, 1994)
• Others (e.g. Takeichi, 1995 Kallay, 1986 Kimia,
  Frankel, Popescu, 2003)

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Descriptions of closure

• Kellman Shipleys relatability

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Descriptions of closure

• Elder Zuckers C
• Gaps in figures bad for closure
• Larger gaps relatively more important

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How can we measure closure?

• Relatability and gap sizes are intuitive measures
• How do we validate these?

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What is closure?

• How can we know if S is (perceived as) a figure?
• Ask subjects
• Subjective
• Higher-order processes
• Recognition speed/accuracy
• Semantic confound
• Accessibility of concepts
• Ambiguity of images

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How can we measure closure?

• Conventional ways of measuring closure are
  insufficient

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What is closure?

• What does it do?
• What does it mean if a stimulus has closure?
• ? Figures have an inside and an outside

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Information in contours

• Feldman Singh (2003,2005)
• Concavities (indentations) contain more
  information than convexities (protrusions)

Turning angle
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Information in contours

• Assuming no prior knowledge

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Information in contours

• Assuming a closed figure ( a gt 0 )

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Information in contours

• Feldman Singh (2003,2005)
• Concavities (indentations) contain more
  information than convexities (protrusions)
• Barenholtz et al. (2003)
• Changes in concavities detected more easily than
  changes in convexities in star-shaped silhouettes
  (concavity effect)

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Reasoning

• Reasonable

• Conversely

This we can test!
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Experiment 1

• Goal
• Does the effect exist?
• Does it exist in contours as well as silhouettes?
• Change detection paradigm (Barenholtz et al.)
• Briefly show two meaningless polygons
• Change or no change?

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Experiment 1
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Experiment 1
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Experiment 1

• Independent variables
• Change / no-change
• Change type (concave / convex)
• Change magnitude (4 levels)
• Stimulus type (contour / silhouette)
• Dependent variable
• Ease of detection (d-prime)

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Results Experiment 1
Concavities
Concavities
Convexities
Convexities
Change size
Change size
Silhouettes
Contours
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Results Experiment 1

• Data analysis (usual method)
• Enter d values within each condition as raw data
  into ANOVA

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Results Experiment 1

• ANOVA showed
• Replicated the concavity effect (F1,192 231.80,
  p lt 10-4, ?² .303)
• Large effect of change size (F3,192 108.74, p lt
  10-4, ?² .424)
• Small effect of stimulus type (F1,192 6.75, p
  .01, ?² .008)
• Found no interactions

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Experiment 2

• Goal
• Effect of saliency of straight edges and sharp
  angles? (Kristjansson Tse, 2001)
• Change detection paradigm
• Use smoothed images

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Experiment 2
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Experiment 2

• Independent variables
• Change / no-change
• Change type (concave / convex)
• Dependent variable
• Ease of detection (d-prime)

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Results Experiment 2

• Concavity effect persisted(t20 2.50, p .02,
  r² .238)
• Mean d' concavities 1.717
• Mean d' convexities 1.146

Concavities
Convexities
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Experiment 3

• Goal
• Concavity effect
• An effect of changes in part structure?

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Experiment 3
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Experiment 3

• Goal
• Concavity effect
• An effect of changes in part structure?
• Or are concavities special in themselves?

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Experiment 3

• Goal
• Concavity effect
• An effect of changes in part structure?
• Or are concavities special in themselves?
• Change detection paradigm
• Keep part structure constant in half of trials

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Experiment 3

• Independent variables
• Change / no change
• Change type (concave / convex)
• Change quality
• Qualitative add a vertex
• Quantitative increase a vertex

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Experiment 3
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Experiment 3

• Independent variables
• Change / no change
• Change type (concave / convex)
• Change quality
• Qualitative add a vertex
• Quantitative increase a vertex
• Dependent variable
• Ease of detection (d-prime)

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Results Experiment 3

• Concavity effect remained
• Change type (F1,36 8.66, p lt .01, w² .142)
• Part structure effect
• Change quality (F1,36 7.07, p .01, w² .112)
• Interaction did not reach significance
• (F1,36 1.23, p .28)

Concavities
Convexities
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Experiment 4

• Goal
• Investigate descriptions of closure
• Change detection paradigm
• Manipulate closure of images
• Measured in relatability
• Measured in gap size

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Experiment 4
relatable
unrelatable
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Experiment 4

• Independent variables
• Change / no change
• Change type (concave / convex)
• Gap size (3 levels)
• Relatability (yes / no)
• Dependent variable
• Size of concavity effect (delta-prime)
  difference in d-primes

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Results Experiment 4
d
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Results Experiment 4

• Gap size predicts concavity effect(F2,42 3.58,
  p .04, w² .097)
• Relatability does not(F1,42 .49, p .49)
• No significant interaction(F2,42 1.22, p .31)

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Results Experiment 4

• What happened?
• We can quite plainly see the interaction

d
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Results Experiment 4

• Yet the ANOVA reports
• No significant interaction(F2,42 1.22, p .31)

But we had tens of thousands of data points
This indicates the degrees of freedom for the
linear model
What happened?
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New data analysis

• Standard analysis (ANOVA) uses ds as raw data
  points

• But d is not just a point
• It is a distribution

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New data analysis

• Bootstrap analysis Resample from the original
  dataset

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New data analysis

• Repeat (n 1,000)
• Bootstrap data

(Observer FM)
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New data analysis

• Distributions in all conditions are now known
  quite well (central tendencies, standard
  deviation, skew, kurtosis)
• But
• Distributions cannot be processed in factorial
  ANOVA
• Raw data needed

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New data analysis

• We would need to simulate data from these
  distributions (Monte Carlo simulation)
• Preferably, using as much information about the
  distributions as possible
• But we already have a dataset available with
  data that follow exactly the distributions we need

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New data analysis

• Use the bootstrapped ds as raw data in ANOVA
• (and calculate something interesting, like w²)
• But
• This is only one iteration of the Monte Carlo
  simulation
• Repeat 1,000 times (or until stable)

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Results bootstrap/simulation

• Experiment 1 original results
• Concavity effect(F1,192 231.80, p lt 10-4, ?²
  .303)
• Change size(F3,192 108.74, p lt 10-4, ?²
  .424)
• InteractionsNo interactions significant

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Results bootstrap/simulation

• Experiment 1 bootstrap results
• Concavity effect (F1,192 231.80, p lt 10-4, ?²
  .303)(F1,4976 124008, p 0, ?² .404)
• Change size (F3,192 108.74, p lt 10-4, ?²
  .424)(F3,4976 55858, p 0, ?² .546)
• InteractionsNo interactions significantAll
  highly significant, but small ?²s
• Total R² .984

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Results bootstrap/simulation

• Experiment 2 original results
• Concavity effect(t20 2.50, p .02, r² .238)
• Experiment 2 bootstrap results
• Concavity effect(t1758 45.5, p lt 10-298, r²
  .541)

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Results bootstrap/simulation

• Experiment 3 original results
• Concavity effect(F1,36 8.66, p lt .01, w²
  .142)
• Part structure effect(F1,36 7.07, p .01, w²
  .112)
• Interaction(F1,36 1.23, p .28)

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Results bootstrap/simulation

• Experiment 3 bootstrap results
• Concavity effect(F1,36 8.66, p lt .01, w²
  .142)(F1,3196 33808, p 0, w² .499)
• Part structure effect(F1,36 7.07, p .01, w²
  .112)(F1,3196 26618, p 0, w² .393)
• Interaction(F1,36 1.23, p .28)(F1,3196
  4062, p 0, w² .060)
• Total R² .953

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Results bootstrap/simulation

• Experiment 4 original results
• Gap size (w² .097)
• Relatability (ns)
• Interaction (ns)

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Results bootstrap/simulation

• Experiment 4 bootstrap results
• Gap size (w² .097)
• Gap size (w² .418)
• Relatability (ns)
• Relatability (w² .044)
• Interaction (ns)
• Interaction (w² .221)
• Total R² .684

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Conclusions

• The concavity effect is
• real
• a compound effect
• Change detection as a measure of closure works
• You need to take care of your data
• Theres more to closure than meets the eye
• Next Formulate and test a more comprehensive
  model for closure

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That is all.