Simplicity in vision - KU Leuvenu0084530/reprints/siv-lecture.pdf · Simplicity in vision: Topics...
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Simplicity in vision
Peter A. van der Helm
Laboratory of Experimental PsychologyKU Leuven – University of Leuven
Peter A. van der Helm Simplicity in vision
Simplicity in vision
Introduction
The veridicality of simplicity
Symmetry perception
Cognitive architecture
Peter A. van der Helm Simplicity in vision
Human visual perceptual organization
The neuro-cognitive process that enables us to perceive scenes asstructured wholes consisting of objects arranged in space.
Yes No
YesNo
Peter A. van der Helm Simplicity in vision
Human visual perceptual organization
Visual perceptual organization may seem to occur effortlessly, butby all accounts, it must be both complex and flexible:
It singles out one hypothesis about the distal stimulus fromamong a myriad of hypotheses that fit the proximal stimulus.
To this end, multiple sets of features at multiple locations in astimulus have to be grouped in parallel.
This implies that the process must cope with a large numberof competing combinations simultaneously.
Hence, the combinatorial capacity of the process must be high,which, together with its high speed (it completes in the range of100–300 ms), reveals its truly impressive nature (Gray, 1999).
Peter A. van der Helm Simplicity in vision
Human visual perceptual organization
Visual perceptual organization may seem to occur effortlessly, butby all accounts, it must be both complex and flexible:
It singles out one hypothesis about the distal stimulus fromamong a myriad of hypotheses that fit the proximal stimulus.
To this end, multiple sets of features at multiple locations in astimulus have to be grouped in parallel.
This implies that the process must cope with a large numberof competing combinations simultaneously.
Hence, the combinatorial capacity of the process must be high,which, together with its high speed (it completes in the range of100–300 ms), reveals its truly impressive nature (Gray, 1999).
Peter A. van der Helm Simplicity in vision
Why do things look as they do?
The likelihood principle (von Helmholtz, 1909)
Vision produces interpretations that are most likely to be true.
The Gestalt law of Pragnanz (as formulated by Koffka, 1935)
”Of several geometrically possible organizations that one willactually occur which possesses the best, the most stable shape.”
The minimum principle (Hochberg & McAlister, 1953)
”The less the amount of information needed to define a givenorganization as compared to the other alternatives, the more likelythat the figure will be so perceived.”
The simplicity principleVision produces simplest organizations.
Peter A. van der Helm Simplicity in vision
Why do things look as they do?
The likelihood principle (von Helmholtz, 1909)
Vision produces interpretations that are most likely to be true.
The Gestalt law of Pragnanz (as formulated by Koffka, 1935)
”Of several geometrically possible organizations that one willactually occur which possesses the best, the most stable shape.”
The minimum principle (Hochberg & McAlister, 1953)
”The less the amount of information needed to define a givenorganization as compared to the other alternatives, the more likelythat the figure will be so perceived.”
The simplicity principleVision produces simplest organizations.
Peter A. van der Helm Simplicity in vision
Why do things look as they do?
The likelihood principle (von Helmholtz, 1909)
Vision produces interpretations that are most likely to be true.
The Gestalt law of Pragnanz (as formulated by Koffka, 1935)
”Of several geometrically possible organizations that one willactually occur which possesses the best, the most stable shape.”
The minimum principle (Hochberg & McAlister, 1953)
”The less the amount of information needed to define a givenorganization as compared to the other alternatives, the more likelythat the figure will be so perceived.”
The simplicity principleVision produces simplest organizations.
Peter A. van der Helm Simplicity in vision
Keep it simple!
William of Occam (c. 1287–1347)
Occam’s razor:”Pluralitas non est ponenda sine necessitate.”(”Plurality is not to be posited without necessity.”)
”We consider it a good principle to explain phenomena by thesimplest hypothesis possible.” — Ptolemy (c. 90–168)
”We may assume the superiority, all things being equal, of thedemonstration which derives from fewer postulates or hypotheses.”
— Aristotle (c. 384–322 BC)
Peter A. van der Helm Simplicity in vision
Keep it simple!
William of Occam (c. 1287–1347)
Occam’s razor:”Pluralitas non est ponenda sine necessitate.”(”Plurality is not to be posited without necessity.”)
”We consider it a good principle to explain phenomena by thesimplest hypothesis possible.” — Ptolemy (c. 90–168)
”We may assume the superiority, all things being equal, of thedemonstration which derives from fewer postulates or hypotheses.”
— Aristotle (c. 384–322 BC)
Peter A. van der Helm Simplicity in vision
What if all things are not equal?
Observations on planet orbits
Simple theory Many unexplained observations
priorcomplexity
conditionalcomplexity
Before 1600, planet orbits were thought to be circular
priorcomplexity
conditionalcomplexity
Complex theory Few unexplained observations
Johannes Kepler (1571–1630): planet orbits are elliptical
Peter A. van der Helm Simplicity in vision
What if all things are not equal?
It is not only a matter of how good a shape is in itself (the prior),but also of how well it fits the proximal stimulus (the conditional).
Peter A. van der Helm Simplicity in vision
Could simplicity guide perceptual organization?
A competitive approach toperceptual organization
Leeuwenberg, E., & van der Helm, P. A. (2013).
Structural information theory.
Cambridge University Press.
Fundamental issues inperceptual organization
van der Helm, P. A. (2014).
Simplicity in vision.
Cambridge University Press.
Peter A. van der Helm Simplicity in vision
Levels of description
Marr’s (1982) levels of description in vision:
The computational level — what is the logic that defines thenature of resulting mental representations of incoming stimuli?
The algorithmic level — how are the input and the outputrepresented and how is one transformed in the other?
The implementational level — how are those representationsand transformations neurally realized?
Epistemological pluralism: Complementary descriptions mayexplain how the goal is reached via a method allowed by the means.
Peter A. van der Helm Simplicity in vision
Levels of description
Marr’s (1982) levels of description in vision:
The computational level — what is the logic that defines thenature of resulting mental representations of incoming stimuli?
The algorithmic level — how are the input and the outputrepresented and how is one transformed in the other?
The implementational level — how are those representationsand transformations neurally realized?
Epistemological pluralism: Complementary descriptions mayexplain how the goal is reached via a method allowed by the means.
Peter A. van der Helm Simplicity in vision
Marr’s levels in the kitchen
Peter A. van der Helm Simplicity in vision
Marr’s levels in biology
GOAL:Origin of species (Darwin, 1844)
Evolution theory
METHOD:Experiments in plant hybridization (Mendel, 1865)
Hereditary theory, classical genetics
MEANS:Molecular structure of DNA (Watson & Crick, 1953)
Molecular biology, modern genetics
Peter A. van der Helm Simplicity in vision
Representations (”what”) versus processes (”how”)
Operating bases of the three major research paradigms:
Computational goal ← representational theory
l ”what”: molar – behavioral – competence – cognitive
Algorithmic method ← connectionist modeling
l ”how”: molecular – physiological – performance – neural
Implementational means ← dynamic systems theory
According to Marr, answers to both the ”what” and ”how”questions are needed, even though answering these questions maybe totally different endeavours using totally different tools.
Peter A. van der Helm Simplicity in vision
Representations (”what”) versus processes (”how”)
Operating bases of the three major research paradigms:
Computational goal ← representational theory
l ”what”: molar – behavioral – competence – cognitive
Algorithmic method ← connectionist modeling
l ”how”: molecular – physiological – performance – neural
Implementational means ← dynamic systems theory
According to Marr, answers to both the ”what” and ”how”questions are needed, even though answering these questions maybe totally different endeavours using totally different tools.
Peter A. van der Helm Simplicity in vision
Representations (”what”) versus processes (”how”)
Operating bases of the three major research paradigms:
Computational goal ← representational theory
l ”what”: molar – behavioral – competence – cognitive
Algorithmic method ← connectionist modeling
l ”how”: molecular – physiological – performance – neural
Implementational means ← dynamic systems theory
According to Marr, answers to both the ”what” and ”how”questions are needed, even though answering these questions maybe totally different endeavours using totally different tools.
Peter A. van der Helm Simplicity in vision
Levels of evaluation
Multidisciplinary research cycles:
The empirical cycle — has roots in physics; the idea is toconduct controlled experiments to test predictions inferredfrom theories and models (de Groot, 1961/1969).
The theoretical cycle — has roots in mathematics; the idea isto formalize ideas and assumptions in theories and models, tosee if they can be derived from first principles.
The tractability cycle — has roots in computer science; theidea is to assess if theories and models allow for feasibleimplementations in computers or brains (van Rooij, 2008).
Peter A. van der Helm Simplicity in vision
Multidisciplinary research cycles
Empiricalcycle
Tractabilitycyclecycle
Theoretical
Formalizations Implementations
Experiments
Theories & Models
Peter A. van der Helm Simplicity in vision
Simplicity in vision: Topics
Theoreticalcycle
Empiricalcycle
Tractabilitycycle
The computabilityof simplicity
The nature ofvisual regularity in the brain
The visual hierarchy
The veridicalityof simplicity
Form classification, amodal completion,
Cognitive architecture
symmetry perception
Peter A. van der Helm Simplicity in vision
Simplicity in vision: Topics
Theoreticalcycle
Empiricalcycle
Tractabilitycycle
The computabilityof simplicity
The nature ofvisual regularity in the brain
The visual hierarchy
The veridicalityof simplicity
Cognitive architecture
Form classification, amodal completion, symmetry perception
Peter A. van der Helm Simplicity in vision
Part 1
The veridicality of simplicity
Peter A. van der Helm Simplicity in vision
Vision and the world
Image properties
Perceived objects
Perceived objects
Image
Object properties
Likelihood principle: percepts are most likely to be true.→ external criterion — highly veridical by definition!
Simplicity principle: percepts have simplest representations.→ internal criterion — sufficiently veridical?
Peter A. van der Helm Simplicity in vision
Bayes’ rule
Thomas Bayes (1702–1761)
Bayes’ rule: p(H|D) =p(H)∗p(D|H)
p(D)
The posterior probability p(H|D) that hypothesis H is true forgiven data D can be found by multiplying:
the prior probability p(H) that hypothesis H is true, and
the conditional probability p(D|H) that data D arises ifhypothesis H is true.
Note: p(D) is a normalization factor and is currently less relevant.
Peter A. van der Helm Simplicity in vision
Bayes’ rule: An example
Imagine an HIV test for which 90% of all test results are correct:
90% of the HIV patients score positive.
90% of the others score negative.
Imagine further that you are one of 1000 arbitrarily chosenparticipants in a population test, and that you score positive... how worried should you be?
Bayes would say: That depends on how many people of the totalpopulation actually have HIV.
OK, say that 2% of the total population has HIV ... what then?
Peter A. van der Helm Simplicity in vision
Bayes’ rule: An example
Imagine an HIV test for which 90% of all test results are correct:
90% of the HIV patients score positive.
90% of the others score negative.
Imagine further that you are one of 1000 arbitrarily chosenparticipants in a population test, and that you score positive... how worried should you be?
Bayes would say: That depends on how many people of the totalpopulation actually have HIV.
OK, say that 2% of the total population has HIV ... what then?
Peter A. van der Helm Simplicity in vision
Bayes’ rule: An example
Bayesian prior probabilities (before the test starts):
About 20 (2%) of the 1000 participants has HIV.
About 980 (98%) of the 1000 participants does not have HIV.
Bayesian conditional probabilities (test results 90% correct):
Of the about 20 HIV patients, about 18 (90%) score positive.
Of the about 980 others, about 98 (10%) also score positive.
Hence, in total, about 116 positive scores are to be expected:
About 18 positive scores are correct (15.5% of 116).
About 98 positive scores are false alarms (84.5% of 116).
Bayes would say: Retest those 116 persons – prior then is 15.5%.
Note: If prior is 40%, then 85.7% correct and 14.3% false alarms.
Peter A. van der Helm Simplicity in vision
Bayes’ rule: An example
Bayesian prior probabilities (before the test starts):
About 20 (2%) of the 1000 participants has HIV.
About 980 (98%) of the 1000 participants does not have HIV.
Bayesian conditional probabilities (test results 90% correct):
Of the about 20 HIV patients, about 18 (90%) score positive.
Of the about 980 others, about 98 (10%) also score positive.
Hence, in total, about 116 positive scores are to be expected:
About 18 positive scores are correct (15.5% of 116).
About 98 positive scores are false alarms (84.5% of 116).
Bayes would say: Retest those 116 persons – prior then is 15.5%.
Note: If prior is 40%, then 85.7% correct and 14.3% false alarms.
Peter A. van der Helm Simplicity in vision
Bayes’ rule: An example
Bayesian prior probabilities (before the test starts):
About 20 (2%) of the 1000 participants has HIV.
About 980 (98%) of the 1000 participants does not have HIV.
Bayesian conditional probabilities (test results 90% correct):
Of the about 20 HIV patients, about 18 (90%) score positive.
Of the about 980 others, about 98 (10%) also score positive.
Hence, in total, about 116 positive scores are to be expected:
About 18 positive scores are correct (15.5% of 116).
About 98 positive scores are false alarms (84.5% of 116).
Bayes would say: Retest those 116 persons – prior then is 15.5%.
Note: If prior is 40%, then 85.7% correct and 14.3% false alarms.
Peter A. van der Helm Simplicity in vision
Bayes’ rule: An example
Bayesian prior probabilities (before the test starts):
About 20 (2%) of the 1000 participants has HIV.
About 980 (98%) of the 1000 participants does not have HIV.
Bayesian conditional probabilities (test results 90% correct):
Of the about 20 HIV patients, about 18 (90%) score positive.
Of the about 980 others, about 98 (10%) also score positive.
Hence, in total, about 116 positive scores are to be expected:
About 18 positive scores are correct (15.5% of 116).
About 98 positive scores are false alarms (84.5% of 116).
Bayes would say: Retest those 116 persons – prior then is 15.5%.
Note: If prior is 40%, then 85.7% correct and 14.3% false alarms.
Peter A. van der Helm Simplicity in vision
Bayes’ rule in vision
high conditional low conditionalprobability probability
But what are their prior probabilities?
Peter A. van der Helm Simplicity in vision
Bayes’ rule in vision
high conditional low conditionalprobability probability
But what are their prior probabilities?
Peter A. van der Helm Simplicity in vision
Helmholtzian likelihood principle in certainty terms
posteriorprobability
priorprobability
conditionalprobability
Likelihood principle: interpretation of data on the basis of the world
independencyviewpoint
dependencyviewpoint
maximize certainty p(H|D) = p(H) ∗ p(D|H)
Peter A. van der Helm Simplicity in vision
Prior complexities: shapes as such
A descriptive code is a reconstruction recipe.
If y = 5 cm, z = 3 cm, a = 70◦, and b = 110◦, thenthe code 2 ∗ (yazb) is a recipe for a parallelogram.
If y = z = 3 cm and a = b = 90◦,then the parallelogram-code would yield a square.
But for a square, a shorter code is 4 ∗ (ya)... this square-code is simpler than theparallelogram-code, because it containsfewer structural information parameters (sip).
The prior complexity of a shape is given by the number of sip in itssimplest code – this is the minimum amount of structuralinformation needed to reconstruct the shape as such.
Peter A. van der Helm Simplicity in vision
Prior complexities: shapes as such
A descriptive code is a reconstruction recipe.
If y = 5 cm, z = 3 cm, a = 70◦, and b = 110◦, thenthe code 2 ∗ (yazb) is a recipe for a parallelogram.
If y = z = 3 cm and a = b = 90◦,then the parallelogram-code would yield a square.
But for a square, a shorter code is 4 ∗ (ya)... this square-code is simpler than theparallelogram-code, because it containsfewer structural information parameters (sip).
The prior complexity of a shape is given by the number of sip in itssimplest code – this is the minimum amount of structuralinformation needed to reconstruct the shape as such.
Peter A. van der Helm Simplicity in vision
Prior complexities: shapes as such
A descriptive code is a reconstruction recipe.
If y = 5 cm, z = 3 cm, a = 70◦, and b = 110◦, thenthe code 2 ∗ (yazb) is a recipe for a parallelogram.
If y = z = 3 cm and a = b = 90◦,then the parallelogram-code would yield a square.
But for a square, a shorter code is 4 ∗ (ya)... this square-code is simpler than theparallelogram-code, because it containsfewer structural information parameters (sip).
The prior complexity of a shape is given by the number of sip in itssimplest code – this is the minimum amount of structuralinformation needed to reconstruct the shape as such.
Peter A. van der Helm Simplicity in vision
Prior complexities: structural classes
Good patterns have few alternatives (Garner, 1970).
Peter A. van der Helm Simplicity in vision
Conditional complexities: relative positions
The specific outcomes A and D are equally likely,but outcomes like A and outcomes like D are not.
Probabilities presuppose categories.
Peter A. van der Helm Simplicity in vision
Conditional complexities: relative positions
The specific outcomes A and D are equally likely
,but outcomes like A and outcomes like D are not.
Probabilities presuppose categories.
Peter A. van der Helm Simplicity in vision
Conditional complexities: relative positions
The specific outcomes A and D are equally likely,but outcomes like A and outcomes like D are not.
Probabilities presuppose categories.
Peter A. van der Helm Simplicity in vision
Conditional complexities: relative positions
From left to right:
In likelihood terms: increasing number of coincidences.
In simplicity terms: decreasing number of degrees of freedom.
Peter A. van der Helm Simplicity in vision
Conditional complexities: relative positions
The conditional complexity Iexternal reflects the effort to bring the twosticks in their proximal position starting from a general position.
van Lier et al. (1994)
Peter A. van der Helm Simplicity in vision
Conditional complexities: relative positions
The conditional complexity Iexternal reflects the effort to bring the twosticks in their proximal position starting from a general position.
van Lier et al. (1994)
Peter A. van der Helm Simplicity in vision
Conditional complexities: relative positions
The conditional complexity Iexternal reflects the effort to bring the twosticks in their proximal position starting from a general position.
van Lier et al. (1994)
Peter A. van der Helm Simplicity in vision
Conditional complexities: relative positions
The conditional complexity Iexternal reflects the effort to bring the twosticks in their proximal position starting from a general position.
van Lier et al. (1994)
Peter A. van der Helm Simplicity in vision
Conditional complexities: relative positions
The conditional complexity Iexternal reflects the effort to bring the twosticks in their proximal position starting from a general position.
van Lier et al. (1994)
Peter A. van der Helm Simplicity in vision
Conditional complexities: relative positions
Peter A. van der Helm Simplicity in vision
Occamian simplicity principle in information terms
A set of raw data as such explains nothing; it is better to searchfor a hypothesis (theory/model) by means of which the data canbe described more succinctly.
The best hypothesis H for data D then is the one that minimizesthe sum I (H|D) of:
the information I (H) needed to describe the hypothesis, and
the information I (D|H) needed to describe the data by meansof the hypothesis.
Analogous to Bayesian terminology:• the information I (H) is called the prior complexity;• the information I (D|H) is called the conditional complexity;• the sum I (H|D) is called the posterior complexity.
Peter A. van der Helm Simplicity in vision
Occamian simplicity principle in information terms
A set of raw data as such explains nothing; it is better to searchfor a hypothesis (theory/model) by means of which the data canbe described more succinctly.
The best hypothesis H for data D then is the one that minimizesthe sum I (H|D) of:
the information I (H) needed to describe the hypothesis, and
the information I (D|H) needed to describe the data by meansof the hypothesis.
Analogous to Bayesian terminology:• the information I (H) is called the prior complexity;• the information I (D|H) is called the conditional complexity;• the sum I (H|D) is called the posterior complexity.
Peter A. van der Helm Simplicity in vision
Prior and conditional complexities
Observations on planet orbits
Simple theory Many unexplained observations
priorcomplexity
conditionalcomplexity
Before 1600, planet orbits were thought to be circular
priorcomplexity
conditionalcomplexity
Complex theory Few unexplained observations
Johannes Kepler (1571–1630): planet orbits are elliptical
Peter A. van der Helm Simplicity in vision
Prior and conditional complexities
Yes No
YesNo
Peter A. van der Helm Simplicity in vision
Occamian simplicity principle in information terms
posteriorcomplexity
priorcomplexity
conditionalcomplexity
Simplicity principle: interpretation of the world on the basis of data
independencyviewpoint
dependencyviewpoint
minimize information I(H|D) = I(H) + I(D|H)
Peter A. van der Helm Simplicity in vision
The duality of simplicity and likelihood
posteriorprobability
posteriorcomplexity
priorprobability
priorcomplexity
conditionalprobability
conditionalcomplexity
Likelihood principle: interpretation of data on the basis of the world
Simplicity principle: interpretation of the world on the basis of data
independencyviewpoint
dependencyviewpoint
maximize certainty p(H|D) = p(H) ∗ p(D|H)
minimize information I(H|D) = I(H) + I(D|H)
Peter A. van der Helm Simplicity in vision
From surprisals to precisals
minimize information I(H|D) = I(H) + I(D|H)
maximize certainty p(H|D) = p(H) ∗ p(D|H)
likelihood: objective p
simplicity: descriptive I
precisal p = 2−I
modern IT
surprisal I = − log p
classical IT
Peter A. van der Helm Simplicity in vision
From surprisals to precisals
minimize information I(H|D) = I(H) + I(D|H)
maximize certainty p(H|D) = p(H) ∗ p(D|H)
likelihood: objective p
surprisal I = − log p simplicity: descriptive I
precisal p = 2−I
modern ITclassical IT
Peter A. van der Helm Simplicity in vision
From surprisals to precisals
minimize information I(H|D) = I(H) + I(D|H)
maximize certainty p(H|D) = p(H) ∗ p(D|H)
likelihood: objective p precisal p = 2−I
surprisal I = − log p simplicity: descriptive I
modern ITclassical IT
Peter A. van der Helm Simplicity in vision
Classical information theory: From Morse to Shannon
Samuel Morse (1792–1872)
The Morse Code (1835)
More frequently used lettersget shorter codes:
V (1%) → dot-dot-dot-dashE (10%) → dot
Claude Shannon (1916–2001)
A mathematical theory ofcommunication (1948)
Proved that surprisalsI = − log p
are optimal code lengths
Problems: • Codes are just labels, not representations of content.• Often, the required probabilities p are unknown.
Peter A. van der Helm Simplicity in vision
Classical information theory: From Morse to Shannon
Samuel Morse (1792–1872)
The Morse Code (1835)
More frequently used lettersget shorter codes:
V (1%) → dot-dot-dot-dashE (10%) → dot
Claude Shannon (1916–2001)
A mathematical theory ofcommunication (1948)
Proved that surprisalsI = − log p
are optimal code lengths
Problems: • Codes are just labels, not representations of content.• Often, the required probabilities p are unknown.
Peter A. van der Helm Simplicity in vision
Modern information theory in vision
Julian Hochberg (1923–)
The minimum principle (1953)
Wendell Garner (1921–2008)
Inferred subsets (1962)
Herbert Simon (1916–2001)
Language invariance (1972)
Peter A. van der Helm Simplicity in vision
Modern information theory in mathematics
Andrey Kolmogorov (1903–1987):The complexity of an object is givenby the length of its shortestreconstruction recipe (1966).
Ray Solomonoff (1926–2009):Universal probabilities, based onKolmogorov complexities, might beused to make predictions (1964).
Both proved that it doesn’t matter much which coding language isused to describe objects (the Invariance Theorem).
Peter A. van der Helm Simplicity in vision
The Fundamental Inequality
For the infinite number of enumerable probability distributionsP(x) over objects x holds, under some mild conditions, that:
K (x)− K (P) ≤ − log P(x) ≤ K (x)
where K is the Kolmogorov complexity.
In words: if a distribution P is simple, i.e., if K (P) is small,then K (x) ≈ − log P(x), and inversely, also P(x) ≈ 2−K(x).
Hence, if K (P) is small, one could use precisals 2−K(x) instead ofthe often unknown real probabilities P(x) to make predictions.
Note. An enumerable distribution is a rational-valued function of twononnegative integer arguments; examples are the uniform distribution,the normal distribution, and the Poisson distribution.
Li & Vitanyi (1997)
Peter A. van der Helm Simplicity in vision
The Fundamental Inequality
For the infinite number of enumerable probability distributionsP(x) over objects x holds, under some mild conditions, that:
K (x)− K (P) ≤ − log P(x) ≤ K (x)
where K is the Kolmogorov complexity.
In words: if a distribution P is simple, i.e., if K (P) is small,then K (x) ≈ − log P(x), and inversely, also P(x) ≈ 2−K(x).
Hence, if K (P) is small, one could use precisals 2−K(x) instead ofthe often unknown real probabilities P(x) to make predictions.
Note. An enumerable distribution is a rational-valued function of twononnegative integer arguments; examples are the uniform distribution,the normal distribution, and the Poisson distribution.
Li & Vitanyi (1997)
Peter A. van der Helm Simplicity in vision
The margin between simplicity and likelihood
Complexity K (P) of P is the length of the shortest descriptivecode that specifies the probabilities P(x) of things x .
The more categories, the more probabilities, the larger K (P).
Viewpoint-independent priors
The natural world exhibits an enormous shape diversity:K (P) probably large and prior precisals not very veridical.
Man-made environments exhibit a restricted shape diversity:K (P) probably small and prior precisals fairly veridical.
Viewpoint-dependent conditionals
An object generally gives rise to only a few view-categories:K (P) generally small and conditional precisals fairly veridical.
van der Helm (2000)
Peter A. van der Helm Simplicity in vision
The margin between simplicity and likelihood
Complexity K (P) of P is the length of the shortest descriptivecode that specifies the probabilities P(x) of things x .
The more categories, the more probabilities, the larger K (P).
Viewpoint-independent priors
The natural world exhibits an enormous shape diversity:K (P) probably large and prior precisals not very veridical.
Man-made environments exhibit a restricted shape diversity:K (P) probably small and prior precisals fairly veridical.
Viewpoint-dependent conditionals
An object generally gives rise to only a few view-categories:K (P) generally small and conditional precisals fairly veridical.
van der Helm (2000)
Peter A. van der Helm Simplicity in vision
The margin between simplicity and likelihood
Complexity K (P) of P is the length of the shortest descriptivecode that specifies the probabilities P(x) of things x .
The more categories, the more probabilities, the larger K (P).
Viewpoint-independent priors
The natural world exhibits an enormous shape diversity:K (P) probably large and prior precisals not very veridical.
Man-made environments exhibit a restricted shape diversity:K (P) probably small and prior precisals fairly veridical.
Viewpoint-dependent conditionals
An object generally gives rise to only a few view-categories:K (P) generally small and conditional precisals fairly veridical.
van der Helm (2000)
Peter A. van der Helm Simplicity in vision
Priors versus conditionals
Simpler (i.e., more regular)objects belong to smallercategories.
Simpler (i.e., less coincidental)relative positions of objectsbelong to larger categories.
Peter A. van der Helm Simplicity in vision
Everyday perception
You take a first glance
... and you make a first interpretation.
You move to take a second glance ... and you might see
... which will trigger you to update your interpretation.
Peter A. van der Helm Simplicity in vision
Everyday perception
You take a first glance ... and you make a first interpretation.
You move to take a second glance ... and you might see
... which will trigger you to update your interpretation.
Peter A. van der Helm Simplicity in vision
Everyday perception
You take a first glance ... and you make a first interpretation.
You move to take a second glance
... and you might see
... which will trigger you to update your interpretation.
Peter A. van der Helm Simplicity in vision
Everyday perception
You take a first glance ... and you make a first interpretation.
You move to take a second glance ... and you might see
... which will trigger you to update your interpretation.
Peter A. van der Helm Simplicity in vision
Everyday perception
A moving observer gets a growing sample of views of a distalscene, and can interpret it by recursively applying Bayes’ rule:
Sample D1: p1(H|D1) = p(D1|H) ∗ p(H)with p(H) as first prior.
Sample D2: p2(H|D2) = p(D2|H) ∗ p1(H|D1)with D1’s posterior as new prior.
etc ....
Well-chosen first priors speed up convergence, but their effect soonfades away, and the conditionals become decisive.
Prior precisals may not be veridical but conditional precisals are→ precisals and real probabilities give about the same predictivepower in everyday perception.
Peter A. van der Helm Simplicity in vision
Everyday perception
A moving observer gets a growing sample of views of a distalscene, and can interpret it by recursively applying Bayes’ rule:
Sample D1: p1(H|D1) = p(D1|H) ∗ p(H)with p(H) as first prior.
Sample D2: p2(H|D2) = p(D2|H) ∗ p1(H|D1)with D1’s posterior as new prior.
etc ....
Well-chosen first priors speed up convergence, but their effect soonfades away, and the conditionals become decisive.
Prior precisals may not be veridical but conditional precisals are→ precisals and real probabilities give about the same predictivepower in everyday perception.
Peter A. van der Helm Simplicity in vision
Everyday perception
A moving observer gets a growing sample of views of a distalscene, and can interpret it by recursively applying Bayes’ rule:
Sample D1: p1(H|D1) = p(D1|H) ∗ p(H)with p(H) as first prior.
Sample D2: p2(H|D2) = p(D2|H) ∗ p1(H|D1)with D1’s posterior as new prior.
etc ....
Well-chosen first priors speed up convergence, but their effect soonfades away, and the conditionals become decisive.
Prior precisals may not be veridical but conditional precisals are→ precisals and real probabilities give about the same predictivepower in everyday perception.
Peter A. van der Helm Simplicity in vision
Everyday perception
A moving observer gets a growing sample of views of a distalscene, and can interpret it by recursively applying Bayes’ rule:
Sample D1: p1(H|D1) = p(D1|H) ∗ p(H)with p(H) as first prior.
Sample D2: p2(H|D2) = p(D2|H) ∗ p1(H|D1)with D1’s posterior as new prior.
etc ....
Well-chosen first priors speed up convergence, but their effect soonfades away, and the conditionals become decisive.
Prior precisals may not be veridical but conditional precisals are→ precisals and real probabilities give about the same predictivepower in everyday perception.
Peter A. van der Helm Simplicity in vision
Summary (Part 1)
Helmholtzian likelihood principle:
Vision produces interpretations most likely to be true.
Priors cannot be quantified – conditionals probably can.
Special purpose principle:
highly veridical in – or adapted to – one environment.
Occamian simplicity principle:
Vision produces simplest organizations.
Priors perhaps not veridical – conditionals probably are.
General purpose principle:
fairly veridical in – or adaptive to – many environments.
Peter A. van der Helm Simplicity in vision
Summary (Part 1)
Helmholtzian likelihood principle:
Vision produces interpretations most likely to be true.
Priors cannot be quantified – conditionals probably can.
Special purpose principle:
highly veridical in – or adapted to – one environment.
Occamian simplicity principle:
Vision produces simplest organizations.
Priors perhaps not veridical – conditionals probably are.
General purpose principle:
fairly veridical in – or adaptive to – many environments.
Peter A. van der Helm Simplicity in vision
Part 2
Symmetry perception
Peter A. van der Helm Simplicity in vision
William Blake (1794)
Tyger! Tyger! Burning bright,In the forests of the night,What immortal hand or eyeCould frame thy fearful symmetry?
Peter A. van der Helm Simplicity in vision
Why symmetry perception?
Simplest organizations are obtained by capturing visual regularities,that is, regularities the visual system is sensitive to.
Fundamental questions
Which regularities?
What made them visual regularities:
evolutionary relevance of individual regularities?common underlying detection mechanism?
What is their perceptual nature?
What is their role in perceptual organization?
Peter A. van der Helm Simplicity in vision
Why symmetry perception?
Simplest organizations are obtained by capturing visual regularities,that is, regularities the visual system is sensitive to.
Fundamental questions
Which regularities?
What made them visual regularities:
evolutionary relevance of individual regularities?common underlying detection mechanism?
What is their perceptual nature?
What is their role in perceptual organization?
Peter A. van der Helm Simplicity in vision
What is visual regularity?
Dots arranged equidistantly along an invisible rectangular spiral.
Peter A. van der Helm Simplicity in vision
What is visual regularity?
Dots arranged equidistantly along an invisible rectangular spiral.
Peter A. van der Helm Simplicity in vision
What is visual regularity?
Apparently, without the spiral, this is not a visual regularity.
Peter A. van der Helm Simplicity in vision
What is visual regularity?
Apparently, without the spiral, this is not a visual regularity.
Peter A. van der Helm Simplicity in vision
What is visual regularity?
Key phenomenon: Symmetry and Glass patterns are about equallydetectable, and generally better detectable than repetition.
Glass (1969)
Peter A. van der Helm Simplicity in vision
What is visual regularity?
Key phenomenon: Symmetry and Glass patterns are about equallydetectable, and generally better detectable than repetition.
Glass (1969)
Peter A. van der Helm Simplicity in vision
Evolutionary considerations
PerceptionBiology
Growth
symmetry preferencein mate assessment
degree of body symmetryindicates genetic quality sensitivity to symmetry
high perceptual
in object recognitionsymmetry is useful cue
convergence on symmetricalforms in nature and art
Peter A. van der Helm Simplicity in vision
Evolutionary considerations
PerceptionBiology
mental representationsnatural construction ofGrowth
symmetry preferencein mate assessment
degree of body symmetryindicates genetic quality sensitivity to symmetry
high perceptual
in object recognitionsymmetry is useful cue
convergence on symmetricalforms in nature and art
Peter A. van der Helm Simplicity in vision
Transformational regularity: Invariance under motion
Regular patterns remain the same after rigid transformations.
Rotational symmetry Translational symmetry
Mathematically sound.
Suited for object classification.
Also suited for symmetry perception?
Peter A. van der Helm Simplicity in vision
Transformational regularity: Invariance under motion
Regular patterns remain the same after rigid transformations.
RepetitionSymmetry
Symmetry: symmetry halves identified by a 3D rotation.Repetition: repeats identified by a 2D translation.
Thus, both regularities are assigned a block structure.
Palmer (1983)
Peter A. van der Helm Simplicity in vision
Transformational regularity: Invariance under motion
Regular patterns remain the same after rigid transformations.
RepetitionSymmetry
Symmetry: symmetry halves identified by a 3D rotation.Repetition: repeats identified by a 2D translation.
Thus, both regularities are assigned a block structure.
Palmer (1983)
Peter A. van der Helm Simplicity in vision
Regularity detection anchors
Virtual lines between corresponding elements are the anchors forthe regularity detection process.
Symmetry: parallel lines which are midpoint collinear.Repetition: parallel lines which are of constant length.
Thus, both regularities are assigned a point structure.
Jenkins (1983, 1985); Wagemans et al. (1993)
Peter A. van der Helm Simplicity in vision
Regularity detection anchors
Virtual lines between corresponding elements are the anchors forthe regularity detection process.
Symmetry: parallel lines which are midpoint collinear.Repetition: parallel lines which are of constant length.
Thus, both regularities are assigned a point structure.
Jenkins (1983, 1985); Wagemans et al. (1993)
Peter A. van der Helm Simplicity in vision
Why is symmetry more salient than repetition?
Bruce & Morgan (1975)
”It is important to realize that a repetition and a symmetry areequally redundant [in the transformational ”block” sense].
Attneave (1954) suggested that symmetric patterns contained anextra kind of perceptual redundancy, in that they could bedescribed by the relationship of each point in the figure to a singleaxis of symmetry.
But this is an intuitive rather than a mathematical notion: Arepetition pattern is equally constrained by the translation rule thatsimilar elements are all positioned the same distance apart.”
Peter A. van der Helm Simplicity in vision
Holographic regularity: Invariance under growth
Regular patterns can be expanded preserving the regularity in them.
Symmetry
Pointwise body growth
Repetition
Blockwise queue growth
van der Helm & Leeuwenberg (1991)
Peter A. van der Helm Simplicity in vision
Holographic regularity: Invariance under growth
Symmetry gets a point structure – repetition gets a block structure.
ModelW = E/n Wsym = 0.5 Wrep = 0.1
where n is the total number of elements in the pattern and E thenumber of holographic identities that constitute the regularity.
W = E/n is the weight of evidence for the regularity.
Mathematically sound.
Suited for symmetry perception: it predicts a number effect inrepetition but not symmetry, and many other phenomena...
van der Helm & Leeuwenberg (1996, 1999, 2004); Csatho et al. (2003)
Peter A. van der Helm Simplicity in vision
Holographic regularity: Invariance under growth
Symmetry gets a point structure – repetition gets a block structure.
ModelW = E/n Wsym = 0.5 Wrep = 0.1
where n is the total number of elements in the pattern and E thenumber of holographic identities that constitute the regularity.
W = E/n is the weight of evidence for the regularity.
Mathematically sound.
Suited for symmetry perception: it predicts a number effect inrepetition but not symmetry, and many other phenomena...
van der Helm & Leeuwenberg (1996, 1999, 2004); Csatho et al. (2003)
Peter A. van der Helm Simplicity in vision
Holographic regularity: Invariance under growth
Symmetry gets a point structure – repetition gets a block structure.
ModelW = E/n Wsym = 0.5 Wrep = 0.1
where n is the total number of elements in the pattern and E thenumber of holographic identities that constitute the regularity.
W = E/n is the weight of evidence for the regularity.
Mathematically sound.
Suited for symmetry perception: it predicts a number effect inrepetition but not symmetry, and many other phenomena...
van der Helm & Leeuwenberg (1996, 1999, 2004); Csatho et al. (2003)
Peter A. van der Helm Simplicity in vision
Holographic weight of evidence W = E/n
Blobs strengthen repetition but weaken symmetry
Symmetry Repetition
Csatho et al. (2003)
Peter A. van der Helm Simplicity in vision
Holographic weight of evidence W = E/n
Graceful degradation
R symmetry pairs, N noise elements: W = E/n = R/n = 1−N/n2
W = 0.4
W = 0.3
Barlow & Reeves’ (1979) data:
0
1
2
3
4
5
.1 .2 .3 .4 .5 .6 .7 .8 .90 1
Detectability(d
′ )
Noise proportion N/n
van der Helm (2010)
Peter A. van der Helm Simplicity in vision
Holographic weight of evidence W = E/n
Graceful degradation
For a symmetry on R symmetry pairs or a Glass pattern on R dotdipoles, perturbed by N noise elements: E = R and n = 2R + N.
Then, W = E/n can be rewritten into W = 12+1/S with S = R/N.
On the basis of signal-detection considerations, Maloney et al.(1987) proposed the same formula for Glass patterns, and foundthat it fitted their empirical data on Glass patterns well.
Peter A. van der Helm Simplicity in vision
Holographic weight of evidence W = E/n
Graceful degradation
For a symmetry on R symmetry pairs or a Glass pattern on R dotdipoles, perturbed by N noise elements: E = R and n = 2R + N.
Then, W = E/n can be rewritten into W = 12+1/S with S = R/N.
On the basis of signal-detection considerations, Maloney et al.(1987) proposed the same formula for Glass patterns, and foundthat it fitted their empirical data on Glass patterns well.
Peter A. van der Helm Simplicity in vision
Holographic weight of evidence W = E/n
Graceful degradation
For a symmetry on R symmetry pairs or a Glass pattern on R dotdipoles, perturbed by N noise elements: E = R and n = 2R + N.
Then, W = E/n can be rewritten into W = 12+1/S with S = R/N.
On the basis of signal-detection considerations, Maloney et al.(1987) proposed the same formula for Glass patterns, and foundthat it fitted their empirical data on Glass patterns well.
Peter A. van der Helm Simplicity in vision
Holographic weight of evidence W = E/n
Weber-Fechner’s law Holographic law
∆d ′ ∝ ∆SS d ′ ∝W = E/n
d ′ = k ln (S) + C d ′ = g 12+1/S
3
4
5
2
1
0
3
4
5
2
1
0
Barlow & Reeves’ (1979) data
for g = 7.64Best fit by g/(2 + 1/S)
Barlow & Reeves’ (1979) data
for k = 0.75, C = 2.34Best fit by k ∗ ln(S) + C
5 100.05 0.1 0.25 0.5 1 2.5 5 100.05 0.1 0.25 0.5 1 2.50.025 0.025
Regularity-to-noise ratio S = R/NRegularity-to-noise ratio S = R/N
Detectability(d
′ )
Detectability(d
′ )
0.01 0.01
van der Helm (2010)
Peter A. van der Helm Simplicity in vision
Holographic weight of evidence W = E/n
Symmetry effect: overestimation of amounts of symmetry.Asymmetry effect: underestimation of amounts of symmetry.
The overall level of symmetry matters – but at every level, thedecisive factor is whether symmetry or noise is manipulated.
No incorrect estimates of amounts of symmetry or noise,but correct estimates of regularity-to-noise ratios.
Freyd & Tversky (1984); Csatho et al. (2004)
Peter A. van der Helm Simplicity in vision
Holographic weight of evidence W = E/n
Symmetry effect: overestimation of amounts of symmetry.Asymmetry effect: underestimation of amounts of symmetry.
The overall level of symmetry matters – but at every level, thedecisive factor is whether symmetry or noise is manipulated.
No incorrect estimates of amounts of symmetry or noise,but correct estimates of regularity-to-noise ratios.
Freyd & Tversky (1984); Csatho et al. (2004)
Peter A. van der Helm Simplicity in vision
Holographic weight of evidence W = E/n
Symmetry effect: overestimation of amounts of symmetry.Asymmetry effect: underestimation of amounts of symmetry.
The overall level of symmetry matters – but at every level, thedecisive factor is whether symmetry or noise is manipulated.
No incorrect estimates of amounts of symmetry or noise,but correct estimates of regularity-to-noise ratios.
Freyd & Tversky (1984); Csatho et al. (2004)
Peter A. van der Helm Simplicity in vision
Symmetry perception and perceptual organization
On the one hand
Theoretically, in structural description approaches such as
RBC (Biederman, 1987), and
SIT (Leeuwenberg & van der Helm, 2013),
symmetry is taken to be a crucial component of how perceptionimposes view-independent, or object-centered, structure on stimuli.
Empirically, symmetry has been shown to play a role in
object recognition (Pashler, 1990; Vetter & Poggio, 1994);
figure-ground segregation (Driver et al., 1992; Leeuwenberg &
Buffart, 1984; Machilsen et al., 2009);
amodal completion (Kanizsa, 1985; van Lier et al., 1995).
Peter A. van der Helm Simplicity in vision
Symmetry perception and perceptual organization
On the other hand
Is symmetry really a cue for the presence of a single object, andis repetition really a cue for the presence of multiple objects?
The proximal features of a regularity vary with viewpoint, so, howcan it be an effective grouping factor if viewed non-orthofrontally?
Symmetry Repetition
The Hoffding step, or the problem of viewpoint generalization:
How does vision arrive at a view-independent representationof a 3D scene, starting from a 2D view of the scene?
Corballis & Roldan (1974); Treder & van der Helm (2007);Szlyk et al. (1995); van der Vloed et al. (2005);Hoffding (1891); Wagemans (1993); Schmidt & Schmidt (2013)
Peter A. van der Helm Simplicity in vision
Symmetry perception and perceptual organization
On the other hand
Is symmetry really a cue for the presence of a single object, andis repetition really a cue for the presence of multiple objects?
The proximal features of a regularity vary with viewpoint, so, howcan it be an effective grouping factor if viewed non-orthofrontally?
Symmetry Repetition
The Hoffding step, or the problem of viewpoint generalization:
How does vision arrive at a view-independent representationof a 3D scene, starting from a 2D view of the scene?
Corballis & Roldan (1974); Treder & van der Helm (2007);Szlyk et al. (1995); van der Vloed et al. (2005);Hoffding (1891); Wagemans (1993); Schmidt & Schmidt (2013)
Peter A. van der Helm Simplicity in vision
Symmetry perception and perceptual organization
On the other hand
Is symmetry really a cue for the presence of a single object, andis repetition really a cue for the presence of multiple objects?
The proximal features of a regularity vary with viewpoint, so, howcan it be an effective grouping factor if viewed non-orthofrontally?
Symmetry Repetition
The Hoffding step, or the problem of viewpoint generalization:
How does vision arrive at a view-independent representationof a 3D scene, starting from a 2D view of the scene?
Corballis & Roldan (1974); Treder & van der Helm (2007);Szlyk et al. (1995); van der Vloed et al. (2005);Hoffding (1891); Wagemans (1993); Schmidt & Schmidt (2013)
Peter A. van der Helm Simplicity in vision
Symmetry perception and perceptual organization
Sawada, Li, & Pizlo (2011): Any pair of 2D curves is consistentwith a 3D symmetric interpretation (but is not always seen as such).
http://www.tadamasasawada.com/demos/sym2011
Peter A. van der Helm Simplicity in vision
Multiple symmetry perception
Two-fold versus three-fold symmetry (bootstrapping)
Detection of symmetry propagates via trapezoids:
One-fold symmetry has ”1-way” trapezoids.
Two-fold symmetry has accelerating ”2-way” trapezoids.
Three-fold symmetry only has ”1-way” trapezoids.
Wagemans et al. (1993)
Peter A. van der Helm Simplicity in vision
Multiple symmetry perception
Two-fold versus three-fold symmetry (descriptive coding)
abbaabbaabba 3*(abba)
S[(a)(b)(c)(c)(b)(a)]abccbaabccba
abbaabbaabba S[(a)(b)(b)(a)(a)(b)]
The regularity in two-fold symmetry can be captured completely— that in three-fold symmetry only partly.
Three-fold symmetry contains ”hidden order”, which is known totrigger curiosity, interest, and aesthetical feelings.
Boselie & Leeuwenberg (1985)
Peter A. van der Helm Simplicity in vision
Multiple symmetry perception
Two-fold versus three-fold symmetry (descriptive coding)
abbaabbaabba 3*(abba)
S[(a)(b)(c)(c)(b)(a)]abccbaabccba
abbaabbaabba S[(a)(b)(b)(a)(a)(b)]
The regularity in two-fold symmetry can be captured completely— that in three-fold symmetry only partly.
Three-fold symmetry contains ”hidden order”, which is known totrigger curiosity, interest, and aesthetical feelings.
Boselie & Leeuwenberg (1985)
Peter A. van der Helm Simplicity in vision
Multiple symmetry perception
Predicted detectability
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 2 3 4 5 6 7 8
Predicted
goodness
Number of symmetry axes
Transformational: 1− 1/(2A) with A is #axes
Holographic: E/n with E is #identities in code
The detectability of multiple symmetry is not as might be expectedon the basis of the number of global symmetry axes alone.
van der Helm (2011); Wenderoth & Welsh (1998); Treder et al. (2011)
Peter A. van der Helm Simplicity in vision
Multiple symmetry perception
Predicted detectability
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 2 3 4 5 6 7 8
Predicted
goodness
Number of symmetry axes
Transformational: 1− 1/(2A) with A is #axes
Holographic: E/n with E is #identities in code
The detectability of multiple symmetry is not as might be expectedon the basis of the number of global symmetry axes alone.
van der Helm (2011); Wenderoth & Welsh (1998); Treder et al. (2011)
Peter A. van der Helm Simplicity in vision
Multiple symmetry in nature and art
Skewed distribution in flowers
monocotyledons dicotyledons
80% 70%
Perhaps, 3-fold and 5-fold symmetrical flowers have a procreationadvantage over others, because their visual appearance attractsmore pollinators.
Note. Insect vision exists 400 million years — flowers 150 million years.
Heywood (1993), van der Helm (2011)
Peter A. van der Helm Simplicity in vision
Multiple symmetry in nature and art
Skewed distribution in flowers
monocotyledons dicotyledons
80% 70%
Perhaps, 3-fold and 5-fold symmetrical flowers have a procreationadvantage over others, because their visual appearance attractsmore pollinators.
Note. Insect vision exists 400 million years — flowers 150 million years.
Heywood (1993), van der Helm (2011)
Peter A. van der Helm Simplicity in vision
Multiple symmetry in nature and art
Skewed distribution in designs
10
20
30
40
50
60
87654321
Per
cen
tag
e o
f d
eco
rati
ve b
and
s
Number of symmetry axes in motifs
Decorative art Mystical art
Throughout history, humans have seen 3-fold and 5-foldsymmetrical motifs as being more appropriate for mystical art.
Hardonk (1999); van der Helm (2011)
Peter A. van der Helm Simplicity in vision
Multiple symmetry in nature and art
Skewed distribution in designs
10
20
30
40
50
60
87654321
Per
cen
tag
e o
f d
eco
rati
ve b
and
s
Number of symmetry axes in motifs
Decorative art Mystical art
Throughout history, humans have seen 3-fold and 5-foldsymmetrical motifs as being more appropriate for mystical art.
Hardonk (1999); van der Helm (2011)
Peter A. van der Helm Simplicity in vision
Summary (Part 2)
Symmetry perception
Evolution did not select individual visual regularities, but itselected a detection mechanism with sufficient survival value.
Many known regularity-detection phenomena can be explainedin terms of representation and/or process properties.
It is clear that symmetry plays a role in perceptualorganization, but its exact role is still unclear.
Peter A. van der Helm Simplicity in vision
Part 3
Cognitive architecture
Peter A. van der Helm Simplicity in vision
Cognitive architecture
In artificial intelligence research, a cognitive architecture is acomputational model of not only resulting behaviour but alsostructural properties of intelligent systems.
These structural properties can be abstract as well as physicalproperties implemented in such systems.
In cognitive neuroscience, cognitive architectures
are blueprints for systems that act like the human system;
should have an eye for neural plausibility;
unify processes and representations.
Anderson (1983); Newell (1990); Thagard (2012)
Peter A. van der Helm Simplicity in vision
Cognitive architecture
In artificial intelligence research, a cognitive architecture is acomputational model of not only resulting behaviour but alsostructural properties of intelligent systems.
These structural properties can be abstract as well as physicalproperties implemented in such systems.
In cognitive neuroscience, cognitive architectures
are blueprints for systems that act like the human system;
should have an eye for neural plausibility;
unify processes and representations.
Anderson (1983); Newell (1990); Thagard (2012)
Peter A. van der Helm Simplicity in vision
Visual pathways in the brain
Visualcortex
(b)(a)
LGN
OC
Retina Object perception
Spatial perception
Ungerleider & Mishkin (1982)
Peter A. van der Helm Simplicity in vision
PATVISH: Combined action of perception and attention
Attention
Binding of similar features
Extraction of visual features
Global structures
Unorganized parts
Organized wholes
RepresentationsSubprocesses
Binding of similar features
Perception
Selection of different features
Local features
Perception comprises three neurally intertwined subprocesses(Lamme, Super, & Spekreijse, 1998; van der Helm, 2012)
Resulting percepts reflect hierarchical stimulus organizations(Leeuwenberg & van der Helm, 1991)
Attention subserves top-down scrutiny of established percepts(Hochstein & Ahissar, 2002)
Peter A. van der Helm Simplicity in vision
Hierarchical organizations: Global vs local
Stimulus
Local features
Compatible with perceived global structure
Incompatible with perceived global structure
Perceived global organization
Peter A. van der Helm Simplicity in vision
The reverse hierarchy theory of perceptual learning
Attention can be deployed in a top-down fashion to any level in thevisual hierarchy (Hochstein & Ahissar, 2002; see also Wolfe, 2007)
Thus, it first captures global structures coded in higher areas and– if required by task and allowed by time – it may descend alongrecurrent connections to capture local features coded in lower areas
Peter A. van der Helm Simplicity in vision
Wholes versus parts
Local features are the first ones processed by perception,but global structures are the first ones encountered by attention.
This agrees with the Gestalt idea that, behaviourally, wholesdominate parts — which also has been framed in terms of
global precedence (Navon, 1977);
configural superiority (Pomerantz et al., 1977);
superstructure dominance (Leeuwenberg & van der Helm, 1991);
primacy of holistic properties (Kimchi, 2003).
Note. Participants in behavioural experiments respond on the basis ofwhat they have perceived, so, responses are indicative of properties ofpercepts rather than of properties of the perceptual process itself.
Peter A. van der Helm Simplicity in vision
Wholes versus parts
Local features are the first ones processed by perception,but global structures are the first ones encountered by attention.
This agrees with the Gestalt idea that, behaviourally, wholesdominate parts — which also has been framed in terms of
global precedence (Navon, 1977);
configural superiority (Pomerantz et al., 1977);
superstructure dominance (Leeuwenberg & van der Helm, 1991);
primacy of holistic properties (Kimchi, 2003).
Note. Participants in behavioural experiments respond on the basis ofwhat they have perceived, so, responses are indicative of properties ofpercepts rather than of properties of the perceptual process itself.
Peter A. van der Helm Simplicity in vision
Global structures mask incompatible local features
Stimulus
Local features
Compatible with perceived global structure
Incompatible with perceived global structure
Perceived global organization
Peter A. van der Helm Simplicity in vision
PATVISH: Combined action of perception and attention
Attention
Binding of similar features
Extraction of visual features
Global structures
Unorganized parts
Organized wholes
RepresentationsSubprocesses
Binding of similar features
Perception
Selection of different features
Local features
Perception comprises three neurally intertwined subprocesses(Lamme, Super, & Spekreijse, 1998; van der Helm, 2012)
Resulting percepts reflect hierarchical stimulus organizations(Leeuwenberg & van der Helm, 1991)
Attention subserves top-down scrutiny of established percepts(Hochstein & Ahissar, 2002)
Peter A. van der Helm Simplicity in vision
Neurally intertwined subprocesses of perception
Selection of different features
Binding of similar features
Binding of similar features
Extraction of visual features
Integrated percepts (perceptual organizations) are yielded by:
feedforward extraction of – or tuning to – visual features
horizontal binding of similar features
— synchronization
recurrent selection of different features
Peter A. van der Helm Simplicity in vision
Neurally intertwined subprocesses of perception
Selection of different features
Binding of similar features
Binding of similar features
Extraction of visual features
Integrated percepts (perceptual organizations) are yielded by:
feedforward extraction of – or tuning to – visual features
horizontal binding of similar features — synchronization
recurrent selection of different features
Peter A. van der Helm Simplicity in vision
Neuronal synchronization
Neuronal synchronization
The phenomenon that, depending on the input, transientassemblies of neurons temporarily synchronize their activity.
How those transient assemblies of neurons physically go in and outof existence is typically a topic in dynamic systems theory.(e.g., van Leeuwen et al., 1997; Campbell et al., 1999; Harris et al., 2003)
Neuronal synchronization has been associated with corticalintegration, and more general, with cognitive processing.(Milner, 1974; von der Malsburg, 1981)
Synchronization in the gamma band (30–70 Hz), in particular, hasbeen associated with ”horizontal” feature binding in vision.(Eckhorn et al., 1988; Gray & Singer, 1989; Gilbert, 1992)
Peter A. van der Helm Simplicity in vision
Perceptual integration capability
In PATVISH, gamma synchronization is taken to subserve bindingof similar features – thereby, it also has an effect on selection ofdifferent features, so, in total, it underlies perceptual integration.(or incremental grouping, as Roelfsema, 2006, called it)
What happens if gamma synchronization is impaired?(as in autism and schizophrenia; Sun et al., 2012; Uhlhaas et al., 2005)
Then, by PATVISH, one gets reduced perceptual integration,that is, reduced construction of global structures ...so that top-down atention has better access to local features.(as in autism and Williams syndrome; Frith, 1989; Bernardino et al., 2012)
Peter A. van der Helm Simplicity in vision
Perceptual integration capability
In PATVISH, gamma synchronization is taken to subserve bindingof similar features – thereby, it also has an effect on selection ofdifferent features, so, in total, it underlies perceptual integration.(or incremental grouping, as Roelfsema, 2006, called it)
What happens if gamma synchronization is impaired?(as in autism and schizophrenia; Sun et al., 2012; Uhlhaas et al., 2005)
Then, by PATVISH, one gets reduced perceptual integration,that is, reduced construction of global structures ...so that top-down atention has better access to local features.(as in autism and Williams syndrome; Frith, 1989; Bernardino et al., 2012)
Peter A. van der Helm Simplicity in vision
Perceptual integration capability
In PATVISH, gamma synchronization is taken to subserve bindingof similar features – thereby, it also has an effect on selection ofdifferent features, so, in total, it underlies perceptual integration.(or incremental grouping, as Roelfsema, 2006, called it)
What happens if gamma synchronization is impaired?(as in autism and schizophrenia; Sun et al., 2012; Uhlhaas et al., 2005)
Then, by PATVISH, one gets reduced perceptual integration,that is, reduced construction of global structures ...so that top-down atention has better access to local features.(as in autism and Williams syndrome; Frith, 1989; Bernardino et al., 2012)
Peter A. van der Helm Simplicity in vision
The local advantage phenomenon in autism
The local advantage phenomenon: Autistics perform betterthan typical on tasks in which local features are to be discerned.(Shah & Frith, 1983, 1993; Jolliffe & Baron-Cohen, 1997)
Embedded figures taskBlock design task
Perceived global structures mask incompatible local features— in autism, this masking is weaker than typical, due to reducedperceptual integration caused by impaired gamma synchronization.
Peter A. van der Helm Simplicity in vision
The local advantage phenomenon in autism
The local advantage phenomenon: Autistics perform betterthan typical on tasks in which local features are to be discerned.(Shah & Frith, 1983, 1993; Jolliffe & Baron-Cohen, 1997)
Embedded figures taskBlock design task
Perceived global structures mask incompatible local features— in autism, this masking is weaker than typical, due to reducedperceptual integration caused by impaired gamma synchronization.
Peter A. van der Helm Simplicity in vision
Neurally intertwined subprocesses of perception
Selection of different features
Binding of similar features
Binding of similar features
Extraction of visual features
Integrated percepts (perceptual organizations) are yielded by:
feedforward extraction of visual features
horizontal binding of similar features
recurrent selection of different features
Peter A. van der Helm Simplicity in vision
The minimal-coding algorithm PISA
PISA computes – for symbol strings – simplest hierarchical codesby capturing a maximum amount of visual regularity.
Brain PISA
Selection of different features
Extraction of visual features
Binding of similar features
Binding of similar features
All-pairs shortest path method
All-substrings identification
Hyperstrings
Hyperstrings
The correspondence between the three intertwined subprocesses isstriking, but does this correspondence go any deeper?
van der Helm (2004, 2012, 2014)
Peter A. van der Helm Simplicity in vision
The minimal-coding algorithm PISA
PISA computes – for symbol strings – simplest hierarchical codesby capturing a maximum amount of visual regularity.
Brain PISA
Selection of different features
Extraction of visual features
Binding of similar features
Binding of similar features
All-pairs shortest path method
All-substrings identification
Hyperstrings
Hyperstrings
The correspondence between the three intertwined subprocesses isstriking, but does this correspondence go any deeper?
van der Helm (2004, 2012, 2014)
Peter A. van der Helm Simplicity in vision
Structural information theory (initiated by Leeuwenberg, 1968)
Structural information theory (SIT)
A general theory of human visual perceptual organization.
It adopts the simplicity principle, which holds that thesimplest organization of a stimulus is the one perceived.
To make predictions, it proposes a coding language todetermine simplest codes of symbol strings (which mayrepresent visual patterns) by capturing a maximumamount of repetitions, symmetries, and alternations.
Note: Repetitions, symmetries, and alternations are the only transparentholographic regularities – this mathematical notion explains much of humansymmetry perception (van der Helm & Leeuwenberg, 1991, 1996, 1999, 2004).
Leeuwenberg & van der Helm (2013); van der Helm (2014)
Peter A. van der Helm Simplicity in vision
Computing simplest codes of strings: The basic idea
String:
a b a b a b q c d e p d e c f p q k p q l m p q u
Substrings:
a b a b a b → 3 ∗ (ab)
c d e p d e c → S [(c)(de), (p)]
p q k p q l m p q u → 〈(pq)〉/〈(k)(lm)(u)〉
Once every substring has thus been encoded in the simplest way,there are O(2N) candidate codes for the entire string, but thenDijkstra’s (1959) O(N2) shortest path method can be applied toselect a simplest one – which, in this example, is:
3 ∗ (ab) q S [(c)(de), (p)] f 〈(pq)〉/〈(hk)(lm)(u)〉
van der Helm & Leeuwenberg (1986)
Peter A. van der Helm Simplicity in vision
Computing simplest codes of strings: The basic idea
String:
a b a b a b q c d e p d e c f p q k p q l m p q u
Substrings:
a b a b a b → 3 ∗ (ab)
c d e p d e c → S [(c)(de), (p)]
p q k p q l m p q u → 〈(pq)〉/〈(k)(lm)(u)〉
Once every substring has thus been encoded in the simplest way,there are O(2N) candidate codes for the entire string, but thenDijkstra’s (1959) O(N2) shortest path method can be applied toselect a simplest one – which, in this example, is:
3 ∗ (ab) q S [(c)(de), (p)] f 〈(pq)〉/〈(hk)(lm)(u)〉
van der Helm & Leeuwenberg (1986)
Peter A. van der Helm Simplicity in vision
Distributed representations of SIT codes
Assume that, for the string ababfabab, a simplest ISA-form is known foreach of the O(N2) substrings (a few are shown):
1 2 3 4 5 6 7 8 9 10
S[(a),(b)] <(a)>/<(bf) 2*((b))>
b b f
S[(2*(ab)), (f)]
2*(ab)2*(ab) S[(b),(fa)]
S[(ab),(f)]
b ba a aa
Then, O(2N) codes for the entire string are possible – for instance, thepath along nodes 1, 4, 5, 6, 10 yields code S [(a), (b)] b f 2 ∗ (ab)
How to select the simplest code?
Peter A. van der Helm Simplicity in vision
Distributed representations of SIT codes
Assume that, for the string ababfabab, a simplest ISA-form is known foreach of the O(N2) substrings (a few are shown):
1 2 3 4 5 6 7 8 9 10
<(a)>/<(bf) 2*((b))>
b
S[(2*(ab)), (f)]
2*(ab) S[(b),(fa)]
S[(ab),(f)]
b b
S[(a),(b)]
b f
2*(ab)
a a aa
Then, O(2N) codes for the entire string are possible – for instance, thepath along nodes 1, 4, 5, 6, 10 yields code S [(a), (b)] b f 2 ∗ (ab)
How to select the simplest code?
Peter A. van der Helm Simplicity in vision
Distributed representations of SIT codes
Assume that, for the string ababfabab, a simplest ISA-form is known foreach of the O(N2) substrings (a few are shown):
1 2 3 4 5 6 7 8 9 10
<(a)>/<(bf) 2*((b))>
b
S[(2*(ab)), (f)]
2*(ab) S[(b),(fa)]
S[(ab),(f)]
b b
S[(a),(b)]
b f
2*(ab)
a a aa
Then, O(2N) codes for the entire string are possible – for instance, thepath along nodes 1, 4, 5, 6, 10 yields code S [(a), (b)] b f 2 ∗ (ab)
How to select the simplest code?
Peter A. van der Helm Simplicity in vision
Serial distributed processing to select simplest codes
Take the complexities of the ISA-forms as the lengths of the edges ...
1 2 3 4 5 6 7 8 9 10
4
3 4
4
3
6
1 11 1 1
2
1 11 1
and apply Dijkstra’s (1959) shortest path method which yields theminimal distance dmin(1,N) from node 1 to node N, by determining
dmin(1, k) = MINp<k{dmin(1, p) + d(p, k)} for k = 2, 3, ...,N.
This is a ”smart” O(N2) method to evaluate O(2N) paths.
Dijkstra (1959)
Peter A. van der Helm Simplicity in vision
Serial distributed processing to select simplest codes
Take the complexities of the ISA-forms as the lengths of the edges ...
1 2 3 4 5 6 7 8 9 10
4
3 4
4
3
6
1 11 1 1
2
1 11 1
and apply Dijkstra’s (1959) shortest path method which yields theminimal distance dmin(1,N) from node 1 to node N, by determining
dmin(1, k) = MINp<k{dmin(1, p) + d(p, k)} for k = 2, 3, ...,N.
This is a ”smart” O(N2) method to evaluate O(2N) paths.
Dijkstra (1959)
Peter A. van der Helm Simplicity in vision
Serial distributed processing to select simplest codes
Take the complexities of the ISA-forms as the lengths of the edges ...
1 2 3 4 5 6 7 8 9 10
4
3 4
4
3
6
1 11 1 1
2
1 11 1
and apply Dijkstra’s (1959) shortest path method which yields theminimal distance dmin(1,N) from node 1 to node N, by determining
dmin(1, k) = MINp<k{dmin(1, p) + d(p, k)} for k = 2, 3, ...,N.
This is a ”smart” O(N2) method to evaluate O(2N) paths.
Dijkstra (1959)
Peter A. van der Helm Simplicity in vision
Parallel distributed processing to select shortest paths
”Smart” hilly tube system
T = 0
1
3
4
5
2
0
Fluid takes one time unit to ”exite” one straight tube segment
-
Peter A. van der Helm Simplicity in vision
Parallel distributed processing to select shortest paths
”Smart” hilly tube system
T = 1
0
1
2
3
4
5
Fluid, arriving at a node, ”inhibits” other incoming tubes
-
Peter A. van der Helm Simplicity in vision
Parallel distributed processing to select shortest paths
”Smart” hilly tube system
T = 2
0
2
3
4
5
1
Fluid flows on, also in blocked tubes
-
Peter A. van der Helm Simplicity in vision
Parallel distributed processing to select shortest paths
”Smart” hilly tube system
T = 3
0
1
2
3
4
5
Fluid in blocked tubes hardens in one time unit
-
Peter A. van der Helm Simplicity in vision
Parallel distributed processing to select shortest paths
”Smart” hilly tube system
T = 4
0
1
3
4
5
2
Fluid exits through the shortest path
-
Peter A. van der Helm Simplicity in vision
Parallel distributed processing to select shortest paths
”Smart” hilly tube system
T = 5
0
1
2
3
4
5
All other paths harden, leaving a flow in only the shortest path
-
Peter A. van der Helm Simplicity in vision
Computing simplest codes of strings: The problem
Say, for some string, substring ababpbaba has been encoded into
S [(a)(b)(a)(b), (p)]
then, argument (a)(b)(a)(b) can be recoded hierarchically into
2 ∗ ((a)(b))
yielding the simpler hierarchical code S [2 ∗ ((a)(b)), (p)]
In principle, a substring can be encoded into an exponentialnumber of symmetries – or, likewise, alternations – which, each,have to be recoded hierarchically in order to find a simplest one.
Hierarchical recoding of each symmetry and alternation separatelywould require an intractable, superexponential, amount of work.
Peter A. van der Helm Simplicity in vision
Computing simplest codes of strings: The problem
Say, for some string, substring ababpbaba has been encoded into
S [(a)(b)(a)(b), (p)]
then, argument (a)(b)(a)(b) can be recoded hierarchically into
2 ∗ ((a)(b))
yielding the simpler hierarchical code S [2 ∗ ((a)(b)), (p)]
In principle, a substring can be encoded into an exponentialnumber of symmetries – or, likewise, alternations – which, each,have to be recoded hierarchically in order to find a simplest one.
Hierarchical recoding of each symmetry and alternation separatelywould require an intractable, superexponential, amount of work.
Peter A. van der Helm Simplicity in vision
Selection of longest pencil (1)
Measure the pencil lengths serially or in parallel ..... not smart!
Peter A. van der Helm Simplicity in vision
Selection of longest pencil (1)
Measure the pencil lengths serially or in parallel
..... not smart!
Peter A. van der Helm Simplicity in vision
Selection of longest pencil (1)
Measure the pencil lengths serially or in parallel ..... not smart!
Peter A. van der Helm Simplicity in vision
Selection of longest pencil (2)
Is this serial or parallel processing? No, it is transparallel processing!
Peter A. van der Helm Simplicity in vision
Selection of longest pencil (2)
Is this serial or parallel processing? No, it is transparallel processing!
Peter A. van der Helm Simplicity in vision
Selection of longest pencil (2)
Is this serial or parallel processing?
No, it is transparallel processing!
Peter A. van der Helm Simplicity in vision
Selection of longest pencil (2)
Is this serial or parallel processing? No, it is transparallel processing!
Peter A. van der Helm Simplicity in vision
Computing simplest codes of strings: The solution
Gather, in O(N2) time, the arguments of the O(2N) symmetriesinto which a substring can be encoded in a directed acyclic graph.
Substring: a b a b f a b a b g b a b a f b a b a
6
7
8
9
101
2
3
4
5
(a)
(b)
(bab)(bab)
(a)
(b)
(f)
(b)
(a)
(b)
(a)
(aba) (aba)
S [(aba)(b)(f )(a)(bab), (g)]
The graph is provably a hyperstring, which implies that thoseO(2N) arguments can be recoded in a transparallel fashion, thatis, simultaneously as if only one argument were concerned.
van der Helm (2004, 2014)
Peter A. van der Helm Simplicity in vision
Computing simplest codes of strings: The solution
Gather, in O(N2) time, the arguments of the O(2N) symmetriesinto which a substring can be encoded in a directed acyclic graph.
Substring: a b a b f a b a b g b a b a f b a b a
6
7
8
9
101
2
3
4
5
(a)
(b)
(bab)
(a)(b)
(a)
(b)
(aba)(aba)
(b)
(f)
(a)
(bab)
S [(aba)(b)(f )(a)(bab), (g)]
The graph is provably a hyperstring, which implies that thoseO(2N) arguments can be recoded in a transparallel fashion, thatis, simultaneously as if only one argument were concerned.
van der Helm (2004, 2014)
Peter A. van der Helm Simplicity in vision
Computing simplest codes of strings: The solution
Gather, in O(N2) time, the arguments of the O(2N) symmetriesinto which a substring can be encoded in a directed acyclic graph.
Substring: a b a b f a b a b g b a b a f b a b a
6
7
8
9
101
2
3
4
5
(a)
(b)
(bab)
(a)(b)
(a)
(b)
(aba)(aba)
(b)
(f)
(a)
(bab)
S [(aba)(b)(f )(a)(bab), (g)]
The graph is provably a hyperstring, which implies that thoseO(2N) arguments can be recoded in a transparallel fashion, thatis, simultaneously as if only one argument were concerned.
van der Helm (2004, 2014)
Peter A. van der Helm Simplicity in vision
Hyperstrings
Manystrings
h1 h8h7h6h5h4h3h2One string
representationDistributed
xcv
abcfabcg
abcv
xcfabcg
ayv
abcfw
abcfayg
xcfw
xcfxcg
xcfayg
ayfxcg
ayfayg
ayfabcg
abcfxcg
ayfw
1 2 3 4 5 6 7 8 9
v
w
gf
x
a b c
y
a
x
b
y
c
Peter A. van der Helm Simplicity in vision
Hyperstrings
representationDistributed
Manystrings
h1 h8h7h6h5h4h3h2One string
xcv
abcfabcg
abcv
xcfabcg
ayv
abcfw
abcfayg
xcfw
xcfxcg
xcfayg
ayfxcg
ayfayg
ayfabcg
abcfxcg
ayfw
1 2 3 4 5 6 7 8 9
v
w
gf
x
a b c
y
a
x
b
y
c
Peter A. van der Helm Simplicity in vision
Hyperstrings
representationDistributed
Manystrings
h1 h8h7h6h5h4h3h2One string
xcv
abcfabcg
abcv
xcfabcg
ayv
abcfw
abcfayg
xcfw
xcfxcg
xcfayg
ayfxcg
ayfayg
ayfabcg
abcfxcg
ayfw
1 2 3 4 5 6 7 8 9
x
v
x
y y
w
gcbafcba
Peter A. van der Helm Simplicity in vision
Hyperstrings
representationDistributed
Manystrings
h1 h8h7h6h5h4h3h2
xcv
abcfabcg
abcv
xcfabcg
ayv
abcfw
abcfayg
xcfw
xcfxcg
xcfayg
ayfxcg
ayfayg
ayfabcg
abcfxcg
ayfw
One string
1 2 3 4 5 6 7 8 9
x
v
x
y y
w
gcbafcba
Peter A. van der Helm Simplicity in vision
Transparallel processing by hyperstrings
h1 h8h7h6h5h4h3h2
1 2 3 4 5 6 7 8 9
x
v
x
y y
w
gcbafcba
Substrings h1h2h3 and h5h6h7 are identical, so that the string canbe encoded into the alternation 〈(h1h2h3)〉/〈(h4)(h8)〉 which, inone go, represents alternations in three different strings, namely:
〈(abc)〉/〈(f )(g)〉 in the string abcfabcg〈(xc)〉/〈(f )(g)〉 in the string xcfxcg〈(ay)〉/〈(f )(g)〉 in the string ayfayg
Hence, the O(2N) strings in a hyperstring can be encoded as ifonly one string were concerned – an exponential reduction in work.
Peter A. van der Helm Simplicity in vision
Transparallel processing by hyperstrings
h1 h8h7h6h5h4h3h2
1 2 3 4 5 6 7 8 9
x
v
x
y y
w
gcbafcba
Substrings h1h2h3 and h5h6h7 are identical, so that the string canbe encoded into the alternation 〈(h1h2h3)〉/〈(h4)(h8)〉 which, inone go, represents alternations in three different strings, namely:
〈(abc)〉/〈(f )(g)〉 in the string abcfabcg〈(xc)〉/〈(f )(g)〉 in the string xcfxcg〈(ay)〉/〈(f )(g)〉 in the string ayfayg
Hence, the O(2N) strings in a hyperstring can be encoded as ifonly one string were concerned – an exponential reduction in work.
Peter A. van der Helm Simplicity in vision
Transparallel processing by hyperstrings
PISA computes – for symbol strings – simplest hierarchical codesby capturing a maximum amount of visual regularity.
Brain PISA
Selection of different features
Extraction of visual features
Binding of similar features
Binding of similar features
All-pairs shortest path method
All-substrings identification
Hyperstrings
Hyperstrings
Proposal: Hyperstrings correspond to transient neural assemblies,whose synchronization manifests transparallel feature processing.
van der Helm (2012, 2014)
Peter A. van der Helm Simplicity in vision
Transparallel processing by hyperstrings
PISA computes – for symbol strings – simplest hierarchical codesby capturing a maximum amount of visual regularity.
Brain PISA
Selection of different features
Extraction of visual features
Binding of similar features
Binding of similar features
All-pairs shortest path method
All-substrings identification
Hyperstrings
Hyperstrings
Proposal: Hyperstrings correspond to transient neural assemblies,whose synchronization manifests transparallel feature processing.
van der Helm (2012, 2014)
Peter A. van der Helm Simplicity in vision
Hypotheses about the mind
Inspired by Feynman’s (1982) idea of quantum computers – which,for some applications, promise an exponential reduction in the timeneeded to complete a computing job – Penrose (1989) proposed:
The quantum mind hypothesis: Quantum mechanicalphenomena, such as quantum entanglement andsuperposition, are the basis of neuronal synchronization.
However, quantum phenomena do not seem to last long enough tobe useful for neuro-cognitive processing (e.g., Tegmark, 2000).
Transparallel processing can be done on classical computers andimplies, for some applications, an exponential reduction too.
The transparallel mind hypothesis: Flexible cognitivearchitecture is implemented in the brain by synchronizedneural assemblies mediating transparallel feature processing.
Koffka, 1935; Hebb, 1949; Kelso, 1995; Lehar, 2003; Buzsaki, 2006
Peter A. van der Helm Simplicity in vision
Hypotheses about the mind
Inspired by Feynman’s (1982) idea of quantum computers – which,for some applications, promise an exponential reduction in the timeneeded to complete a computing job – Penrose (1989) proposed:
The quantum mind hypothesis: Quantum mechanicalphenomena, such as quantum entanglement andsuperposition, are the basis of neuronal synchronization.
However, quantum phenomena do not seem to last long enough tobe useful for neuro-cognitive processing (e.g., Tegmark, 2000).
Transparallel processing can be done on classical computers andimplies, for some applications, an exponential reduction too.
The transparallel mind hypothesis: Flexible cognitivearchitecture is implemented in the brain by synchronizedneural assemblies mediating transparallel feature processing.
Koffka, 1935; Hebb, 1949; Kelso, 1995; Lehar, 2003; Buzsaki, 2006
Peter A. van der Helm Simplicity in vision
Summary (Part 3)
Cognitive architectures call for specifications of ingredients neededto build unified theories of cognition — thereby, they stimulateresearchers to think about metatheoretical aspects such as
representational theory — connectionism — DST;
forms of neuro-cognitive processing;
metaphors of cognition;
and more specifically, about things such as
tractability of proposed processes;
unification of processes and representations;
neural building blocks of cognition;
different than typical cognitive processing.
Peter A. van der Helm Simplicity in vision
Conclusion
Could simplicity guide perceptual organization?
Well, there is still much to do before cognitive neuroscience mayarrive at a ”grand unified theory” of perceptual organization, but:
The high combinatorial capacity and speed of the perceptualorganization process might be enabled by a flexible cognitivearchitecture, constituted by transient neural assemblies exhibitingsynchronization as manifestation of transparallel feature processing.
The resulting mental representation of a scene can, at the neurallevel, be described as a relatively stable physical state, and at thecognitive level, as a state which is informationally simplest due tomaximal extraction of visual regularities.
A perceptual organization process yielding simplest organizationscan be conceived of as a form of unconscious inference which is
an efficient user of internal resources;a fairly reliable source of knowledge about the external world.
Peter A. van der Helm Simplicity in vision
Conclusion
Could simplicity guide perceptual organization?
Well, there is still much to do before cognitive neuroscience mayarrive at a ”grand unified theory” of perceptual organization, but:
The high combinatorial capacity and speed of the perceptualorganization process might be enabled by a flexible cognitivearchitecture, constituted by transient neural assemblies exhibitingsynchronization as manifestation of transparallel feature processing.
The resulting mental representation of a scene can, at the neurallevel, be described as a relatively stable physical state, and at thecognitive level, as a state which is informationally simplest due tomaximal extraction of visual regularities.
A perceptual organization process yielding simplest organizationscan be conceived of as a form of unconscious inference which is
an efficient user of internal resources;a fairly reliable source of knowledge about the external world.
Peter A. van der Helm Simplicity in vision
Conclusion
Could simplicity guide perceptual organization?
Well, there is still much to do before cognitive neuroscience mayarrive at a ”grand unified theory” of perceptual organization, but:
The high combinatorial capacity and speed of the perceptualorganization process might be enabled by a flexible cognitivearchitecture, constituted by transient neural assemblies exhibitingsynchronization as manifestation of transparallel feature processing.
The resulting mental representation of a scene can, at the neurallevel, be described as a relatively stable physical state, and at thecognitive level, as a state which is informationally simplest due tomaximal extraction of visual regularities.
A perceptual organization process yielding simplest organizationscan be conceived of as a form of unconscious inference which is
an efficient user of internal resources;a fairly reliable source of knowledge about the external world.
Peter A. van der Helm Simplicity in vision
Conclusion
Could simplicity guide perceptual organization?
Well, there is still much to do before cognitive neuroscience mayarrive at a ”grand unified theory” of perceptual organization, but:
The high combinatorial capacity and speed of the perceptualorganization process might be enabled by a flexible cognitivearchitecture, constituted by transient neural assemblies exhibitingsynchronization as manifestation of transparallel feature processing.
The resulting mental representation of a scene can, at the neurallevel, be described as a relatively stable physical state, and at thecognitive level, as a state which is informationally simplest due tomaximal extraction of visual regularities.
A perceptual organization process yielding simplest organizationscan be conceived of as a form of unconscious inference which is
an efficient user of internal resources;a fairly reliable source of knowledge about the external world.
Peter A. van der Helm Simplicity in vision