what rules are used to group objects?

28 September, 2000 HKU 1

What rules are used to group objects?

• Definitions (Feature Lists)• Family Resemblance• Similarity to Prototypes• Exemplar models


Definitions and Features

• Dogs are animals that have four legs, have fur, bark, wag their tails…

Animal Four legs Fur Barks Wags tail

Banyan Tree X X X X X

Goldish √ X X X X

Persian Cat √ √ √ X X

German Shepherd √ √ √ √ √

Dachshund √ √ √ √ √

Mexican Hairless √ √ X √ √

Barking Deer √ √ √ √ ?


Family Resemblance

• Ludwig Wittgenstein (1953) proposed that games could not be defined or categorized by features.

• Rather, any game shares some resemblance to some (but not all) other games.


Similarity to Prototypes

• Rosch (1978). Prototype is a central, average, representation (real or constructed) of a category.

• Tokens sufficiently similar to the prototype are considered members of that category.

• Memory for specific exemplars.


Exemplar Models

• To remember a category, just remember all the members of the category.

• Head-filling-up problem.

• Evidence for abstractions.


Perception

Top-down

Or

Bottom-up?


The problem of perception

• How does our perceptual system arrive at a “best” representation of the world?

• Conflicting demands:– Accuracy– Efficiency


Data-driven processing(bottom-up)CognitionNeural ProcessingThe Real World


• Standard (naïve) assumption is that perception is entirely data-driven

• Why is this naïve?– Perception must be accomplished in

sub-optimal conditions• Need for speed• Need for computational efficiency• But also need for accuracy!

– A common solution: “Best guess”


Concealed and bi-stable figures: Evidence for a role of knowledge in perception


Application of knowledge changes the way concealed

and bi-stable figures are perceived

Cognition

Neural Processing

The Real World

• Changes conscious processing (interpretation, object recognition)

• Changes unconscious processes (patterns of eye movements)


Application of Knowledge

• Can be automatic – Either innately, or once learned

• Can also be controlled


Rabbit/Duck

Jastrow (1900)


Impossible Trident


Illusions: Obligatory application of

knowledge in contradiction to available data.


Application of knowledge is obligatory in these illusions

Cognition

Neural Processing

The Real World


Sources of Illusions

• Illusions arise because our perceptual system is structured to act as if certain assumptions about the world are true.

• We can construct situations in which those assumptions appear to be true, but in fact are not. These situations are called illusions.


Sources of Illusions

• Knowledge of visual cues to distance – The Müller Lyer Illusion

• Filling in missing information– Object occlusion

• Using context– Circles of relative size

– Text tricks

– Shades of white

– Circularity in pitch perception


The Müller-Lyer Illusion

• Which vertical line is longer?

• Neither! They are the same length!

Müller-Lyer (1889)


Explanation

• We need to be able to adjust our knowledge of an object’s size based on our perception of how far away from us it is.

• The arms of the arrows make the vertical lines look like the edges of corners – one pointing toward us, one pointing away.

• That makes it appear as if the vertex of the corner (the vertical line) is a different distance from us in each figure.


What triangle?


Explanation

• Most things in the world do not have abrupt, regular discontinuities.

• It makes more sense to assume that the black spots are circles rather than Pac Men.

• It also makes sense, then, to assume that the 3 “bites” are caused by the same object which lies in front of the circles.

• “Makes sense” means is more likely to be a correct representation of the world.


Contextual cues

Which of the two middle circles is smaller?


Is this a letter or a number?

BBAC12B14


Circularity in pitch perception

Waterfall (M. C. Escher)

Mac/AIFFPC/.wav


Bibliography• Sheperd, R. N. (1964). Circularity in judgements of relative pitch. Journal of the Acoustical Society

of America, 36, 2346-2353.• Rosch, E. (1978). Principles of categorization. In Rosch, E. & Lloyd, B. (Eds.) Cognition and

Categorization. Hillsdale, NJ, Lawrence Erlbaum Associates.• Wittgenstein, L. (1953). Philosophical Investigations. New York, Macmillan.

• Note: The illusions used in this demonstration come from various sources. When the original source is identifiable, it is given above. Otherwise, as much information as possible is provided to identify the illusion’s original author. Many illusions are so widely distributed that they appear to be in the public domain. The following texts and other sources are recommended:

• Deutsch, D. (1975). Musical Illusions. Scientific American, 233(4), 92-104.• Ernst, B. (1976). The Magic Mirror of M. C. Escher. New York, Ballantine.• Ernst, B. (1992). Optical Illusions. Trans. K. Williams. Originally published as Het Begoochelde

Oog. Taschen Verlag.• Held, R. (1974). Image, Object, and Illusion: Readings from Scientific American. Scientific

American, Inc.• Houtsma, A. J. M., Rossing, T. D., Wagenaars, W. M. (1987). Auditory Demonstrations (CD).

Eindhoven, The Netherlands, Institute for Perception Research (IPO) and the Acoustical Society of America (ASA).

what rules are used to group objects?

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