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Trigonometric Identities I01:27

Trigonometric Identities I

Trigonometric identities are equations that relate trigonometric functions and hold for all angles within their domains. A fundamental identity among these is the Pythagorean identity, which arises directly from the geometry of the unit circle. For any angle θ, a point on the unit circle has coordinates (cos⁡ θ, sin ⁡θ), and since the radius of the circle is one, the Pythagorean Theorem gives:This identity serves as the basis for deriving additional identities. Dividing the Pythagorean identity...
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Related Experiment Video

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Creating Virtual-hand and Virtual-face Illusions to Investigate Self-representation
06:53

Creating Virtual-hand and Virtual-face Illusions to Investigate Self-representation

Published on: March 1, 2017

Implicit learning of geometric eigenfaces.

Xiaoqing Gao1, Hugh R Wilson1

  • 1Centre for Vision Research, York University, Canada.

Vision Research
|August 6, 2013
PubMed
Summary
This summary is machine-generated.

Adults implicitly learn face prototypes and key variations. This visual learning includes understanding feature correlations, optimizing how we perceive individual faces and their differences.

Keywords:
Face learningImplicit learningPrincipal componentsPrototypeSummary statistics

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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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Area of Science:

  • Cognitive Psychology
  • Computational Neuroscience
  • Computer Vision

Background:

  • The human visual system efficiently encodes object categories by learning prototypes.
  • Discriminating individual objects necessitates encoding variations within a category.
  • Previous research established implicit prototype learning (Posner & Keele, 1968).

Purpose of the Study:

  • To investigate if humans implicitly learn feature correlations representing geometric variations in faces.
  • To determine if this implicit learning extends beyond simple prototypes.
  • To explore the nature of summary statistics extracted by the visual system.

Main Methods:

  • Participants studied a set of synthetic faces.
  • Recognition tasks were used to assess memory for studied faces.
  • Analysis focused on misrecognition rates for novel faces representing principal components (eigenfaces).

Main Results:

  • Observers showed significantly higher false recognition rates for novel faces representing the first two principal components (eigenfaces) of the studied set.
  • This indicates implicit learning of significant geometric variations.
  • Performance exceeded correct recognition rates for the actually studied faces.

Conclusions:

  • Human adults implicitly learn not only prototypes but also significant feature correlations (eigenfaces) of visual objects like faces.
  • This implicit learning of principal components is an optimal strategy for encoding variations.
  • The visual system extracts complex summary statistics, including multiple principal components, implicitly.