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Related Concept Videos

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Curvature and Its Interpretation

Curvature describes how rapidly a curve changes direction at a particular point. A curve with a small curvature bends gently, while a curve with a large curvature turns sharply. For a space curve, the position of a moving object can be described by a vector-valued function r(t), where t often represents time. The direction of motion is determined by the tangent vector, and the unit tangent vector is obtained by normalizing the derivative of the position vector.The unit tangent vector gives the...
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In vector calculus, flux measures the total flow of a vector field through a surface. For a closed surface in three-dimensional space, this means measuring how much of the field passes outward through every point on the boundary. Directly calculating this flux can be difficult when the surface has a complicated or irregular shape. The Divergence Theorem provides a powerful alternative by relating surface flux to behavior inside the enclosed region.The Divergence Theorem states that the outward...
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Extended Versions of Green’s Theorem01:27

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Related Experiment Video

Updated: Jul 17, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Bayesian contour extrapolation: geometric determinants of good continuation.

Manish Singh1, Jacqueline M Fulvio

  • 1Department of Psychology and Center for Cognitive Science, Rutgers University, New Brunswick Campus, 152 Frelinghuysen Road, Piscataway, NJ 08854-8020, USA. manish@ruccs.rutgers.edu

Vision Research
|February 13, 2007
PubMed
Summary

The visual system does not use the rate of change of contour curvature when extrapolating shapes. Instead, extrapolated contours show decaying curvature, suggesting a Bayesian model influences contour perception.

Related Experiment Videos

Last Updated: Jul 17, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Area of Science:

  • Visual perception
  • Computational neuroscience
  • Psychophysics

Background:

  • Contour extrapolation is crucial for object recognition.
  • Previous models assumed the visual system extrapolates curvature and its rate of change.

Purpose of the Study:

  • To investigate if the rate of change of curvature influences visual contour extrapolation.
  • To determine the characteristics of visually extrapolated contour shapes.

Main Methods:

  • Observers extrapolated occluded Euler spiral contours.
  • Participants adjusted a line probe to match the perceived extrapolated shape.
  • Euler spiral models were fitted to extrapolation data.

Main Results:

  • Extrapolated contours consistently exhibited negative rate of change of curvature (decaying curvature).
  • This decay occurred regardless of the inducer contour's rate of change.
  • Extrapolation rate of change was independent of the inducer's rate of change.

Conclusions:

  • The visual system does not extrapolate the rate of change of contour curvature.
  • Results support a Bayesian model where contour extrapolation is influenced by likelihood and prior biases.
  • Decaying curvature in extrapolation arises from minimizing contour curvature, not extrapolating its rate of change.