The Gravity Lens Illusion and its Mathematical Model

  • Seiichiro Naito
  • James B. Cole
Part of the Recent Research in Psychology book series (PSYCHOLOGY)


A small dot near a large circle is perceived as being displaced towards the circle. We call this the Gravity Lens Illusion because it can be described using a geometric model in which the large circle induces changes in the geometrical properties of a surrounding “perception manifold” involving an analogy with general relativity theory in which a massive object changes the geometry of physical space. We regard perceived objects and their orientations as contours and vectors on the perception manifold. In order to compare two objects, they must be moved to a common location. This transport can be carried out either by the mathematical process of Lie dragging or by parallel transport. The latter process assumes that the perception manifold is Riemannian. We follow the Schwarzschild model of general relativity to model the geometry of the perceptual manifold. We find that a dot is easily displaced, while a line segment resists being shifted in a perpendicular direction.


Line Segment Parallel Transport Illusory Contour Visual Illusion Subjective Contour 
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Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • Seiichiro Naito
    • 1
  • James B. Cole
    • 2
  1. 1.NTT Basic Research LaboratoriesTokyoJapan
  2. 2.Acoustics DivisionNaval Research LaboratoryUSA

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