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Geometry of shadows

D C Knill1, P Mamassian, D Kersten

  • 1Department of Psychology, University of Pennsylvania, Philadelphia 19104, USA. knill@cattell.psych.upenn.edu

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|December 11, 1997
PubMed
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Analyzing intrinsic shadows reveals how surface geometry and light direction create them. This research shows shadows can infer light source direction and surface shape, aiding 3D reconstruction.

Area of Science:

  • Computer Vision
  • Computational Geometry
  • Geometric Modeling

Background:

  • Shadows offer rich cues for understanding 3D object geometry.
  • Analyzing shadow contours is crucial for inferring surface properties.

Purpose of the Study:

  • To analyze the geometric structure of intrinsic shadow contours on piecewise smooth surfaces.
  • To investigate how intrinsic shadows relate to surface shape and light source direction.
  • To explore the potential of intrinsic shadows for inferring surface properties and light source characteristics.

Main Methods:

  • Analysis of local geometric structure of shadow contours.
  • Mathematical investigation of invariants linking surface shape, light direction, and shadow contour features.
  • Examination of shadow contour singularities and their relation to surface creases.

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Main Results:

  • Intrinsic shadow contours provide information about light source direction and qualitative surface shape.
  • Invariants were identified relating surface geometry and illuminant tilt to shadow contour properties.
  • Shadow contours at surface creases indicate surface concavity or convexity.

Conclusions:

  • Intrinsic shadows can be directly used to infer illuminant tilt and global surface structure.
  • The analysis extends to convex extended light sources.
  • Shadow analysis offers a robust method for 3D surface reconstruction and scene understanding.