Differential Geometry, Surface Patches and Convergence Methods.

Abstract

The problem of constructing a surface from the information provided by the Marr-Poggio theory of human stereo vision is investigated. It is argued that not only does this theory provide explicit boundary conditions at certain points in the image, but that the imaging process also provides implicit conditions on all other points in the image. This argument is used to derive conditions on possible algorithms for computing the surface. Additional constraining principles are applied to the problem; specifically that the process be performable by a local-support parallel network. Some mathematical tools, differential geometry, Coons surface patches and iterative methods of convergence, relevant to the problem of constructing the surface are outlined. Specific methods for actually computing the surface are examined. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1979
Accession Number
ADA078061

Entities

People

  • W. E. L. Grimson

Organizations

  • Massachusetts Institute of Technology

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Artificial Intelligence
  • Calculus Of Variations
  • Computations
  • Computer Stereo Vision
  • Coordinate Systems
  • Curvature
  • Difference Equations
  • Differential Geometry
  • Equations
  • Geometry
  • Grids
  • Image Processing
  • Intensity
  • Reflectance
  • Shape
  • Two Dimensional

Readers

  • Computer Vision.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Theoretical Analysis.