Gradient Space

  • Alan Bundy
  • Lincoln Wallen
Part of the Symbolic Computation book series (SYMBOLIC)


A two dimensional space used to represent surface orientation in terms of its vertical and horizontal components. Thus the plane surface −Z = P. X + Q. Y + C is represented by the point (P. Q) in gradient space. The steepness of the surface is squareroot(P2 + Q2) and the direction of the slope is tan−1(Q/P). Such a representation does not make explicit the spatial location or extent of surface planes. Convex and concave edges and curvatures will be represented by lines in the gradient space, in the case of planar surface discontinuity edges these will be perpendicular to the edge in the image space, with order along the line determined by the convexity/concavity.


Image Space Plan Execution Goal Structure Semantic Module Automatic Planning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [Draper 81]
    Draper. S. W. The Use of Gradient Space and Dual Space in Line Drawing Interpretation. Artificial Intelligence 17, 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Alan Bundy
    • 1
  • Lincoln Wallen
  1. 1.Department of Artificial IntelligenceEdinburgh UniversityEdinburghScotland

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