Modelling Surface Normal Distribution Using the Azimuthal Equidistant Projection

  • William A. P. Smith
  • Edwin R. Hancock
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3604)


This paper describes how surface shape, and in particular facial shape, can be modeled using a statistical model that captures variations in surface normal direction. To construct this model we make use of the azimuthal equidistant projection to map surface normals from the unit sphere to points on a local tangent plane. The variations in surface normal direction are captured using the covariance matrix for the projected point positions. This allows us to model variations in surface shape using a standard point distribution model. We show how this model can be trained using surface normal data acquired from range images. We fit the model to intensity data using constraints on the surface normal direction provided by Lambert’s law. We demonstrate the utility of the method on the recovery of 3D surface shape from 2D images.


Surface Normal Tangent Plane Range Image Facial Shape Active Appearance Model 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • William A. P. Smith
    • 1
  • Edwin R. Hancock
    • 1
  1. 1.Department of Computer ScienceThe University of YorkYorkUK

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