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Towards representation of 3D shape: Global surface parametrization

C. Brechbühler, G. Gerig and O. Kübler
Visual Form, Proc. of the IWVF (Internatinal Workshop on Visual Form), Capri
May 1991


A procedure for the parametrization of the surface of a simply connected object is presented. Starting from a relational data structure describing surface nodes and links to edges and vertices, a distance transform is applied to determine two distant poles. The physical model of a heat conducting surface is then used to obtain latitude and longitude parameters. The net created assigns a unique coordinate pair to each surface node, but its structure depends on the selection of the poles and comprises a systematic nonuniformity of node distributions over the sphere. To correct distortions and to achieve independence of starting conditions, an isotropic non-linear relaxation of the node locations on the sphere is developed. This dynamic modelling procedure is used to obtain the final parametrization. The advantage of the proposed technique is a unique mapping of arbitrary simply connected, but not necessarily convex or star-shaped, objects to spherical coordinates. The example demonstrates the uniform distribution of nodes projected onto the sphere and the object symmetries that are reproduced. The mapping of a surface to a sphere represents a prerequisite processing stage to the representation of 3D shape in terms of an elliptic harmonic decomposition and is illustrated by a simple example.

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  author = {C. Brechb\"uhler and G. Gerig and O. K\"ubler},
  title = {Towards representation of 3D shape: Global surface parametrization},
  booktitle = {Visual Form, Proc. of the IWVF (Internatinal Workshop on Visual Form), Capri},
  year = {1991},
  month = {May},
  pages = {79--88},
  editor = {C. Arcelli et al.},
  publisher = {Plenum Press},
  keywords = {surface, shape, measurement, parametric, deformable, volume, fitting, morphometry}