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The Isophotic Metric and Its Application to Feature Sensitive Morphology on Surfaces

  • Helmut Pottmann
  • Tibor Steiner
  • Michael Hofer
  • Christoph Haider
  • Allan Hanbury
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3024)

Abstract

We introduce the isophotic metric, a new metric on surfaces, in which the length of a surface curve is not just dependent on the curve itself, but also on the variation of the surface normals along it. A weak variation of the normals brings the isophotic length of a curve close to its Euclidean length, whereas a strong normal variation increases the isophotic length. We actually have a whole family of metrics, with a parameter that controls the amount by which the normals influence the metric. We are interested here in surfaces with features such as smoothed edges, which are characterized by a significant deviation of the two principal curvatures. The isophotic metric is sensitive to those features: paths along features are close to geodesics in the isophotic metric, paths across features have high isophotic length. This shape effect makes the isophotic metric useful for a number of applications. We address feature sensitive image processing with mathematical morphology on surfaces, feature sensitive geometric design on surfaces, and feature sensitive local neighborhood definition and region growing as an aid in the segmentation process for reverse engineering of geometric objects.

Keywords

Principal Curvature Parameter Domain Mathematical Morphology Implicit Surface Triangle Mesh 
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 2004

Authors and Affiliations

  • Helmut Pottmann
    • 1
  • Tibor Steiner
    • 1
  • Michael Hofer
    • 1
  • Christoph Haider
    • 2
  • Allan Hanbury
    • 3
  1. 1.Geometric Modeling and Industrial Geometry GroupVienna Univ. of TechnologyWienAustria
  2. 2.Advanced Computer Vision, Tech Gate ViennaWienAustria
  3. 3.Pattern Recognition and Image Processing GroupVienna Univ. of TechnologyWienAustria

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