6. Morphological Operations on Nonconvex Objects

  1. Pijush K. Ghosh1 and
  2. Koichiro Deguchi2

Published Online: 28 JAN 2010

DOI: 10.1002/9780470823095.ch6

Mathematics of Shape Description: A Morphological Approach to Image Processing and Computer Graphics

Mathematics of Shape Description: A Morphological Approach to Image Processing and Computer Graphics

How to Cite

Ghosh, P. K. and Deguchi, K. (2008) Morphological Operations on Nonconvex Objects, in Mathematics of Shape Description: A Morphological Approach to Image Processing and Computer Graphics, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470823095.ch6

Author Information

  1. 1

    National Centre for Software Technology (now Centre for Development of Advanced Computing), India

  2. 2

    Graduate School of Information Sciences, Tohoku University, Japan

Publication History

  1. Published Online: 28 JAN 2010
  2. Published Print: 26 MAR 2008

ISBN Information

Print ISBN: 9780470823071

Online ISBN: 9780470823095

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Keywords:

  • morphological operations on nonconvex objects;
  • Minkowski operations, nonconvex and convex objects - viewed through single algorithmic framework;
  • extending notion of supporting hyperplane to relative/local supporting hyperplane;
  • anomalous behavior of outer normals at nonconvex faces;
  • nonconvex polygon slope diagrams;
  • Minkowski decomposition;
  • simple polygon and self-crossing polygon slope diagrams and their differences;
  • nonconvex polyhedron slope diagram - on unit sphere, captured by facet points, edge arcs and vertex regions;
  • unified algorithm for Minkowski operations;
  • Minkowski addition - two regions bounded by smooth curves

Summary

This chapter contains sections titled:

  • Problems with Nonconvex Objects

  • Slope Diagrams for Nonconvex Polygons

  • A Unified Algorithm for Minkowski Operations