Selected Chapters in Pattern Recognition

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Selected Chapters in Pattern Recognition Prof.
Dr. Walter G.Kropatsch
Pyramids Topology Prof. Dr. Walter G.
Kropatsch krw_at_prip.tuwien.ac.at Helena
Molina-Abril habril_at_prip.tuwien.ac.at
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Selected Chapters in Pattern Recognition Pyramids
Topology

• Web page http//www.prip.tuwien.ac.at/teaching/ws
  /AKME
• Organisation
• VO Wednesday, 15.10.-10.12.2007 1600 - 1800
• UE December 2008 January 2009
• Discussion Student presentations
• Where Seminarraum 183/2, Favoritenstr.9-11, 4.
  Stock

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Selected Chapters in Pattern Recognition Pyramids
Topology
MOTIVATION
Aim of the course To learn the concepts of
pyramids and topology, and how to extract
properties and features of digital images using
both of them.
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Selected Chapters in Pattern Recognition Pyramids
Topology
APPICATION DOMAIN

• Geometric Modeling

• Digital Image Processing

• Pattern Recognition

• Medical Imaging

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Selected Chapters in Pattern Recognition Pyramids
Topology
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Selected Chapters in Pattern Recognition Pyramids
Topology

• Image Pyramids
• What are Image Pyramids?
• Image pyramids and discrete 2D images.
• Structure and types of Image Pyramids..

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Selected Chapters in Pattern Recognition Pyramids
Topology

• Topology
• What is Topology?
• Digital topology in 2D and 3D images.

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Selected Chapters in Pattern Recognition Pyramids
Topology

• Segmentation
• Segmentation with Pyramids.
• Pyramid Linking.

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Selected Chapters in Pattern Recognition Pyramids
Topology

• Graph Pyramids
• Graphs.
• Planar and Dual Graphs.
• Dual Image Graph.
• Dual Graph Pyramid
• Segmentation with Graph Pyramids
• Minimal Spanning Tree

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Selected Chapters in Pattern Recognition Pyramids
Topology

• Distance and Eccentricity Transform
• Distance Transform.
• Eccentricity Transform.
• Application and usages.

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Selected Chapters in Pattern Recognition Pyramids
Topology

• Topology preservation and Homology generators
• Topology preservation.
• Cell complex.
• Chain Complex.
• Homology and Homology generators.
• Integral Operators.

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Selected Chapters in Pattern Recognition Pyramids
Topology
RELATED READING AND BIBLIOGRAPHY

• Kropatsch, W.G. Building Irregular Pyramids by
  Dual Graph Contraction. Technical Report
  PRIP-TR-35, Institute f. Automation 183/2, Dept.
  for Pattern Recognition and Image Processing, TU
  Wien, Austria, 1994.
• Kropatsch, W.G., BenYacoub, S. A revision of
  pyramid segmentation. In Walter G. Kropatsch,
  editor, 13th International Conference on Pattern
  Recognition, volume II, pages 477481. IEEE
  Comp.Soc., 1996.
• Brun, L., Kropatsch, W.G. Introduction to
  Combinatorial Pyramids. In Gilles Bertrand,
  Atsushi Imiya, and Reinhard Klette, editors,
  Digital and Image Geometry, volume Vol. 2243 of
  Lecture Notes in Computer Science, pages 108128.
  Springer, Berlin, Heidelberg, 2001.
• Haxhimusa, Y., Kropatsch, W.G. Segmentation
  Graph Hierarchies. In Ana Fred, Terry Caelli,
  Robert P.W. Duin, Aurelio Campilho, and Dick de
  Ridder, editors, Structural, Syntactic, and
  Statistical Pattern Recognition, Joint IAPR
  International Workshops on SSPR 2004 and SPR
  2004, volume LNCS 3138 of Lecture Notes in
  Computer Science, pages 343351, Lisbon,
  Portugal, August 2004. Springer, Berlin
  Heidelberg, New York.
• Haxhimusa, Y. The Structurally Optimal Dual
  Graph Pyramid and its Application in Image
  Partitioning. AKA and IOS Press, ISBN
  978-1-58603-743-7. June 2007.

Pyramids
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Selected Chapters in Pattern Recognition Pyramids
Topology
RELATED READING AND BIBLIOGRAPHY
Topology and Digital Images

• Lohmann, G. Volumetric Image Analysis. Wiley
  Sons, 1998.
• Kong, T.Y., Rosenfeld, A. Topological Algorithms
  for Digital Image Processing. Elsevier, 1996.
• González-Díaz, R., Real, P. On the Cohomology of
  3D Digital Images. Discrete Applied Math, vol.
  147 (2-3), 245-263 (2005).
• Gonzalez-Diaz, R., Medrano, B., Sánchez-Peláez,
  J., Real, P. Reusing Integer Homology
  Information of Binary Digital Images. Lecture
  Notes in Computer Science, vol. 4245, 199-210
  (2006).
• Gonzalez-Diaz, R., Jimenez, M.J., Medrano, B.,
  Molina-Abril, H., Real, P. Integral Operators
  for Computing Homology Generators at Any
  Dimension, 2007.

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Selected Chapters in Pattern Recognition Pyramids
Topology
RELATED READING AND BIBLIOGRAPHY
Distance and Eccentricity Transform

• http//www.cee.hw.ac.uk/hipr/html/distance.html
• Klette, Rosenfeld Digital Geometry, 2004
• Ion, A., Kropatsch, W.G, Andres, E. Euclidean
  Eccentricity Transform by Discrete Arc Paving. In
  David Coeurjolly and Isabelle Sivignon, editors,
  Discrete Geometry for Computer Imagery, volume
  4992 of Lecture Notes in Computer Science, pages
  213224, Lyon, France, 2008. Springer, Berlin
  Heidelberg.
• Ion, A, Peltier, S.,Haxhimusa, Y., Kropatsch,
  W.G. Decomposition for Efficient Eccentricity
  Transform of Convex Shapes. In A. Hanbury W.
  Kropatsch, M. Kampel, editor, The 12th
  International Conference on Computer Analysis of
  Images and Patterns (CAIP07), volume LNCS 4673 of
  Lecture Notes in Computer Science, pages 653660,
  Vienna, Austria, August 2007. Springer, Berlin
  Heidelberg.