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A computational model for periodic pattern perception based on frieze and wallpaper groups.

Yanxi Liu1, Robert T Collins, Yanghai Tsin

  • 1Robotics Institute, School of Computer Science, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213, USA. yanxi@cs.cmu.edu

IEEE Transactions on Pattern Analysis and Machine Intelligence
|September 21, 2004
PubMed
Summary

This study introduces a computational model for understanding periodic patterns using crystallographic group theory. The model identifies pattern symmetries and motifs, enabling applications in image analysis and synthesis.

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Area of Science:

  • Computational mathematics
  • Computer vision
  • Crystallography

Background:

  • Periodic patterns are ubiquitous in nature and artificial designs.
  • Understanding pattern symmetry is crucial for analysis and synthesis.
  • Existing methods may not efficiently classify complex periodic structures.

Purpose of the Study:

  • To develop a computational model for analyzing periodic patterns based on crystallographic group theory.
  • To automatically identify the underlying lattice, symmetry group, and motifs of a given pattern.
  • To extend the model for analyzing near-periodic patterns.

Main Methods:

  • Utilizing the mathematical framework of crystallographic groups (frieze and wallpaper groups).
  • Developing computer algorithms to detect lattice, symmetry, and motifs.

Related Experiment Videos

  • Employing geometric AIC for analyzing near-periodic patterns.

    • Main Results:

    • A computational model capable of characterizing periodic patterns by their symmetry groups.
    • Algorithms successfully identify underlying structures and representative motifs.
    • Extension to near-periodic patterns demonstrates model's versatility.

    Conclusions:

    • The computational model provides a robust framework for periodic pattern analysis.
    • This approach has potential applications in pattern indexing, texture synthesis, image compression, and gait analysis.
    • The integration of crystallographic theory offers novel insights into pattern perception.