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A Computational Model for Repeated Pattern Perception using Crystallographic Groups
Head: Yanxi Liu
Contact: Yanxi Liu (yanxi@cs.cmu.edu)

Mailing address:
Carnegie Mellon University
Robotics Institute
5000 Forbes Avenue
Pittsburgh, PA 15213

Associated center: VASC
Associated lab/group: Computational Symmetry

This page last updated - February 2007.

What do you see when you look at a regularly textured surface? Do you see tiles or do you see structures? We are developing a computational model for repeated pattern perception that is able to automatically classify a given pattern into one of the 7 frieze groups (patterns repeating along one direction), or one of the 17 wallpaper groups (patterns repeating along two linearly independent directions), or one of the 230 space groups (patterns repeating in 3D Euclidean space). It can also automatically generate a finite set of possible tiles (based on our theoretical proofs). Furthermore, we study repeated patterns under different viewing directions to find out what happens to a periodic pattern when it is deformed by Affine or perspective transformations. We are also exploring texture replacement in real images and texture synthesis.

This project is funded by NSF grant No. IIS-0099597

Name - Title <Email Address>
• [Home] Yanxi Liu - Adjunct Associate Research Professor <yanxi@cs.cmu.edu>

• Shape Variation-based Frieze Pattern for Robust Gait Recognition
  S. Lee, Y. Liu, and R. Collins
  Proceedings of CVPR 2007, June, 2007.

• On Improving the Performance of the Wallpaper Symmetry Group Classification Algorithm
  S. Reddy and Y. Liu
  tech. report CMU-RI-TR-05-49, Robotics Institute, Carnegie Mellon University, November, 2005. [Abstract]
  Download: pdf [903 KB] copyrighted

• A Computational Model for Periodic Pattern Perception Based on Frieze and Wallpaper Groups
  Y. Liu, R. Collins, and Y. Tsin
  IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 26, No. 3, March, 2004, pp. 354 - 371. [Abstract]
  Download: pdf [3541 KB] copyrighted

• Gait Sequence Analysis using Frieze Patterns
  Y. Liu, R. Collins, and Y. Tsin
  Proceedings of the 7th European Conference on Computer Vision (ECCV'02), May, 2002. [Abstract]
  Download: pdf [973 KB], ps.gz [567 KB] copyrighted

• Gait Sequence Analysis using Frieze Patterns
  Y. Liu, R. Collins, and Y. Tsin
  tech. report CMU-RI-TR-01-38, Robotics Institute, Carnegie Mellon University, December, 2001. [Abstract]
  Download: pdf [1073 KB], ps.gz [659 KB] copyrighted

• Skewed Symmetry Groups
  Y. Liu and R. Collins
  IEEE Conference on Computer Vision and Pattern Recognition, Vol. 1, December, 2001, pp. 872 - 879. [Abstract]
  Download: pdf [519 KB], ps.gz [773 KB] copyrighted

• Texture Replacement in Real Images
  Y. Tsin, Y. Liu, and V. Ramesh
  IEEE Conference on Computer Vision and Pattern Recognition, Vol. 2, December, 2001, pp. 539 = 544. [Abstract]
  Download: pdf [731 KB], ps.gz [7075 KB] copyrighted

• A Computational Model for Repeated Pattern Perception using Frieze and Wallpaper Groups
  Y. Liu and R. Collins
  2000 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2000), Vol. 1, June, 2000, pp. 537 - 544. [Abstract]
  Download: pdf [979 KB], ps.gz [1433 KB], ps.z [1654 KB] copyrighted

• A Computational Model for Repeated Pattern Perception using Frieze and Wallpaper Groups
  Y. Liu and R. Collins
  tech. report CMU-RI-TR-00-08, Robotics Institute, Carnegie Mellon University, April, 2000. [Abstract]
  Download: pdf [907 KB], ps.gz [1467 KB], ps.z [1693 KB] copyrighted

• Periodic Pattern Analysis Under Affine Distortions Using Wallpaper Groups
  Y. Liu and R. Collins
  2nd International Workshop on Algebraic Frames for the Perception Action Cycle (AFPAC), Lecture Notes in Computer Science 1888, Springer-Verlag Belin, Heidelberg, 2000, pp. 241 - 250.
  Download: pdf [1109 KB], ps.gz [1670 KB], ps.z [1874 KB] copyrighted