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Computational Symmetry
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

A computational model for symmetry is especially pertinent to robotics, computer vision and machine intelligence, because in these fields we are studying how a man-made intelligent being can perceive and interact with the chaotic real world in the most effective way. Recognition of symmetries is the first step towards capturing the essential structure of a real world problem, and minimizing redundancy which can often lead to drastic reductions in computation. One fundamental limitation of computers is their finite representational power. One simple floating point error can destroy any perfect symmetry. One's ability to tolerate departure from perfect symmetry reflects one's level of sophistication in perception, which need to be built into the development of machine/artificial intelligence. Besides our poor understanding of human natural capability of symmetry perception, the mathematical theory for symmetry, group theory, has not been utilized effectively in practice. Group theory is usually introduced in classrooms in an abstract way (if it is introduced to computer science majors at all in the United States) that is hard to relate to everyday life. More importantly, the non-coherent topological nature of symmetry groups poses challenging computation problems on computers.

Name - Title <Email Address>
• [Home] Jeffrey Cohn - Adjunct Faculty (Adjunct) <jeffcohn@cs.cmu.edu>
• James H. Hays - PhD Student, CS <jhhays@cs.cmu.edu>
• [Home] Yanxi Liu - Adjunct Associate Research Professor <yanxi@cs.cmu.edu>
• Sinjini Mitra - PhD Student, Statistics <smitra@andrew.cmu.edu>
• Jeffrey Palmer - Masters Student, Statistics <jppalmer@andrew.cmu.edu>
• [Home] Karen Schmidt - Assistant Professor, Psychiatry, UPitt <kschmidt@pitt.edu>
• [Home] Chenyu Wu - PhD Student, RI <chenyuwu@andrew.cmu.edu>

• A Computational Model for Repeated Pattern Perception using Crystallographic Groups - 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, one of the 17 wallpaper groups, or one of the 230 space groups.
• A Statistical Quantification of Human Brain Asymmetry - Constructing image index features to retrieve medically similar cases from a multimedia medical database.
• Facial Asymmetry as a Biometric - We are investigating the effect of facial asymmetry measurement statistics as a biometric under expression variations.
• Texture Replacement in Real Images - We are developing methods to replace some specified texture patterns in an image while preserving lighting effects, shadows and occlusions.
• Texture Synthesis on Near-regular Patterns - We are developing near regular texture synthesis algorithms for improved natural appearances.

• Quantified Brain Asymmetry for Age Estimation of Normal and Alzheimer's Disease/Mild Cognitive Impairment Subjects
  L. Teverovskiy, J. Becker, O. Lopez, and Y. Liu
  5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, May, 2008.

• Application of Computational Symmetry to Histology Images
  B. Canada and Y. Liu
  tech. report CMU-RI-TR-08-08, Robotics Institute, Carnegie Mellon University, January, 2008. [Abstract]
  Download: pdf [4192 KB] copyrighted

• A Quantitative Evaluation of Symmetry Detection Algorithms
  P. Chen, J.H. Hays, S. Lee, M. Park, and Y. Liu
  tech. report CMU-RI-TR-07-36, Robotics Institute, Carnegie Mellon University, September, 2007. [Abstract]
  Download: pdf [5241 KB] copyrighted

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

• A Lattice-based MRF Model for Dynamic Near-regular Texture Tracking
  W. Lin and Y. Liu
  IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 29, No. 5, May, 2007, pp. 777 - 792. [Abstract]
  Download: pdf [6492 KB] copyrighted

• Discovery of "Biomarkers" for Alzheimer's Disease Prediction from Structural MR Images
  Y. Liu, L. Teverovskiy, O. Lopez, H. Aizenstein, C. Meltzer, and J. Becker
  2007 IEEE International Symposium on Biomedical Imaging, April, 2007.

• Feature-based vs. Intensity-based Neuroimage Registration: Comprehensive Comparison Using Mutual Information
  L. Teverovskiy, O. Carmichael, H. Aizenstein, N. Lazar, and Y. Liu
  2007 IEEE International Symposium on Biomedical Imaging, April, 2007.

• Two-level Method for 3D Non-rigid Registration: with an Application to Statistical Atlases Construction
  C. Wu, P.E. Murtha, A. Mor, and B. Jaramaz
  2nd International Conference on Computer Vision Theory (VISAPP2007), Insticc Press, Barcelona, Vol. 1, March, 2007. [Abstract]
  Download: pdf [1130 KB] copyrighted

• Understanding the Role of Facial Asymmetry in Human Face Identification
  S. Mitra, N. Lazar, and Y. Liu
  Statistics and Computing, Vol. 17, January, 2007, pp. 57 - 70. [Abstract]
  Download: pdf [515 KB] copyrighted

• Quantitative Evaluation on Near Regular Texture Synthesis
  W. Lin, J.H. Hays, C. Wu, V. Kwatra, and Y. Liu
  Computer Vision and Pattern Recognition Conference (CVPR '06), Vol. 1, June, 2006, pp. 427 - 434. [Abstract]
  Download: pdf [815 KB] copyrighted