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[Lab image] 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

Jump to: Lab Description | Personnel | Projects | Publications

Lab Description

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.

Personnel [Past members]

Name Title Email Address
Jeffrey's personal homepage Jeffrey Cohn Adjunct Faculty (Adjunct) jeffcohn@cs.cmu.edu
James H. Hays PhD Student, CS jhhays@cs.cmu.edu
Yanxi's personal homepage 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
Karen's personal homepage Karen Schmidt Assistant Professor, Psychiatry, UPitt kschmidt@pitt.edu
Chenyu's personal homepage Chenyu Wu PhD Student, RI chenyuwu@andrew.cmu.edu

Current Projects

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.
 

Recent publications [View all 59 publications]

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