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Yanxi Liu
Adjunct Associate Research Professor, RI
No longer a member of RI.
Research Interests

My research interests span a range of applications in computer vision and robotics, with a central research theme: computational symmetry. Computational symmetry addresses issues on robust representation, detection, and reasoning about symmetry, as well as diverse applications of applying (a)symmetry analysis on computers (see projects).

Symmetry is a pervasive phenomena in both natural and man-made environments. Humans have an innate ability to perceive and take advantage of symmetry in everyday life, but it is not obvious how to automate this powerful insight on man-made intelligent beings, such as robots. On the surface, symmetry is simple and basic. In essence, the concept of symmetry is much more than a mirror reflection with binary choices, rather, it can span a continuous spectrum of multi-dimensional spaces.

In basic sciences, the understanding of symmetry played a profound role in several important discoveries including: relativity theory (the symmetry of time and space); human DNA structure (double helix); the quasicrystals and their mathematical counterpart penrose tiles. We argue that reasoning about symmetry can likewise play a crucial part in the advance of artificial/machine intelligence.

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?s 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. I am finishing up a textbook for engineering students to learn group theory through concrete examples from applications in robotics (assembly planning) and computer vision (repeated pattern perception).

My current projects related to computational symmetry include:

1) Brain Asymmetry


  • using quantitative, statistical image features extracted from 3D volumetric radiology neuroimages (MR, CT, PET ...) to find similar brains with the same pathology;
  • using asymmetry measure of MRI human brains to detect schizophrenia patients;
  • from large, population-based image databases, we are also interested in finding out the answer to this question:

how symmetrical are the normal (human, mice, . . . ) brains?

2) Facial Asymmetry

Using facial asymmetry as a biometric to identify faces under expression, post and lighting variations. The questions we are seeking the answers for are:


  • is facial asymmetry a characteristic of human identity or expression?
  • does facial asymmetry remain relatively invariant under expression variations?
  • are more attractive people more recognizable?
  • how facial asymmetry changes within the invisible wavelengths (infrared, thermal)?

3) Repeated Pattern Perception using Crystallographic Groups

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?

4) Gait analysis using wallpaper groups

Spatiotemporal representation of human or animal gaits form a naturally appreciable periodic pattern. Different gaits are reflected by different symmetries and symmetry groups of such patterns. We study the possibility of using cues extracted from such patterns for identity and activity classification.

In addition to computational symmetry, I am interested in discovering hidden patterns from large image sets, in particular, large biomedical image databases. These images are especially attractive for studying image meanings since they are normally associated with unambiguous, objective
underlying semantics from physical causes (versus images that can be interpreted one way or the other subjectively by the viewer). With the worldwide trend towards ?paperless? hospitals, the commercially available Picture Archiving and Communication System (PACS) installed in many hospitals collects a large amount of digital biomedical image data monthly, weekly even daily. However, the utilization of such data for research and education is hampered by the lack of intelligent, effective image analysis, comparison and retrieval tools.

My research focus is to learn semantically discriminative image features using statistical learning theory, information theory, and pattern recognition, image processing and computer vision tools. The goal is to seek the true fundamental dimensionality and separability of a given image set and image features. The philosophy of our approach is "un-biased least commitment", and it is executed as follows:


  1. image features are extracted extensively and creatively;
  2. image features are selected objectively;
  3. no image feature is excluded without strong quantitative justifications.

We close the learning loop from imaging process --> image feature extraction --> image feature screening --> image feature grouping --> image feature subset selection --> image classification and image retrieval. We have applied these ideas in multiple application domains (pathological neuroimages, facial expression videos, multispectral microscopic images) with very promising results (see our publications). We have several on-going projects exploring along these research directions intensively (see our projects). The results from this research are directly applicable to the fast growing biomedical informatics industry and hospitals, with which we have and we continue establishing tight collaborations.

Additional Interests

Elected Robotics Institute Faculty Senator, Carnegie Mellon University (2000-2004)

Elected member of the executive committee of CMU Faculty Senator, Carnegie Mellon University (2003-2004)

Research Interest Keywords
artificial intelligenceassemblycomputational symmetrycomputer visionimage databasesimage processingmachine learningmedical applicationsmedical imagingpattern recognition