

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 manmade 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 manmade 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 multidimensional 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 manmade 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, My current projects related to computational symmetry include: 1) Brain Asymmetry
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:
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 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 "unbiased least commitment", and it is executed as follows:
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 ongoing 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 (20002004) Elected member of the executive committee of CMU Faculty Senator, Carnegie Mellon University (20032004) 
Research Interest Keywords 
artificial intelligence, assembly, computational symmetry, computer vision, image databases, image processing, machine learning, medical applications, medical imaging, pattern recognition 
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