I am interested in applied problems where tools of optimization, statistics, and other branches of mathematics may be used to develop better solutions. My approach is to seek theoretical formulations that result in efficient computational algorithms.

Currently my research is in the area of computer vision. The technological advances of the last decade have created a wealth of new opportunities for this field. Digital cameras and PC's with enough power to process video data are now available everywhere. Nonetheless, there are relatively few techniques in computer vision that work reliably. Computational efficiency is still a crucial factor since even very small images have thousands of pixels. In my view, computer vision is an important area with a need for solid theoretical formulations and fast algorithms.

Many computer vision applications would benefit a lot if images could be segmented accurately. My work on early vision was motivated by the fact that existing techniques have difficulties at the borders of objects, and thus yield poor segmentation. For tractability, conventional schemes rely on fixed windows to aggregate information around each pixel which causes problems when outliers are present. We developed a fast algorithm that adaptively builds windows of arbitrary shape while avoiding outliers. Our method significantly improves results near discontinuities. Later we generalized our approach as a multiway cut of a certain graph. This opened a door to a number of new efficient optimization algorithms based on graph cuts. We have shown that these algorithms find a strong local minimum of a large class of energy functions. It has long been thought that minimizing these energy functions should give good results in stereo, optical flows, image restoration, and other computer vision problems, but no practical optimization technique was available. Our method is also applicable to MAP estimation of Markov Random Fields (MRF) with almost arbitrary pairwise cliques.

Our success with MRF models sparked my interest in feature-based object recognition. For tractability, most approaches to recognition assume independence between the features which is an obvious oversimplification. We have developed a new Bayesian framework based on MRF's that allows explicit modeling of dependencies between the features, but is still computationally efficient due to our graph techniques. We also developed a very fast approximation algorithm which can be seen as a generalization of Hausdorff matching. This new Spatially Coherent Matching method significantly outperforms previous techniques, especially in cases with high clutter and occlusion. Our Bayesian recognition framework gives very promising results in tracking objects. Currently we experiment with a new Adaptive Hausdorff-Kalman tracking algorithm that allows effective real time tracking in highly cluttered scenes when the object is partially or (in some frames) completely occluded. A possibility for adaptive object representations that can be learned in the process of tracking is investigated.

My general scientific interests are quite broad. In the past my studies and research involved a wide spectrum of technical sciences. For my Ph.D. thesis (1996) at the department of Operations Research at Cornell I used recent results in mathematical finance to prove some general properties of Bayesian statistical methods. For my thesis I also developed a new efficient numerical scheme for evaluating certain types of exotic options based on a combination of finite differences and analytic approximation.

As a student at the department of Radiotechniques and Cybernetics at Moscow Institute of Physics and Technology I worked in a research group that developed a comprehensive computer model of a space system proposed in the Strategic Defense Initiative. Our goal was to simulate a real system whose components use theoretically optimal algorithms. A part of our simulation included a visual system that used Kalman filtering to track the objects from observations of their combustion flames. My M.S. thesis ``Stochastic dynamic programming in the problem of optimal pursuit'' (1992) was based on my contributions to the project.

Despite my broader interests, I would like to continue my work on computer vision in the future. My current research yields natural extensions in object tracking, image segmentation, learning, identification, and other exciting problems.