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Biomedical Imaging
Fiber Tracking in the Brain
We use diffusion MRIs to develop mathematical frameworks for registration, estimation, segmentation and tracking of white matter nerve fibers in order to discover biomarkers for neurological diseases.Computer Vision
Segmentation of Dynamic Scenes
We develop algorithms for fitting multiple 2D and 3D motion models to a video sequence of a scene containing multiple moving objects, without knowing which pixels move according to which model.Machine Learning
Generalized Principal Component Analysis (GPCA)
Given a set of points lying in multiple linear subspaces, we develop algebraic-geometric algorithms for learning the number of susbpaces, a basis for each subspace, and the segmentation of the data.Robotics
Landing an aerial vehicle
We develop algorithms for vision-based landing of an Unmanned Aerial Vehicle (UAV) on a moving landing deck, using multiple view geometry.Hybrid Systems
Hybrid System Identification
Given input output data generated by a dynamical system with both continuous and discrete dynamics, we look at the problem of identifying the model parameters and the mode sequence.