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VASC Seminar: Hossein Mobahi
Gaussian Smoothing for Nonconvex Optimization with Applications to Computer Vision

Hossein Mobahi
Postdoctoral Research Associate, MIT - CSAIL

February 18, 2013, 3pm - 4pm, NSH 1507
Abstract

The Gaussian function is the center of several relaxation methods for solving difficult optimization problems. When seen as a filter, its smoothing property can be used for eliminating spurious local minima. The idea is to start from a highly smoothed version of the objective that is hopefully easier to minimize. Then, the path of that solution is followed as the function is gradually deformed back to its original shape.
There are fundamental questions around such continuation method that are not well understood. For example, what functions eventually become convex after enough smoothing? For such a function, does its asymptotic minimizer have a simple closed form? I present, application independent and easy to check conditions, related to these properties. In addition to these topics, there are other issues that matter from practical viewpoint. For example, if the optimization space is high dimensional, then smoothing becomes expensive due to the curse of dimensionality in numerical integration. However, I show that sometimes the high-dimensional convolution can be equivalently expressed by a low-dimensional integral operator. I present such operators for the tasks of image alignment and 3D point cloud registration (although the underlying concept may be extendable to other optimization tasks even beyond computer vision). Finally, I will briefly discuss my on going research on using this optimization method for learning visual object representation.


Additional Information

Host: Bernardo Pires

Appointments: Bernardo Pires (bpires@cmu.edu)

Speaker Biography

Hossein Mobahi is a postdoctoral research associate in Computer Science and Artificial Intelligence Lab at Massachusetts Institute of Technology. He received his PhD from University of Illinois at Urbana Champaign in Dec 2012. He has worked on several topics in computer vision and machine learning, including image alignment, image segmentation, 3D reconstruction, face recognition, and manifold learning. His current research focuses on the role of smoothing for solving nonconvex optimization problems arising in vision and machine learning. Throughout his graduate study, he has received several awards including Beckman Institute's AI/Cognitive for two years, and Mavis Memorial Scholarship. He was also awarded UIUC's CSE fellowship for two successive years.