Postdoctoral fellow, Stanford University
Spectral Generalized Multi-Dimensional Scaling
Multidimensional scaling (MDS) is a family of methods that embed a given set of points into a simple, usually flat, domain. The points are assumed to be sampled from some metric space, and the mapping attempts to preserve the distances between each pair of points in the set. Distances in the target space can be computed analytically in this setting. Generalized MDS is an extension that allows mapping one metric space into another, that is, multidimensional scaling into target spaces in which distances are evaluated numerically rather than analytically. Here, we propose an efficient approach for computing such mappings between surfaces based on their natural spectral decomposition, where the surfaces are treated as sampled metric-spaces. The resulting spectral-GMDS procedure enables efficient embedding by incorporating smoothness of the metric structure into the problem, thereby substantially reducing the complexity involved in its solution while practically overcoming its non-convex nature. The method is compared to existing techniques that compute dense correspondence between shapes. Numerical experiments of the proposed method demonstrate its effciency and accuracy compared to state-of-the-art approaches especially when isometry invariance is a dominant property.
Anastasia Dubrovina is a postdoctoral fellow at the Computer Science Department at Stanford University, hosted by Prof. Leonidas Guibas. Her research interests are in machine learning and spectral methods for 3D shape analysis, and variational methods for image and shape processing. In her postdoc, she has been investigating the problem of joint analysis and processing of multi-modal visual data using large data collections, as well as different aspects of data-driven 3D shape analysis and processing.
Anastasia holds an MSc and a BSc in Electrical Engineering, and a PhD in Computer Science, all from the Techinon – Israel Institute of Technology. In her PhD, Anastasia was advised by Prof. Ron Kimmel and studied different aspects of the image segmentation problem, namely, unsupervised and user-assisted segmentation of natural images, and supervised medical image segmentation. In her MSc, Anastasia studied the problem of non-rigid three-dimensional shape matching.
Anastasia is a recipient of the Eric and Wendy Schmidt Postdoctoral Award for Women in Mathematical and Computing Sciences, the IBM PhD fellowship, the Jacobs-Qualcomm Fellowship, and the Technion Excellent TA award.