Event Detail

Event Type: 
Applied Mathematics and Computation Seminar
Date/Time: 
Friday, November 20, 2015 - 12:00 to 13:00
Location: 
GLK 113

Speaker Info

Institution: 
Rice University
Abstract: 

We consider the problem of recovering a set of locations given observations
of the direction between pairs of these locations. This recovery task
arises from the Structure from Motion problem, in which a three-dimensional
structure is sought from a collection of two-dimensional images. In this
context, the locations of cameras and structure points are to be found from
epipolar geometry and point correspondences among images. These
correspondences are often incorrect because of lighting, shadows, and the
effects of perspective. Hence, the resulting observations of relative
directions contain significant corruptions. To solve the location recovery
problem in the presence of corrupted relative directions, we introduce a
tractable convex program called ShapeFit. Empirically, ShapeFit can succeed
on synthetic data with 40% corruption. Rigorously, we prove that ShapeFit
can recover a set of locations exactly when a fraction of the measurements
are adversarially corrupted and when the data model is random. This work is
joint with Choongbum Lee and Vladislav Voroninski.