(Georgia Institute of Technology, 2003-10)
Steedly, Drew; Essa, Irfan; Dellaert, Frank
We propose a spectral partitioning approach for large-scale
optimization problems, specifically structure from motion.
In structure from motion, partitioning methods reduce the
problem into smaller and better conditioned subproblems
which can be efficiently optimized. Our partitioning method
uses only the Hessian of the reprojection error and its eigenvectors.
We show that partitioned systems that preserve the
eigenvectors corresponding to small eigenvalues result in
lower residual error when optimized. We create partitions
by clustering the entries of the eigenvectors of the Hessian
corresponding to small eigenvalues. This is a more general
technique than relying on domain knowledge and heuristics
such as bottom-up structure from motion approaches. Simultaneously,
it takes advantage of more information than
generic matrix partitioning algorithms.