Abstract

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 eigenvector. 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.

Abstract

We present a new technique that improves upon existing structure from motion (SFM) methods. We propose a SFM algorithm that is both recursive and optimal. Our method incorporates innovative information from new frames into an existing solution without optimizing every camera pose and scene structure parameter. To do this, we incrementally optimize larger subsets of parameters until the error is minimized. These additional parameters are included in the optimization by tracing connections between points and frames. In many cases, the complexity of adding a frame is much smaller than full bundle adjustment of all the parameters. Our algorithm is best described us incremental bundle adjustment as it allows new information to be added to art existing non-linear least-squares solution