Student's T Robust Bundle Adjustment Algorithm

Abstract

Bundle adjustment (BA) is the problem of refining a visual reconstruction to produce better structure and viewing parameter estimates. This problem is often formulated as a nonlinear least squares problem, where data arises from interest point matching. Mismatched interest points cause serious problems in this approach, as a single mismatch will affect the entire reconstruction. In this paper, we propose a novel robust Student's t BA algorithm (RST-BA). We model reprojection errors using the heavy tailed Student's t-distribution, and use an implicit trust region method to compute the maximum a posteriori (MAP) estimate of the camera and viewing parameters in this model. The resulting algorithm exploits the sparse structure essential for reconstructing multi-image scenarios, has the same time complexity as standard L2 bundle adjustment (L2-BA), and can be implemented with minimal changes to the standard least squares framework. We show that the RST-BA is more accurate than either L2-BA or L2-BA with a sigma-edit rule for outlier removal for a range of simulated error generation scenarios. The new method has also been used to reconstruct lunar topography using data from the NASA Apollo 15 orbiter, and we present visual and quantitative comparisons of RST-BA and L2-BA methods for this application. In particular, using the RST-BA algorithm we were able to reconstruct a DEM from unprocessed data with many outliers and no ground control points, which was not possible with the L2-BA method.