  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.
