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 L 2 bundle adjustment (L 2 -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 L 2 -BA or L 2 -BA with a σ-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 L 2 -BA methods on 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 L 2 -BA method.

Fast Structure from Motion for Sequential and Wide Area Motion Imagery

“…On the other hand, BA which is usually solved using the LevenbergMarquardt numerical method [51] is highly sensitive to the presence of feature correspondence outliers [4]. Mismatches can cause problems for the standard least squares approach; as stressed in [9] even a single mismatch can globally affect the result. This leads to sub-optimal parameter estimation, and in the worst case a feasible solution is not found [4,35].…”

A Generic Bundle Adjustment Methodology for Indirect RPC Model Refinement of Satellite Imagery

“…Mismatches in the feature track observations can strongly undermine the bundle adjustment performance, leading to failure or strong biases [3,29]. We remove erroneous matches by means of a distance ratio test with a relative threshold of 0.6 [28].…”

“…The rejection of points whose reprojection error exceeds a certain threshold after a series of initial iterations is a popular strategy [39,44,29]. Other approaches use cost functions that enforce robustness to occasional large residuals, or employ iterative reweighting according to the reprojection error of each observation [43,3,47].…”

“…where X k and P m contain the variables to be adjusted. Following (3), the reprojection error is typically defined as the sum of squared Euclidean distances between the estimated reprojected 3D points, i.e. P m (X k ), and their actual 2D observations in the images, i.e.…”

Estimating nuisance parameters in inverse problems

“…This density was also successfully used in the Kalman smoothing context [8], where it was suggested that the EM algorithm can be used to fit meta-parameters. Recent work using the Student's t distribution [2,3,1] has side-stepped the problem, using fixed values for σ and k.…”