Abstract
Abstract. The photogrammetric bundle adjustment is well-behaved in the case of structured aerial imagery looking in the nadir direction. That is less so in the case of ground-level imagery with less structure and potentially looking in any direction. Besides, the cost function based on reprojection errors of tie points is not defined everywhere and exhibits singularities which renders this bundle adjustment process sensitive to initial conditions and outliers. In order to handle difficult configurations without incurring the risks posed by the reprojection function, we propose a new error function that is equivalent to the reprojection error when this error tends to zero, and that enjoys many desirables properties, such as being defined everywhere and being continuous. This allows an easier implementation of a robust bundle adjustment, and incidentally it also allows to solve derivative problems such as triangulating points starting from arbitrary initial positions, or estimating the relative positions of calibrated and oriented cameras starting from arbitrary positions, thus offering a simple solution to the known-orientation structure-from-motion problem.
Highlights
In computer vision a prerequisite to producing a 3D reconstruction is to accurately model the geometry of the images
There is the risk of converging to a local minimum, but this is no different than when using the quadratic sum of reprojection errors which features such local minima (Kahl and Hartley, 2008)
Seeing that the cost function allows to correctly triangulate points, as if the reprojection error were minimized, the step is to plug it into a real bundle adjustment problem and check that it gets the correct solution
Summary
In computer vision a prerequisite to producing a 3D reconstruction is to accurately model the geometry of the images This often involves an approximate initial knowledge of this geometry, followed by a global optimization called bundle adjustment (for an all-around review we refer to (Triggs et al, 2000)). This process typically uses point correspondances between the images, and aims at minimizing the quadratic sum of reprojection errors of the triangulated points. When the triangulated points are used as auxiliary variables, their projection in some images may not be defined, and/or singularities may arise in the course of the process This may be countered by preemptively discarding some points, or discarding them during the optimization, using some ad hoc criteria
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