SINGULARITY-FREE BUNDLE ADJUSTMENT
Keywords: Bundle adjustment, Structure-from-Motion
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.