A bundle adjustment approach with inner constraints for the scaled Orthographic projection

摘要

Bundle adjustment is a method for simultaneously calculating both the interior and exterior orientation Parameters of a set of images, and the object-space coordinates of the observed points. In the case of long focal length lenses and narrow field-of-view (FOV) imaging situations, collinearity based (perspective projeetion) algorithms may result in linear dependencies between Parameters that cause solution instability. The use of a scaled Orthographie projeetion model based on linear algebraic formulations was therefore adopted to reduce this risk. Using quaternions, a new mathematical model is derived that includes the par-tial derivatives as well as the inner constraint equations for a scaled Orthographie bundle adjustment. The model was then tested using two image sets of a Single, small vessel (about 6 m length) with a cube target of known dimensions at two distinct ranges; perspective Solutions were also calculated for comparison. RMS residual errors of 0.74-0.78 pixels associated with the new method compare favorably to a residual error range of 0.59-0.74 pixels using a perspective bundle adjustment of the same target points. Relative preci-sions (as a ratio of target size) of between 1:1650 and 1:750 have been achieved at ranges of 375 m and 850 m, respectively, given comparisons with the known cube dimensions. A third image dataset consisting of a network of 16 images was solved with a 1:2200 relative precision showing the new method can suc-cessfully handle high redundancy. For the experiments that were conducted, the new method was found to produce less precise results than the perspective bundle solution fora FOV of 0.50-0.65° where the objeet fills 5-8% of the image. However, it was found to match the precision of the perspective model (with an uncalibrated camera) for a FOV of 0.20-0.30° where the object of interest fills only 1-2% of the full image.