Modular Bundle Adjustment for Photogrammetric Computations

Abstract

In this paper we investigate how the residuals in bundle adjustment can be split into a composition of simple functions. According to the chain rule, the Jacobian (linearisation) of the residual can be formed as a product of the Jacobians of the individual steps. When implemented, this enables a modularisation of the computation of the bundle adjustment residuals and Jacobians where each component has limited responsibility. This enables simple replacement of components to e.g. implement different projection or rotation models by exchanging a module.<br> The technique has previously been used to implement bundle adjustment in the open-source package DBAT (Börlin and Grussenmeyer, 2013) based on the Photogrammetric and Computer Vision interpretations of Brown (1971) lens distortion model. In this paper, we applied the technique to investigate how affine distortions can be used to model the projection of a tilt-shift lens. Two extended distortion models were implemented to test the hypothesis that the ordering of the affine and lens distortion steps can be changed to reduce the size of the residuals of a tilt-shift lens calibration.<br> Results on synthetic data confirm that the ordering of the affine and lens distortion steps matter and is detectable by DBAT. However, when applied to a real camera calibration data set of a tilt-shift lens, no difference between the extended models was seen. This suggests that the tested hypothesis is false and that other effects need to be modelled to better explain the projection. The relatively low implementation effort that was needed to generate the models suggest that the technique can be used to investigate other novel projection models in photogrammetry, including modelling changes in the 3D geometry to better understand the tilt-shift lens.

The Quality Assessment of Different Geolocalisation Methods for a Sensor System to Monitor Structural Health of Monumental Objects

“…Teunissen [39] applied the well-known Gauss-Markow (Equation (2)) linear model (a linearized form of the input nonlinear relationships). This linear model is also used in the photogrammetric bundle adjustment process [40].…”

Flexible Photogrammetric Computations Using Modular Bundle Adjustment: The Chain Rule and the Collinearity Equations

“…The Damped Bundle Adjustment Toolbox (DBAT) was originally developed to illustrate the behaviour of different damping schemes known from non-linear optimization (Börlin and Grussenmeyer, 2013;. Later work has focused on the use to validate commercial black-box photogrammetric software, e.g., PhotoModeler and Photoscan (Börlin and Grussenmeyer, 2016), especially to provide detailed diagnostics of the photogrammetric network (Dall'Asta et al, 2015;Murtiyoso et al, 2017;Börlin et al, 2018). Recently, the differential observation weighting capabilities of DBAT was used by Menna et al (2018) to mitigate peripheral image quality degradation in underwater photogrammetry.…”

“…A first version of this approach was presented in Börlin et al (2018). This paper is an extended version with an added emphasis on performance vs. flexibility.…”