Bundle Adjustment With Polynomial Point-to-Camera Distance Dependent Corrections for Underwater Photogrammetry

Abstract

Abstract. Uncontrolled refraction of optical rays in underwater photogrammetry is known to reduce its accuracy potential. Several strategies have been proposed aiming at restoring the accuracy to levels comparable with photogrammetry applied in air. These methods are mainly based on rigours modelling of the refraction phenomenon or empirical iterative refraction corrections. The authors of this contribution have proposed two mitigation strategies of image residuals systematic patterns in the image plane: (i) empirical weighting of image observations as function of their radial position; (ii) iterative look-up table corrections computed in a squared grid. Here, a novel approach is developed. It explicitly takes into account the object point-to-camera distance dependent error introduced by refraction in multimedia photogrammetry. A polynomial correction function is iteratively computed to correct the image residuals clustered in radial slices in the image plane as function of the point-to-camera distance. The effectiveness of the proposed method is demonstrated by simulations that allow to: (i) separate the geometric error under investigation from other effects not easily modellable and (ii) have reliable reference data against which to assess the accuracy of the result.

An Efficient Solution to Ray Tracing Problems in Multimedia Photogrammetry for Flat Refractive Interfaces

“…They derive a direct estimation of the parameters by first solving for five degrees of freedom that are independent of refraction and then including an adjusted focal length and ratio of refractive indices of water and air, absorbing the refraction effect of glass by the focal length. Most recently, Nocerino et al (2021) proposed to include a polynomial, explicitly addressing the distance dependence without introducing interface and refraction parameters. Simulation results show a good compensation of refraction effects for both flat and dome ports.…”

Rotation Only Bundle-Adjustment for the Generalized Camera Model and Its Application for Large-Scale Underwater Image-Sets

“…While our solution form is general, we demonstrate its application on underwater flat refractive imaging configurations. It has been identified that the flat refractive configuration is axial by nature (cf., Telem and Filin, 2010), also demonstrating that the nature of this system translates to depth dependence in terms of the image related corrections (Telem and Filin, 2010;Nocerino et al, 2021). The literature shows that the predominant method to handle the axial nature of this system is by approximating it as a perspective one with distortions (Chadebecq et al, 2020).…”

Investigating Distance-Dependent Distortion in Multimedia Photogrammetry for Flat Refractive Interfaces

“…As the general pinhole model is rendered invalid, alternative projection functions were developed over the years. This includes extended pinhole camera models with additional parameters to correct distortions directly (Maas, 1995;Elnashef and Filin, 2019;Nocerino et al, 2021), extensions to non-single viewpoint cameras (Agrawal et al, 2012;Treibitz et al, 2012) or virtually shifted cameras (Telem and Filin, 2010;Jordt-Sedlazeck and Koch, 2012). Kotowski (1987) introduced a fully flexible but computationally very expensive ray tracing bundle adjustment to account for refraction.…”

“…The average reprojection error was increased by more than 50 % when non-perpendicular views through the interface were performed in air. Nocerino et al (2021) tackled the distance dependence by including a second order polynomial as a distance-dependent correction term to the bundle adjustment and evaluated the method in large-scale simulations.…”