On Scale Definition Within Calibration of Multi-Camera Systems in Multimedia Photogrammetry

Abstract

<p><strong>Abstract.</strong> In multimedia photogrammetry, multi-camera systems often provide scale by a calibrated relative orientation. Camera calibration via bundle adjustment is a well-established standard procedure in single-medium photogrammetry. When using standard software and applying the collinearity equations in multimedia photogrammetry, the refractive interfaces are modelled in an implicit form. This contribution analyses different calibration strategies for bundle-invariant interfaces. To evaluate the effects of implicitly modelling the refractive effects within a bundle adjustment, synthetic datasets are simulated. Contrary to many publications, systematic effects of the exterior orientations can be verified with simulated data. The behaviour of interior, exterior and relative orientation parameters is analysed using error-free synthetic datasets. The relative orientation of a stereo camera shows systematic effects, when the angle of convergence varies and when the synthetic interface is set up at different distances to the camera. It becomes clear, that in most cases the implicit modelling is not suitable for multimedia photogrammetry. An explicit modelling of the refractive interfaces is implemented into a bundle adjustment. This strict model is analysed and compared with the implicit form regarding systematic effects in orientation parameters as well as errors in object space. In a real experiment, the discrepancies between the implicit form using standard software and the explicit modelling using our own implementation are quantified. It is highly advisable to model the interfaces strictly, since the implicit modelling might lead to relevant errors in object space.</p>

Impact of Stereo Camera Calibration to Object Accuracy in Multimedia Photogrammetry

“…When no absolute error in object space is determined as in the majority of cases, errors like wrong scaling might remain undetected. As already depicted in [8], systematic errors occur in the forward intersection when the scale is provided only by the relative orientation of a multi-camera system.…”

“…Based on [8], this article focusses on the implicit calibration of a stereo system, aiming to show characteristics regarding two main applications, from a typical scenario of a remotely operated vehicle (ROV) implying small image scales to an ultra-close-range scenario implying large images scales.…”

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

“…Since no commercial photogrammetric or structure-frommotion (SfM) software offer explicit modeling of refraction, this is a widely used practical approach to multi-media photogrammetry. Kang et al (2012), Sedlazeck and Koch (2012) and Kahmen et al (2019) systematically investigated the feasibility of this approach. All studies show that cameras facing orthogonally to the interface with a high percentage of water in the optical ray path, can well be calibrated applying the standard pinhole model with additional distortion parameters.…”

“…This is congruent with other studies observing similar behavior (Kotowski 1988;Treibitz et al 2012;Shortis 2015;Kahmen et al 2020b). However, while Kang et al (2012) and Kahmen et al (2019) solely focus on this case, Sedlazeck and Koch (2012) and Hemmati and Rashtchi (2019) show that deviating from this optimum setup (i.e. non-orthogonality of optical axis and interface) results in unresolvable errors when employing the pinhole camera model.…”

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

“…However, the stated accuracy of 0.7 mm for an object with an extent about 200 mm (equals 1:286 relative accuracy) is well below expectable accuracy in underwater photogrammetry. Kahmen et al (2019) focused on stereo data sets and especially considered relative and exterior orientation when neglecting refraction. Especially, a change in the stereo-baseline which results in erroneous scaling of object space, was found which can only partly be compensated by other correlated parameters of exterior and interior orientation.…”