Refractive Structure-From-Motion Through a Flat Refractive Interface

Recovering 3D scene geometry from underwater images involves the Refractive Structure-from-Motion (RSfM) problem, where the image distortions caused by light refraction at the interface between different propagation media invalidates the single view point assumption. Direct use of the pinhole camera model in RSfM leads to inaccurate camera pose estimation and consequently drift. RSfM methods have been thoroughly studied for the case of a thick glass interface that assumes two refractive interfaces between the camera and the viewed scene. On the other hand, when the camera lens is in direct contact with the water, there is only one refractive interface. By explicitly considering a refractive interface, we develop a succinct derivation of the refractive fundamental matrix in the form of the generalised epipolar constraint for an axial camera. We use the refractive fundamental matrix to refine initial pose estimates obtained by assuming the pinhole model. This strategy allows us to robustly estimate underwater camera poses, where other methods suffer from poor noise-sensitivity. We also formulate a new four view constraint enforcing camera pose consistency along a video which leads us to a novel RSfM framework. For validation we use synthetic data to show the numerical properties of our method and we provide results on real data to demonstrate performance within laboratory settings and for applications in endoscopy

ANALYSIS OF UNCERTAINTY IN UNDERWATER MULTIVIEW RECONSTRUCTION

Multiview reconstruction, a method for creating 3D models from multiple images from different views, has been a popular topic of research in the eld of computer vision in the last two decades. Increased availability of high-quality cameras led to the development of advanced techniques and algorithms. However, little attention has been paid to multiview reconstruction in underwater conditions. Researchers in a wide variety of elds (e.g. marine biology, archaeology, and geology) could benefit from having 3D models of seafloor and underwater objects. Cameras, designed to operate in air, must be put in protective housings to work underwater. This affects the image formation process. The largest source of underwater image distortion results from refraction of light, which occurs when light rays travel through boundaries between media with different refractive indices. This study addresses methods for accounting for light refraction when using a static rig with multiple cameras. We define a set of procedures to achieve optimal underwater reconstruction results, and we analyze the expected quality of the 3D models\u27 measurements

A virtual object point model for the calibration of underwater stereo cameras to recover accurate 3D information

The focus of this thesis is on recovering accurate 3D information from underwater images. Underwater 3D reconstruction differs significantly from 3D reconstruction in air due to the refraction of light. In this thesis, the concepts of stereo 3D reconstruction in air get extended for underwater environments by an explicit consideration of refractive effects with the aid of a virtual object point model. Within underwater stereo 3D reconstruction, the focus of this thesis is on the refractive calibration of underwater stereo cameras

An Online Self-calibrating Refractive Camera Model with Application to Underwater Odometry

This work presents a camera model for refractive media such as water and its application in underwater visual-inertial odometry. The model is self-calibrating in real-time and is free of known correspondences or calibration targets. It is separable as a distortion model (dependent on refractive index $n$ and radial pixel coordinate) and a virtual pinhole model (as a function of $n$). We derive the self-calibration formulation leveraging epipolar constraints to estimate the refractive index and subsequently correct for distortion. Through experimental studies using an underwater robot integrating cameras and inertial sensing, the model is validated regarding the accurate estimation of the refractive index and its benefits for robust odometry estimation in an extended envelope of conditions. Lastly, we show the transition between media and the estimation of the varying refractive index online, thus allowing computer vision tasks across refractive media.Comment: 7 pages, 6 figures, Submitted to the IEEE International Conference on Robotics and Automation, 202

Refractive Geometry for Underwater Domes

Underwater cameras are typically placed behind glass windows to protect them from the water. Spherical glass, a dome port, is well suited for high water pressures at great depth, allows for a large field of view, and avoids refraction if a pinhole camera is positioned exactly at the sphere’s center. Adjusting a real lens perfectly to the dome center is a challenging task, both in terms of how to actually guide the centering process (e.g. visual servoing) and how to measure the alignment quality, but also, how to mechanically perform the alignment. Consequently, such systems are prone to being decentered by some offset, leading to challenging refraction patterns at the sphere that invalidate the pinhole camera model. We show that the overall camera system becomes an axial camera, even for thick domes as used for deep sea exploration and provide a non-iterative way to compute the center of refraction without requiring knowledge of exact air, glass or water properties. We also analyze the refractive geometry at the sphere, looking at effects such as forward- vs. backward decentering, iso-refraction curves and obtain a 6th-degree polynomial equation for forward projection of 3D points in thin domes. We then propose a pure underwater calibration procedure to estimate the decentering from multiple images. This estimate can either be used during adjustment to guide the mechanical position of the lens, or can be considered in photogrammetric underwater applications

Refractive Geometry for Underwater Domes

Underwater cameras are typically placed behind glass windows to protect them from the water. Spherical glass, a dome port, is well suited for high water pressures at great depth, allows for a large field of view, and avoids refraction if a pinhole camera is positioned exactly at the sphere’s center. Adjusting a real lens perfectly to the dome center is a challenging task, both in terms of how to actually guide the centering process (e.g. visual servoing) and how to measure the alignment quality, but also, how to mechanically perform the alignment. Consequently, such systems are prone to being decentered by some offset, leading to challenging refraction patterns at the sphere that invalidate the pinhole camera model. We show that the overall camera system becomes an axial camera, even for thick domes as used for deep sea exploration and provide a non-iterative way to compute the center of refraction without requiring knowledge of exact air, glass or water properties. We also analyze the refractive geometry at the sphere, looking at effects such as forward- vs. backward decentering, iso-refraction curves and obtain a 6th-degree polynomial equation for forward projection of 3D points in thin domes. We then propose a pure underwater calibration procedure to estimate the decentering from multiple images. This estimate can either be used during adjustment to guide the mechanical position of the lens, or can be considered in photogrammetric underwater applications

Structured light sensor with telecentric stereo camera pair for measurements through vacuum windows

Within the Collaborative Research Centre 1153 Tailored Forming a process chain is being developed to manufacture hybrid high performance components made from different materials. The optical geometry characterization of red-hot workpieces directly after the forming process yields diverse advantages, e.g., the documentation of workpiece distortion effects during cooling or the rejection of deficient components in an early manufacturing state. Challenges arise due to the high components temperature directly after forming (approximately 1000°C): The applied structured light method is based on the triangulation principle, which requires homogeneous measurement conditions and a rectilinear expansion of light. This essential precondition is violated when measuring hot objects, as the heat input into the surrounding air leads to an inhomogeneous refractive index field. The authors identified low pressure environments as a promising approach to reduce the magnitude and expansion of the heat induced optical inhomogeneity. To this end, a vacuum chamber has been developed at the Institute of Measurement and Automatic Control. One drawback of a measurement chamber is, that the geometry characterization has to be conducted through a chamber window. The sensors light path is therefore again affected - in this case by the window's discrete increase of refractive index, and also due to the different air density states at sensor location (density at ambient pressure conditions) and measurement object location (density at low pressure conditions). Unlike the heat induced deflection effect, the light path manipulation by the window and the manipulated air density state in the chamber are non-dynamic and constant over time. The reconstruction of 3D geometry points based on a structured light sensor measurement directly depends on the mathematical model of detection and illumination unit. The calibration routine yields the necessary sensor model parameters. The window light refraction complicates this calibration procedure, as the standard pinhole camera model used for entocentric lenses does not comprise enough degrees of freedom to adequately parametrize the pixel-dependent light ray shift induced by thick vacuum windows. Telecentric lenses only map parallel light onto a sensor, therefore the window induced ray shift is constant for all sensor pixels and can be directly reproduced by the so-called affine camera model. In this paper, we present an experimental calibration method, and corresponding calibration data and measurement results for a structured light sensor with and without measurement window. The sensor comprises a telecentric stereo camera pair and an entocentric projector. The calibration of the telecentric cameras is conducted according to the well-known affine camera model. The projector is used as feature generator to solve the correspondence problem between the two cameras. The calibration data illustrates that the window refraction effect is fully reproduced by the affine camera model, allowing a precise geometry characterization of objects recorded through windows. The presented approach is meant to be used with the aforementioned vacuum chamber to enable a geometry characterization of hot objects at low pressure levels

Beyond Gr\"obner Bases: Basis Selection for Minimal Solvers

Many computer vision applications require robust estimation of the underlying geometry, in terms of camera motion and 3D structure of the scene. These robust methods often rely on running minimal solvers in a RANSAC framework. In this paper we show how we can make polynomial solvers based on the action matrix method faster, by careful selection of the monomial bases. These monomial bases have traditionally been based on a Gr\"obner basis for the polynomial ideal. Here we describe how we can enumerate all such bases in an efficient way. We also show that going beyond Gr\"obner bases leads to more efficient solvers in many cases. We present a novel basis sampling scheme that we evaluate on a number of problems

An Optical Digital Twin for Underwater Photogrammetry: GEODT - A Geometrically Verified Optical Digital Twin for Development, Evaluation, Training, Testing and Tuning of Multi-Media Refractive Algorithms

Most parts of the Earth’s surface are situated in the deep ocean. To explore this visually rather adversarial environment with cameras, they have to be protected by pressure housings. These housings, in turn, need interfaces to the world, enduring extreme pressures within the water column. Commonly, a flat window or a half-sphere of glass, called flat-port or dome-port, respectively is used to implement such kind of interface. Hence, multi-media interfaces, between water, glass and air are introduced, entailing refraction effects in the images taken through them. To obtain unbiased 3D measurements and to yield a geometrically faithful reconstruction of the scene, it is mandatory to deal with the effects in a proper manner. Hence, we propose an optical digital twin of an underwater environment, which has been geometrically verified to resemble a real water lab tank that features the two most common optical interfaces. It can be used to develop, evaluate, train, test and tune refractive algorithms. Alongside this paper, we publish the model for further extension, jointly with code to dynamically generate samples from the dataset. Finally, we also publish a pre-rendered dataset ready for use at https://git.geomar.de/david-nakath/geodt