Axial Camera Research Articles

Drift Reduction in Underwater Egomotion Computation by Axial Camera Modeling

Localization of autonomous underwater vehicles is essential for underwater exploration, environmental monitoring, and infrastructure inspections, as only a few examples. As wirelessly transmitted data cannot be used in underwater navigation, and equivalent sensors are costly and not readily deployable, the use of cameras as a localization aid offers an attractive alternative. Nonetheless, the utilization of cameras for underwater navigation is hindered by medium-induced visual deterioration and refraction of the incident ray. While most research has been focusing on addressing the radiometric deterioration effects, we demonstrate that the introduction of a physically aware model of the refraction effect can significantly improve the platform localization. Specifically, we develop a refraction-aware continuous formulation of the egomotion model, which computes the translational and rotational velocities using optical flow measurements. We also demonstrate that a linear model can be reached despite the nonlinear ray's path. Results show an improved navigation solution echoed by a significant reduction in the drift with more than tenfold improvement in the estimated position and angular quantities compared to state-of-the-art methods. They demonstrate the benefit of exact modeling in underwater navigation.

A three-point solution with scale estimation ability for two-view flat-refractive underwater photogrammetry

Underwater photogrammetry can efficiently document complex environments with limited accessibility. As the establishment of reference control networks is involved, using the relative two-view relation, which requires neither knowledge nor estimation of object-space coordinates, offers an attractive solution. In this paper, we study the two-view relation of underwater photogrammetry flat refractive geometry. Through its axial camera form, we show that the necessary correspondences to establish the relative orientation can be reduced to only three points. We also show that all six relative pose parameters can be estimated directly, where the baseline is estimated to its scale, with no external control. For the estimation, we propose direct models, and in seeking optimal minimization forms, we develop a closed-form expression for the epipolar curve. Thereby, we shed light on the epipolar geometry of the flat-refractive imaging system. For a complete evaluation, we also analyze the limits of the baseline estimation to its actual scale. In addition to our scale estimation ability, results show improved accuracy in the relative orientation parameters by order of magnitude or more compared to the state-of-the-art. Experiments demonstrate how our proposed model yields sub-millimeter levels of internal 3-space accuracy without introducing external knowledge.

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 Two-View Reconstruction for Underwater 3D Vision

Recovering 3D geometry from cameras in underwater applications involves the Refractive Structure-from-Motion problem where the non-linear distortion of light induced by a change of medium density invalidates the single viewpoint assumption. The pinhole-plus-distortion camera projection model suffers from a systematic geometric bias since refractive distortion depends on object distance. This leads to inaccurate camera pose and 3D shape estimation. To account for refraction, it is possible to use the axial camera model or to explicitly consider one or multiple parallel refractive interfaces whose orientations and positions with respect to the camera can be calibrated. Although it has been demonstrated that the refractive camera model is well-suited for underwater imaging, Refractive Structure-from-Motion remains particularly difficult to use in practice when considering the seldom studied case of a camera with a flat refractive interface. Our method applies to the case of underwater imaging systems whose entrance lens is in direct contact with the external medium. By adopting the refractive camera model, we provide a succinct derivation and expression for the refractive fundamental matrix and use this as the basis for a novel two-view reconstruction method for underwater imaging. For validation we use synthetic data to show the numerical properties of our method and we provide results on real data to demonstrate its practical application within laboratory settings and for medical applications in fluid-immersed endoscopy. We demonstrate our approach outperforms classic two-view Structure-from-Motion method relying on the pinhole-plus-distortion camera model.

The Pinax-model for accurate and efficient refraction correction of underwater cameras in flat-pane housings

The calibration and refraction correction process for underwater cameras with flat-pane interfaces is presented that is very easy and convenient to use in real world applications while yielding very accurate results. The correction is derived from an analysis of the axial camera model for underwater cameras, which is among others computationally hard to tackle. It is shown how realistic constraints on the distance of the camera to the window can be exploited, which leads to an approach dubbed Pinax Model as it combines aspects of a virtual pinhole model with the projection function from the axial camera model. It allows the pre-computation of a lookup-table for very fast refraction correction of the flat-pane with high accuracy. The model takes the refraction indices of water into account, especially with respect to salinity, and it is therefore sufficient to calibrate the underwater camera only once in air. It is demonstrated by real world experiments with several underwater cameras in different salt and sweet water conditions that the proposed process outperforms standard methods. Among others, it is shown how the presented method leads to accurate results with single in-air calibration and even with just estimated salinity values.

Optimizing rotating gamma camera PET for brain imaging

Several acquisition geometries were investigated to optimize coincidence count rates and coincidence/singles rate ratios for brain imaging on a rotating gamma camera PET system. Detection efficiency and singles count rate limits on these systems dictate that keeping unused singles from hitting the cameras should improve coincidence rates if radiotracer doses can be adjusted to match the singles detection efficiency of the system. Radius of rotation and camera field of view were adjusted within the constraints of patient positioning. Acquisitions were done with transaxial septa on a graded absorber, and with graded absorber alone. Phantoms included a Ge-68 pin source and an extended head-thorax phantom with F-18 solution. Coincidence detection efficiency was best for the absorber only, with a small radius of rotation. Coincidence/singles ratio was best for graded absorber with small radius of rotation and axial camera field limited to 27 cm. The septa yielded a slightly lower coincidence/singles ratio, but their reduction of scatter and restriction of incidence angle of detected photons (leading to higher spatial resolution) makes their use favorable.