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Any inaccuracy will lead to significant errors in the measured dimensions of artefacts Capra et al. Other applications such as structural monitoring or seabed mapping must achieve a specified level of accuracy for the surface shape. Calibration of any camera system is essential to achieve accurate and reliable measurements. Small errors in the perspective projection must be modelled and eliminated to prevent the introduction of systematic errors in the measurements.

Compared to in-air calibration, camera calibration under water is subject to the additional uncertainty caused by attenuation of light through the housing port and water media, as well as the potential for small errors in the refracted light path due to modelling assumptions or non-uniformities in the media. Accordingly, the precision and accuracy of calibration under water is always expected to be degraded relative to an equivalent calibration in-air. Experience demonstrates that, because of these effects, underwater calibration is more likely to result in scale errors in the measurements.

In a limited range of circumstances calibration may be unnecessary.

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If a high level of accuracy is not required, and the object to be measured approximates a 2D planar surface, a straightforward solution is possible. Correction lenses or dome ports such as those described in Ivanoff and Cherney and Moore can be used to provide a near-perfect central projection under water by eliminating the refraction effects. Any remaining, small errors or imperfections can either be corrected using a grid or graticule placed in the field of view, or simply accepted as a small deterioration in accuracy.

The correction lens or dome port has the further advantage that there is little, if any, degradation of image quality near the edges of the port.

Plane camera ports exhibit loss of contrast and intensity at the extremes of the field of view due to acute angles of incidence and greater apparent thickness of the port material. This simplified approach has been used, either with correction lenses or with a pre-calibration of the camera system, to carry out two-dimensional mapping.

A portable control frame with a fixed grid or target reference is imaged before deployment or placed against the object to measured, to provide both calibration corrections as well as position and orient the camera system relative to the object. Typical applications of this approach are shipwreck mapping Hohle , sea floor characterization surveys Moore , length measurements in aquaculture Petrell et al. If accuracy is a priority, however, and especially if the object to be measured is a 3D surface, then a comprehensive calibration is essential.

The correction lens approach assumes that the camera is a perfect central projection and that the entrance pupil of the camera lens coincides exactly with the centre of curvature of the correction lens. Any simple correction approach, such as a graticule or control frame placed in the field of view, will be applicable only at the same distance. Any significant extrapolation outside of the plane of the control frame will inevitably introduce systematic errors. The alternative approach of a comprehensive calibration translates a reliable technique from in-air into the underwater environment.

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Close range calibration of cameras is a well-established technique that was pioneered by Brown , extended to include self-calibration of the camera s by Kenefick et al. The mathematical basis of the technique is reviewed in Granshaw Typical portable calibration fixture left, courtesy of NOAA and test range. Right, from Leatherdale and Turner Top: a set of calibration images from an underwater stereo-video system using a 3D calibration fixture.

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Both the cameras and the object have been rotated to acquire the convergent geometry of the network. Bottom: a set of calibration images of a 2D checkerboard for a single camera calibration, for which only the checkerboard has been rotated. From Bouguet The disadvantage, however, is that the camera system must be transported to the range and then back to the deployment location.

In comparison, accurate information for the positions of the targets on a portable calibration fixture is not required, as coordinates of the targets can be derived as part of a self-calibration approach. Hence, it is immaterial if the portable fixture distorts or is dis-assembled between calibrations, although the fixture must retain its dimensional integrity during the image capture. Scale within the 3D measurement space is determined by introducing distances measured between pre-identified targets into the self-calibration network El-Hakim and Faig The known distances between the targets must be reliable and accurate, so known lengths are specified between targets on the rigid arms of the fixture or between the corners of the checkerboard.

In practice, cameras are most often pre-calibrated using a self-calibration network and a portable calibration fixture in a venue convenient to the deployment. The refractive index of water is insensitive to temperature, pressure or salinity Newton , so the conditions prevailing for the pre-calibration can be assumed to be valid for the actual deployment of the system to capture measurements.

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The assumption is also made that the camera configurations, such as focus and zoom, and the relative orientation for a multi camera system, are locked down and undisturbed. In practice this means that the camera lens focus and zoom adjustments must be held in place using tape or a lock screw, and the connection between multiple cameras, usually a base bar between stereo cameras, must be rigid.

A close proximity between the locations of the calibration and the deployment minimizes the risk of a physical change to the camera system. The process of self-calibration of underwater cameras is straightforward and quick. The calibration can take place in a swimming pool, in an on-board tank on the vessel or, conditions permitting, adjacent to, or beneath, the vessel. The calibration fixture can be held in place and the cameras manoeuvred around it, or the calibration fixture can be manipulated whilst the cameras are held in position, or a combination of both approaches can be used Fig.

For example, a small 2D checkerboard may be manipulated in front of an ROV stereo-camera system held in a tank. A large, towed body system may be suspended in the water next to a wharf and a large 3D calibration fixture manipulated in front of the stereo video cameras. In the case of a diver-controlled stereo-camera system, a 3D calibration fixture may be tethered underneath the vessel and the cameras moved around the fixture to replicate the network geometry shown in Fig.

There are very few examples of in situ self-calibrations of camera systems, because this type of approach is not readily adapted to the dynamic and uncontrolled underwater environment. Nevertheless, there are some examples of a single camera or stereo camera in situ self-calibration Abdo et al.

In most cases a pre- or post-calibration is conducted anyway to determine an estimate of the calibration of the camera system as a contingency. The geometry of perspective projection based on physical calibration parameters.

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Radial distortion is a by-product of the design criteria for camera lenses to produce very even lighting across the entire field of view and is defined by an odd-ordered polynomial Ziemann and El-Hakim Three terms are generally sufficient to model the radial lens distortion of most cameras in-air or in-water. Decentring distortion is described by up to four terms Brown , but in practice only the first two terms are significant. This distortion is caused by the mis-centring of lens components in a multi-element lens and the degree of mis-centring is closely associated with the quality of the manufacture of the lens.

The magnitude of this distortion is much less than radial distortion Figs. Schematic view of a stereo-image measurement of a length from 3D coordinates top and view of a measurement interface bottom. Courtesy E. Comparison of radial lens distortion from in-air and in-water calibrations of a GoPro Hero4 camera operated in HD video mode. Comparison of decentring lens distortion from in-air and in-water calibrations of a GoPro Hero4 camera operated in HD video mode. Note the much smaller range of distortion values vertical axis compared to Fig.

Comparison of parameters from in-air and in-water calibrations for two GoPro Hero4 camera used in HD video mode. The disadvantage of the absorption approach for the refractive effects is that there will always be some systematic errors which are not incorporated into the model. The effect of refraction invalidates the assumption of a single projection centre for the camera Sedlazeck and Koch , which is the basis for the physical parameter model. The errors are most often manifest as scale changes when measurements are taken outside of the range used for the calibration process.

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Experience over many years of operation demonstrates that, if the ranges for the calibration and the measurements are commensurate, then the level of systematic error is generally less than the precision with which measurements can be extracted. This masking effect is partly due to the elevated level of noise in the measurements, caused by the attenuation and loss of contrast in the water medium.

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The alternative to the simple approach of absorption is the more complex process of geometric correction, effectively an application of ray tracing of the light paths through the refractive interfaces. A two-phase approach is developed in Li et al. An in-air calibration is carried out first, followed by an in-water calibration that introduces 11 lens cover parameters such as the centre of curvature of the concave lens and, if not known from external measurements, refractive indices for the lens covers and water.

A more general geometric correction solution is developed for plane port housings in Jordt-Sedlazeck and Koch Additional unknowns in the solution are the distance between the camera perspective centre and the housing, and the normal of the plane housing port, whilst the port thickness and refractive indices must be known.

Using ray tracing, Kotowski develops a general solution to refractive surfaces that, in theory, can accommodate any shape of camera housing port. The shape of the refractive surface and the refractive indices must be known. Maas , develops a modular solution to the effects of plane, parallel refraction surfaces, such as a plane camera port or the wall of a hydraulic testing facility, which can be readily included in standard photogrammetric tools. A variation on the geometric correction is the perspective centre shift or virtual projection centre approach.

A specific solution for a planar housing port is developed in Telem and Filin The parameters include the standard physical parameters, the refractive indices of glass and water, the distance between the perspective centre and the port, the tilt and direction of the optical axis with respect to the normal to the port, and the housing interface thickness.

A modified approach neglects the direction of the optical axis and the thickness of thin ports, as these factors can be readily absorbed by the standard physical parameters. The advantage of these techniques is that, without the approximations in the models, the correction of the refractive effects is exact. The disadvantages are the requirements for two phase calibrations and necessary data such as refractive indices. Further, in some cases the theoretical solution is specific to a housing type, whereas the absorption approach has the distinct advantage that it can be used with any type of underwater housing.

As well as the common approaches described above, some other investigations are worthy of note.