Effects of light refraction on the accuracy of camera calibration and reconstruction in underwater motion analysis

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Abstract
One of the most serious obstacles to accurate quantification of the underwater motion of a swimmer's body is image deformation caused by refraction. Refraction occurs at the water‐air interface plane (glass) owing to the density difference. Camera calibration‐reconstruction algorithms commonly used in aquatic research do not have the capability to correct this refraction‐induced nonlinear image deformation and produce large reconstruction errors. The aim of this paper is to provide a thorough review of: the nature of the refraction‐induced image deformation and its behaviour in underwater object‐space plane reconstruction; the intrinsic shortcomings of the Direct Linear Transformation (DLT) method in underwater motion analysis; experimental conditions that interact with refraction; and alternative algorithms and strategies that can be used to improve the calibration‐reconstruction accuracy. Although it is impossible to remove the refraction error completely in conventional camera calibration‐reconstruction methods, it is possible to improve the accuracy to some extent by manipulating experimental conditions or calibration frame characteristics. Alternative algorithms, such as the localized DLT and the double‐plane method are also available for error reduction. The ultimate solution for the refraction problem is to develop underwater camera calibration and reconstruction algorithms that have the capability to correct refraction.