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

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.     

A control problem with structural choices

The case is considered in which, during the operation of an optimal control system, the optimizer, in addition to applying his usual control, may switch structures. Necessary and sufficient conditions are derived and emphasis is placed on the special characteristics of this problem. Continuous and discrete time set-ups are considered and the separation principle is shown not to hold for the linear quadratic case in the presence of noise.     

Stability analysis of nonlinear control systems with characteristics equations having complex coefficients

In this paper, the stability equation method is applied to the analysis of nonlinear systems with characteristics equations having complex coefficients. Three types of systems are studied: those with unstable open-loop poles, unstable characteristics roots or an equal number of open-loop poles and zeros.