CONJUGATE TRAJECTORY AND ITS UNCERTAINTY OF FLAT-REFRACTIVE STEREO-PAIR IN MULTIMEDIA ENVIRONMENT

Abstract

In a single-media environment, dense image matching can be effectively conducted along one-dimensional epipolar line or by row-to-row corresponding epipolar imagery. In contrast, when the light passes through multi-media in an underwater flat-port camera, incident ray is refracted, and conjugate trajectory becomes a quartic curve, complicating the image matching task. Although the quartic curve can be realized by ray tracing or refractive fundamental matrix, the former is lack of explicit equation of the trajectory, while the latter is mathematically complex. Furthermore, not only the curve itself is crucial, but also the uncertainty, resulting from the errors of relevant parameters, of the trajectory should be taken into consideration during the image matching process, which has not been clearly addressed in the literature yet. In this research, first, the result of conjugate trajectory is provided based on a coplanar condition in axial camera configuration. Second, one of the influential factors, the distance from perspective center it the interface, of the trajectory is analyzed by error propagation with the analytical function. Thus, it is the aim of this study to provide a more efficient way to locate the quartic trajectory and define the error range of the trajectory for the mission of underwater dense image matching as employing flat-refractive imaging system.