A stereo photographic physical model for ocean wave measurement

Abstract

Unlike the traditional models, a new stereo photographic model requiring no sea control points that are difficult to lay on a sea surface is developed in this paper. It is realized according to the order of camera intrinsic parameters calibration, relative orientation and absolute orientation based on average sea surface, and we give the governing equations and its algorithms. First of all, in the paper we present an imaging model that adopts non-measurement camera with considering only the radial distortion coefficients, and then give the method that calculates the camera intrinsic parameters by combining the co-planar equations and the distance equations to form a closed system of equations. For verifying the convergence of the governing equations, we lay four parallel sand ridges on a level ground in laboratory, measure seven lines of different heights and take a pair of the images by two cameras. The intrinsic parameters are successfully calculated by using the method, and further analysis shows that the results are highly precise. When observing the ocean waves in offshore sea, we need to recalculate the relative orientation parameters. At this time the governing equations are the co-planar equations, but the accuracy of the image matching is seriously related to the accuracy of the relative orientation parameters. However, as the mirror reflection of the sea surface, the matching accuracy of the sea image is often low, so we select 407 optimal matching points from among 1600 conjugate points and calculate the parameters. It needs a sequence of sea image pairs to obtain the absolute orientation parameters, 256 pairs in the paper. For each pair, we select firstly 300300 feature points on the left image approximately evenly, then find the conjugate points on the right image by image matching, calculate the coordinates of the corresponding sea surface points in the left camera coordinate system, and then fit the points into a plane; thus a plane sequence can be obtained. We establish a special object coordinate system on the average sea surface that is obtained by summing the plane sequence, and calculate the absolute orientation parameters by the geometric relationship between the two coordinate systems. And it is proved that the methods of relative orientation and absolute orientation proposed in this paper are feasible by reconstructing sea surface height field. The model greatly reduces the difficulty in calibrating the stereoscopic photography for ocean wave measurement, which is beneficial to its popularization and application.