Statistical Properties of Marine Surface Slopes Using Glitter Patterns: The 2-D Case

A glitter pattern is a set of bright spots. To have a bright spot on the water, the slope of a point on the sea surface must provide a specular reflection direction of the sunlight to the detector where the image will be created. This interaction is visible for all of us on a clear day with appropriate wind velocities on the sea surface. In this paper, a mathematical methodology was deduced, which is suggested to apply in real images of the sea. First, the suitable 2-D geometry of the reflection situation was determined. Then, the range of the slopes that satisfies the specular reflection condition for each direction was obtained; in addition, the 2-D statistical relationships between the glitter patterns of the sea surface and the sea surface slopes for different wind velocities on the sea surface were deduced using a 2-D Rect and a Gaussian glitter function, considering Gaussian and non-Gaussian probability density functions. Finally, doing parallel computing, the results consistent with the extension of the 1-D case were obtained. This method could be applied on real images, instead of using pressure sensors and others expensive electronic dispositives to model ocean behavior and other various oceanographic studies.