Some Statistical Properties of Surface Slopes via Remote Sensing Using Variable Reflection Angle Considering a Non-Gaussian Probability Density Function

Relationships to obtain information concerning some statistical properties of surface slope from statistical properties of the image intensity in remotely sensed images, considering a variable detector line-of-sight angle, are shown. The brightness distribution in sunlight reflected from the ruffled sea surface is related to the joint probability distribution of the two components of surface slope. A 1-D section through the brightness distribution provides values of the joint distribution along a line through the joint distribution. Considering the assumption that all the ocean waves are moving along a single direction and that the observer and the sun are both in the vertical plane containing this direction, a new expression between the variance of the intensity in the image and the variance of the surface slopes is derived considering a non-Gaussian statistics where the skewness and kurtosis moments are taken into account. The relation between correlation functions of the intensities in the image and surface slopes is numerically analyzed; in the non-Gaussian statistics, the skewness moment was considered only. The 1-D case is considered, and the results are graphically presented.