Proceedings Article | 6 November 2017

Proc. SPIE. 10424, Remote Sensing of Clouds and the Atmosphere XXII

KEYWORDS: Clouds, Cameras, Stars, Mathematical modeling, Data modeling, Distortion, Statistical modeling, Solar radiation models, Paraxial approximations, Affine motion model

Earlier, we developed a method for estimating the height and speed of clouds from cloud images obtained by a pair of digital cameras. The shift of a fragment of the cloud in the right frame relative to its position in the left frame is used to estimate the height of the cloud and its velocity. This shift is estimated by the method of the morphological analysis of images. However, this method requires that the axes of the cameras are parallel. Instead of real adjustment of the axes, we use virtual camera adjustment, namely, a transformation of a real frame, the result of which could be obtained if all the axes were perfectly adjusted. For such adjustment, images of stars as infinitely distant objects were used: on perfectly aligned cameras, images on both the right and left frames should be identical. In this paper, we investigate in more detail possible mathematical models of cloud image deformations caused by the misalignment of the axes of two cameras, as well as their lens aberration. The simplest model follows the paraxial approximation of lens (without lens aberrations) and reduces to an affine transformation of the coordinates of one of the frames. The other two models take into account the lens distortion of the 3rd and 3rd and 5th orders respectively. It is shown that the models differ significantly when converting coordinates near the edges of the frame. Strict statistical criteria allow choosing the most reliable model, which is as much as possible consistent with the measurement data. Further, each of these three models was used to determine parameters of the image deformations. These parameters are used to provide cloud images to mean what they would have when measured using an ideal setup, and then the distance to cloud is calculated. The results were compared with data of a laser range finder.