Geometric Calibration of Digital Cameras for 3D Cumulus Cloud Measurements

Abstract

A technique for calibrating digital cameras for stereo photogrammetry of cumulus clouds is presented. It has been applied to characterize the formation of summer thunderstorms observed during the Cumulus Photogrammetric, In Situ, and Doppler Observations (CuPIDO) project. Starting from gross measurements of locations, orientations of cameras, and landmark surveys, accurate locations and orientations of the cameras are obtained by minimizing a geometric error (GE). Once accurate camera parameters are obtained, 3D positions of cloud-feature points are computed by triangulation. The main contributions of this paper are as follows. First, it is proven that the GE has only one minimum in the neighborhood of the real parameters of a camera. In other words, searching the minimum of the GE enables the authors to find the right camera parameters even if there are significant differences between the initial measurements and their true values. Second, a new coarse-to-fine iterative algorithm is developed that minimizes the GE and finds the camera parameters. Numerical experiments show that the coarse-to-fine algorithm is efficient and effective. Third, a new landmark survey based on a geographic information system (GIS) rather than field measurements is presented. The GIS landmark survey is an effective and efficient way to obtain landmark world coordinates for camera calibrations in these experiments. Validation of this technique is achieved by the data collected by a NASA/Earth Observing System satellite and an instrumented aircraft. This paper builds on previous research and details the calibration and 3D reconstructions.