Fig. 5

Geometry of image acquisition, camera calibration and plume height estimation. (A) the camera projects a point in 3D space to a point in 2D space based on its internal geometry, or intrinsic parameters (focal length, principal point, distortion coefficients), as well as the camera’s location and orientation. The intrinsic parameters are found by calibration, whereby intrinsic parameters are varied to minimize the difference between the projection of known 3D points onto the image and the actual imaged location of those points (the reprojection error). In a laboratory setting, (B), a pattern of known geometry is imaged from multiple angles by the same camera, and the reprojection error of identified features (red points) is minimised for the orientation and location of the camera for each image, and the intrinsics common to all images. Alternatively, cameras can be calibrated vicariously using natural features visible in a scene after it is installed in the field. Here the camera location is known, as is the location of features (red points) in the landscape (C) or astronomical bodies (D), and the error is minimised for the intrinsics and camera orientation. With the camera intrinsics, orientation and location known, a point at a height h above a notional vent location and distance d downwind can be projected onto the image (E). By varying d, a line in 3D space can be traced out on the image and by varying h the line adjusted to measure the height of some level in a plume (e.g. plume top, base, etc.)