1790 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 20 Terrestrial Photogrammetry of Weather Images Acquired in Uncontrolled Circumstances ERIK N. RASMUSSEN Cooperative Institute for Mesoscale Meteorological Studies, and NOAA/National Severe Storms Laboratory, Norman, Oklahoma ROBERT DAVIES-JONES NOAA/National Severe Storms Laboratory, Norman, Oklahoma RONALD L. HOLLE Tucson, Arizona (Manuscript received 12 August 2002, in ®nal form 14 April 2003) ABSTRACT This paper describes an accurate automated technique of terrestrial photogrammetry that is applied to weather images obtained in uncontrolled circumstances such as unknown focal length and 3D camera orientation (azimuth and tilt of the optical axis, and roll about this axis), principal point unmarked on the image, and undetermined lens horizon. With the possible exception of the principal point, these quantities are deduced rapidly by a computer algorithm, with input consisting of accurate azimuth and elevation angles of landmarks that appear in the image. The algorithm works for wide-angle as well as for telephoto images and is more accurate than previous methods, which are based on assumptions of small angles and zero roll. Results are insensitive to the exact position of the principal point for telephoto images. For wide-angle photography, the principal point can be determined only if there is a suf®cient number of accurately measured landmarks with diverse azimuth and elevation angles. If all the landmarks have low elevation angles, the principal point is impossible to determine and must be assumed to lie at the intersection of the diagonals of the uncropped image. The algorithm also provides the azimuth and elevation angle of any object, given the position of its image in the photograph. A photogrammetric search technique is described for ®nding an entity, which is visible in one camera's photography, in the simultaneous image obtained from a different direction by a second camera. Once the same object has been identi®ed in both images, its 3D position is determined by triangulation. 1. Introduction metrically. Wakimoto and Bringi (1988) utilized radar data overlaid on still photographs to document the de- This paper describes an accurate automated technique velopment and descent of precipitation in deep cumulus of terrestrial1 photogrammetry that applies to weather clouds during the Microburst and Severe Thunderstorm images obtained in uncontrolled circumstances. Tradi- tionally, photogrammetry has been performed on care- (MIST) project. Colorado microbursts were similarly fully obtained images from special airborne cameras analyzed using still photographs (Wakimoto et al. 1994). with carefully calibrated focal length and orientation A set of images of a Colorado tornado was overlaid (Slama 1980). In meteorological terrestrial photogram- with Doppler radar data in the analysis of Wakimoto metry, images have provided much useful information. and Martner (1992). These studies were performed with For example, Hoecker (1960), Golden and Purcell telephoto images obtained under relatively controlled (1978), and others cited in Bluestein and Golden (1993) circumstances: that is, known focal length lenses and have measured wind speeds in tornadoes photogram- negligible difference between the lens and visible ho- rizons (for de®nitions of terms, see Table 1). This is not always the case with terrestrial weather photographs. 1 Photogrammetry in general is much more often concerned with These investigators used established photogrammetry measurements in airborne photographs obtained at near-vertical inci- dence. Terrestrial photogrammetry is concerned with measurements in procedures (Holle 1982, hereafter H82) that apply only photographs obtained from the ground at incidence close to horizontal. to objects with small angular displacements from the principal axis of the lens and assume that the camera is held perfectly horizontally. In other words, the roll angle Corresponding author address: Erik Rasmussen, 50742 Bear Run Dr., P.O. Box 267, Mesa, CO 81643. of the camera, or the angle at the principal point between E-mail: [email protected] the ``vertical'' side on the photograph and true vertical q 2003 American Meteorological Society Unauthenticated | Downloaded 09/30/21 08:41 PM UTC DECEMBER 2003 RASMUSSEN ET AL. 1791 TABLE 1. De®nitions of common photogrammetry terms. Focal length The distance from the rear nodal point to the plane of best focus for distant objects Lens horizon, horizon line The intersection of the photograph (or image) with the horizontal plane through the rear nodal point of the lens Magni®cation Ratio of size of projected or enlarged image to the size on ®lm (or electronic imager) Nodal points Front and rear nodal points are points on the optical axis of a lens such that when all object distances O are measured along the optical axis from the front nodal point (FNP) and all image distances I are measured similarly from the rear nodal point (RNP), they satisfy the thin lens relation 1/ f 5 1/O 1 1/I. The ray that emerges from the RNP is parallel to the ray that is incident at the FNP Optical axis, principal axis A straight line connecting the center of curvature of the lens elements and passing through the principal point of the image Principal azimuth Azimuth of the camera principal axis relative to true north Principal horizontal line Line through principal point in image, parallel to the bottom edge Principal point Point near the center of the image through which the principal axis passes; at center of image for correctly positioned ®lm or image sensor Principal vertical line Line through principal point in image, parallel to the side Roll Angle at which the camera is rotated about its own optical axis Tilt Angle of the camera optical axis above the true horizon Visible horizon Where the earth meets the sky in object space, is assumed to be identically zero. Saun- Very little information is present in the formal mete- ders (1963) outlined a more general technique that in- orological literature concerning techniques for single- volves ®nding the lens horizon by a manual trial-and- camera or multicamera photogrammetry of images ob- error method. The fast computer algorithm presented in tained in these uncontrolled circumstances. For that mat- this paper is essentially an automated and more precise ter, papers in the formal literature rarely address issues version of Saunders' method with the labor-intensive such as the actual location of the horizon line, camera manual iterations replaced by convergent iterative solu- roll angle about the optical axis, or other crucial details tions of the photogrammetric equations. of photogrammetric analysis. This paper describes a new The methods in this paper apply to movie or video algorithm for analyzing terrestrial weather images ob- images as well as still images. Historically, movies have tained with any type of lens (telephoto, normal, or wide been used to assess the motion of cloud or debris by angle). The input for this algorithm consists of measure- comparing positions of a feature between frames ex- ments obtained in prephotogrammetry surveys from the posed at a known time interval [e.g., Golden and Purcell camera site (section 2). The information that must be (1978), Hoecker (1960), and references cited by Blue- obtained in these surveys consists of locating the exact stein and Golden (1993)]. Much of the literature con- camera position and from this point measuring precisely cerning motion picture weather photogrammetry is in- the azimuth and elevation angles of landmarks that appear formal and will not be cited here. In most cases the in the images. The mathematical method for retrieving small-angle (linear scaling) approximation described in focal length, principal azimuth, and camera tilt and roll section 3 was appropriately utilized for image scaling, is developed in section 3. Once these parameters are and prephotogrammetry determination of landmark az- found, the azimuth and elevation angle of any feature in imuth and elevation was used for image orientation. the image can be determined. The scale distortion in- In recent ®eld programs such as the Veri®cation of herent in photographs obtained with wide-angle lenses is Rotation in Tornadoes Experiment (VORTEX; Rasmus- accommodated by the nonlinear equations developed sen et al. 1994) numerous photographs and video images herein. The algorithm is tested in section 4 using a tele- were obtained and proved very useful for deducing cloud photo image obtained during VORTEX and also simu- and tornado locations. These photographs were typically lated wide-angle photography. The range of a visible fea- obtained with unknown focal length and camera orien- ture from a camera is unknown unless further information tation, unmarked principal point, and poorly calibrated is available such as the map of the damage path in the image placement with respect to the camera optical axis. case of a tornado or a simultaneous image from a second Often, cameras were hand-held with little attention to camera with a different viewing angle. Section 5 de- careful orientation with respect to the horizon. The cam- scribes a search method used in analyses of VORTEX eras used lenses with a variety of focal lengths that often data for locating the same feature in photographs from changed between exposures. Exact camera position was different directions and then deducing its 3D position. seldom recorded. Photographic parameters are not re- corded at the time either