Dr James R. Williamson
Email: [email protected]
When I first started working with photogrammetry the standard commercial method of collecting the photography was with large format cameras of one kind/type/brand or another. The view was almost always straight down from an aircraft (platform) flying in regular patterns/flight-lines and at a constant altitude. Since that time not much has changed, except the platform, camera, method of collection, processing, analysis procedures and time from start to finish. It has not made any difference if the camera is airborne, in the water, or handheld. Later there were some exceptions and the majority of those were on platforms that could be considered off-world platforms within our solar system. At that time, the major commercial use of photogrammetry was in the field of cartography. Eleven years later I was working for the Central Intelligence Agency (CIA), then years later with DoD contractors and even later, in 1990, for myself – photogrammetry has always been a science to be reckoned with in our World’s scientific endeavors. There were photogrammetry projects that involved very sophisticated cameras, collections, delivery, and procedures to get the final product – even with handheld cameras (close-range photogrammetry) which, is the arena of my life. When I started working with close-range photogrammetry the time from collection to finished project could very well be a matter of weeks or months. Then came the great advancements in the computer world and those ingenious digital cameras. In the advancement of close-range photogrammetry, computer programs, and digital cameras, there are now cameras and computer programs that allow the user to provide complete detailed dimensional information, from collection to finished project, in a matter of hours. It is this timely use of photogrammetry, with assistance from good useable geometry in the photography that makes close-range photogrammetry a very useful tool in the analysis of accident photographs.
Although the more adventurous photogrammetry projects seem to be those connected with off-world collections, which actually started from collections made from balloons. It is the high profile (pardon the pun) photogrammetry, that has sparked the art and science of modern day computerized photogrammetry, however one should never forget the fundamentals that began with the analysis of one photograph at a time. There is a wealth of information in accident photography and to obtain that information requires knowledge and experience in the fundamentals of single-photo perspective. The fundamentals are the things that never seem to change and more so with close-range photogrammetry. By definition, close-range photogrammetry is meant to be when the distance (range) from the camera to the object of interest can be from several feet to about 1,000 feet (about 1 to 300 meters). There is a phenomena in photography peculiar to the geometry of the photographic/digital image collected/captured. For the fundamentals we study plane, solid and descriptive geometry because it is the classical configuration of man-made objects. However, in close-range photogrammetry of a single image it is the geometry that we see every day of our lives, perspective geometry, where parallel lines converge to a point called a vanishing point that is utilized. In close-range photogrammetry there are basically four types of perspective imagery: true or direct scale, one-point perspective, two-point perspective and three-point perspective. Actually, these procedures are well established and very useful in the analysis vehicle accident photographs.
The first type, direct scale, is the perspective imagery captured with the camera image plane being parallel to a common plane of the object of interest such that the lines in the common plane are of a “true” scale. All that is needed is a known dimension in the common plane to provide “true” dimensions. (As true as the scale of the known dimension allows.) This image is often referred to as a direct scale image. The orientation of the camera decides whether the common plane is a horizontal or vertical plane in real (object) space. Remember the direct scale image is usually of a constant plane, such as a wall, the side of a vehicle, or an object with no vanishing lines.
The second type of perspective imagery is also where the image plane is parallel to an infinite number of planes leading up to and even beyond the object of interest – this is one-point perspective where all lines perpendicular to the image plane converge to a common point, usually the principal point on the principal ray of the camera. A quick visual reference for one-point perspective is the image of a hall where the image plane is parallel to the end wall of the hall. This same geometry can be obtained when collecting an image of a garage or a basketball court. The simple criteria for this perspective image is that the camera is held such that the principal ray of the lens is parallel to the horizontal reference plane (ground/floor) and the principal ray is perpendicular to the plane parallel to the image plane. It is possible with one-point perspective in a photograph/image to develop a scale model of horizontal and vertical planes shown in the collection.
To describe the remaining two types of perspective imagery, without illustrations, is an effort greater than was used to describe the first two types without illustrations. It supposes that the reader has not only a great imagination but also has a very good grasp of the three dimensional space lines and planes. Therefore I would like to describe one-point perspective again using a prop that everyone can easily visualize. We are standing at the camera position in the middle of an endless plane. Resting on this plane, in front of us, is a very large rectangular building that is four stories tall. This large building is twice as long as it is wide, and each side has two doors and a row of windows along each floor – five windows on the short side and ten windows on the long side. All of the door frames are of the same size and all of the window openings are of the same size. What we see is what the camera “sees.” We collect a one-point perspective image and the camera (our right eye) is oriented such that the image plane is parallel to the longest side of the rectangular building. All vertical lines are perpendicular to all of the horizontal lines, thus all vertical lines are parallel and all horizontal lines are parallel. By knowing the width of any window opening, or the width of a door frame, or the distance between any two windows, and so on, we can determine the dimensions of all items of this side of the building. In effect we have a very detailed orthographic elevation view of the long side of the building.
Now, we move our camera position such that instead of looking directly into the long side of the building we are looking directly at the closest corner of the building such that the short side recedes to our right and the long side recedes to our left. All of the vertical lines are still parallel and the lines are also parallel to the image plane. The horizontal lines of the short side of the building (to the right) will appear to converge to a common point (a vanishing point right) somewhere to our camera station right. That is, all of the horizontal lines on the short side of the building will converge to this vanishing point right. The same perspective geometry applies to the long side whose horizontal lines will converge left to a common point (a vanishing point left). Since we have not rotated our camera about the principal ray and have kept the bottom image frame edge parallel to our flat plane, our two vanishing points will rest on a horizontal line through the middle of our image frame. This is a simple description of two-point perspective.
To achieve the next perspective type we use the same camera location of the two-point camera location and simply rotate our camera up at an angle greater than six degrees. Now, none of the vertical and horizontal lines of our large building are parallel to the image plane. We still have the horizontal lines converging to the vanishing point right and vanishing point left, as before, plus we now have vertical lines from both sides of the building converging to a common point (vanishing point up). This is a simple description of three-point perspective.
Hopefully it will have been noticed how the descriptions became shorter in length as these descriptions progressed from one-point to three point perspective. They certainly did that, however one other fact must be noted – the photogrammetry has just began. A certain piece of information was left out of describing the geometry of images relating to close-range single photo/image photogrammetric analysis – that is the photo/image parameters. In general/classical photogrammetry there are nine parameters, which are relevant to the analysis of photographs/imagery. It is not always necessary in analytical and graphical photogrammetry that these nine parameters be know, however it does help provide a certain level of confidence when the final results have been obtained. In single-photo analysis the basic nine parameters are: the camera station object-space coordinates (Xc Yc Zc), camera image space coordinates (xpp ypp -f), and the three rotation angles of azimuth, tilt and swing (a t s). In multi-photo simultaneous photogrammetric adjustment analysis the last three parameters, the rotation angles, will vary by name according to the procedure used, however the resulting orientation matrix values will be the same.
In the close-range photogrammetry analysis of accident photography it is the geometry contained in the photograph that needs to be identified to enable the photogrammetrist to select the correct method/procedure. It is quite possible for the photograph to contain perspective geometry for more than one perspective analysis, or multiple applications of the same type of perspective geometry. In this short description of the four types of perspective geometry, the purpose was to provide information to help identify what could be available. In future articles the application of the methods will be presented with graphic examples. Photographs/digital-images provide a wealth of knowledge concerning the man-made objects shown. They provide the best database available and the resulting analysis- graphical or analytical provides the proof.