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Close-Range Photogrammetry
The remaining two types of perspective imagery deal with the two and three dimensions of object space. Thus, starting again, with one-point perspective which is fairly easy for everyone to visualize. You (the camera) are standing at a camera position in the middle of an endless plane. Resting on this plane, in front of us (the camera), is a very large and tall rectangular building. This large building is twice as long as it is wide, with doors and windows along each floor. The door frames are of the same size and as are all of the window openings. What we see is what the camera “sees,” one side of the building. 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 in this image of the building. In effect we have a very detailed orthographic elevation view of the side of the building.
Moving 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 with the short side receding to our right and the long side receding to our left. All of the vertical lines are parallel to each other and 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 line of the camera lens (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.
An example of the use of close-range photogrammetry is that of a tractor-trailer (18 wheeler) and two four wheeled vehicles. To describe the many details of this graphical analysis is beyond the scope of this article, however there were many single-photo perspective analyses completed to provide the data necessary to produce the two dimensional plot of the accident site for the use in the accident reconstruction. One of the photographs that were scanned and used in the analysis, along with a plot developed from a number of photographs are shown. This is a typical simple image to plot analysis, whereas there are many such cases involving more than 20 vehicles where the accident scene covers as much as a half a mile (more than 800 meters) in length.
In the situation of the accident imagery shown it is the roadway lane lines and the overpass (bridge) that provide the lines defining this image as two-point perspective. With this information the stripes dividing the lanes were used to define rectangles of known dimensions. With this information the plot plan view was developed. In addition to this information the investigating police officers provided dimensional information about lane widths, stripe lengths, bridge column diameters and separation between columns, along with several other dimensions of the accident scene. This field data (dimensions) and the photographs taken by the police were required to generate this basic plot as shown. Those who have used close-range photogrammetry procedures such as the one shown in this article know full well that only the tip of the work effort has been shown/discussed.
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 data base available and the resulting analysis, graphical or analytical, provide the proof.
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