4.12. Determination of Height from Vertical Aerial Photographs

One of the important application of stereo-photographs is the determination of elevations of various points in the overlap region. For this purpose, a parallax bar, also known as a stereo-meter, is used for taking the measurements. The pre-requisite is that the elevation of at least one control point is known in the common area (like ground leveling method) before the computation of elevations of other unknown points. The details of the control points are sometimes supplied along with the aerial photographs, else some permanent point is selected and its elevation is determined either from the contour map or leveling or GPS observations.

This chunk introduces the concept of using stereo-photographs to determine the height of various ground points. In aerial photography, stereo-photographs are pairs of photographs taken from different angles, allowing for a 3D perception of the terrain. To compute the height of unknown points, at least one control point with a known elevation must exist. This known point acts as a reference. The information regarding control points may accompany the photographs, or it may need to be gathered separately using contour maps, leveling methods, or GPS. Essentially, this step is critical because without a reference height, accurate height calculations for other points cannot occur.

Think of the control point as a ‘starting line’ in a race. Just like runners need a defined starting point to measure how far they’ve run, aerial photographs need a known height to accurately compute the elevations of other unseen terrain points. If you have one runner's distance (the height of the control point), you can figure out the distances traveled by other runners based on that reference.

The first step in creating a stereo-model is that the stereo-pair must be properly oriented under the stereoscope. The process of orientation is called base lining, which is performed as below: 1. On both the photographs, their respective principal point and conjugate principal point are marked, as shown in Figure 4.18a. Principal point and conjugate principal point are joined by a straight line and the line extended on each photo. This line represents the flight line. 2. Under a mirror stereoscope, two photographs are to be kept apart in the direction of flight line on a flat surface with overlap region inwards. 3. The stereo-pair is aligned in such a way that the line drawn on both the photos lies in a straight line, as shown in Figure 4.18a. 4. The stereo-pair is seen through the stereoscope so that the left lens is over the left photograph and the right lens is over the right photograph. The line joining the centre of the lens should almost be matching with the direction of the flight line. 5. The distance between the photographs may be adjusted inward or outward till the two images are fused in the brain and a 3D model of the overlap region is created. 6. In the beginning, it might appear a bit difficult to see the two images fusing together to create a stereo-vision, but with a little more practice and concentration, it will appear to be easy. 7. Once the perfect 3D model is created and the lines drawn on the photographs fall in a line, the photographs are said to be properly oriented (or base lining is completed). 8. Select the features/points on both the photographs in the overlap region whose heights are to be determined. The visual interpretation elements (size, shape, shadow, tone, texture and surrounding objects) will help identifying the objects; but now with the addition of relief, a more natural view of terrain may be seen. 9. Use parallax bar for taking the measurements of these points. The difference between two parallax bar readings will provide parallax differences between the two points.

In this chunk, the process of orienting the stereo-pair of photographs, also known as base lining, is detailed. This process helps ensure the photographs align correctly for accurate measurements. First, important points on the photographs, called principal points, are identified and connected to form a flight line. The stereo-pair is then positioned so that two images can be viewed simultaneously through a stereoscope. Adjustments are made until a clear 3D effect is observable. The observer may need practice to merge the images successfully. Once this clarity is achieved, features of interest in the overlap area, whose heights need to be measured, are selected. Lastly, changes in readings on a parallax bar will provide important measurements for determining heights.

Imagine trying to view a 3D movie without your glasses on. Everything looks blurry, and you can't make out the details. Once you put on the glasses (the stereoscope), the images come into focus, allowing you to see the depth of the scenes. Similarly, base lining the stereo-pair ensures that when we view the photographs through the stereoscope, they align properly, allowing us to perceive the true shapes and heights of the objects.

The change in position of an image from one photo to the next due to aircraft’s motion is called stereoscopic parallax, x-parallax, or simply parallax. The parallax is directly related to the elevation of the point, and is greater for high points than for low points. The parallax bar is a device used to measure the difference of parallax between any two points on the stereo-photographs, more precisely. The parallax bar consists of a graduated metallic rod (in mm) attached with two bars, as shown in Figure 4.19. Left bar is fixed with the rod and right bar is movable with micrometer drum attached on right end of the graduated rod. A pair of glass graticules, one at each bar can be inserted into the grooves provided in the bar. Each graticule is etched with three small identical index marks (cross, dot or circle), called floating marks. The left hand bar is generally clamped at any required distance so that the entire overlap area is covered by the separation of left and right floating marks.

This chunk explains the concept of parallax and how it can be measured with a parallax bar. Parallax refers to the apparent change in position of an object when viewed from two different angles—in this case, from two photos taken from slightly different locations by an aircraft. High points on the ground create a larger parallax effect than low points. The parallax bar is a specialized tool designed to measure this effect very accurately. It consists of a rigid rod and two bars, with the left bar fixed and the right bar movable. This design allows for precise measurement of the distance between corresponding points on the stereo-photographs. Each bar has marked graticules (like little measuring points) that can be adjusted for accurate parallax readings.

Think of the parallax effect like looking at a distant mountain from two different viewpoints. When you shift your position, the mountain appears to move against the background of the sky. By measuring how it moves (the parallax), we can infer how tall it is based on distances we already know. Similarly, the parallax bar quantifies this effect from the photographs, allowing us to measure elevations accurately.

The absolute parallax of a point on a stereo-pair is determined as the algebraic difference between two distances which are measured from the corresponding principal points, parallel to the direction of flight (air base). It is also called x-parallax. Figure 4.20 shows a stereo-pair where locations of two points a and b are marked with their x-coordinates. Let the distance on left photo be x and x on right photo be x' and x'. The absolute parallax of a point is determined as the algebraic difference between two distances of a point, it is computed as given below. p = x - x'. The distances on the left and right photos are measured with the help of parallax scale, which is shown in Figure 4.21. This scale has a better least count that the normal scale (ruler) available for manual measurements. It has a main scale and a vernier scale and the addition of both the readings is the final distance.

Here, the focus is on how to compute height measurements from the parallax readings obtained from the stereo-pair. Absolute parallax is the difference in measurement between two corresponding points in both photographs (left and right). It helps us understand how much a point's position shifts due to its elevation—higher points show a larger parallax compared to lower ones. This measurement is done using a parallax scale, which provides more accuracy than regular scales because it includes a main scale and a vernier scale.

Imagine trying to measure how high a friend is standing on a hill compared to another friend lower down. If you take a picture of them from two different angles, the one higher up will appear to shift more in the second photo than the one down low. By measuring how that shift appears (the parallax) using a precise ruler (the parallax scale), you can calculate just how much higher your friend on the hill actually is.

Let A and B be two points whose images are a and b on left photo and a and b on right photo (Figure 4.22). The stereo images are taken from L and L with B as air base distance and H as the flying height. Let h and h be the heights of these points with respect to a datum. The parallax difference is related with the difference in parallax bar readings. The parallax p at point A is related as follows. Since the elevation of a ground point A (h_a) is known from reference map or field observation or contour map, the elevation of unknown point B can be determined (say h_b) using parallax bar measurements.

In this chunk, we see how height is estimated using the measurements obtained earlier. In essence, given two points (A and B) on a stereo-pair, the relationship between their respective parallax readings helps in calculating their heights. We can calculate the height of an unknown point (B) by utilizing the height of a known point (A) and factoring in the difference in their parallax readings. This shows the practical use of all previous measurements and aligns them with known data to provide accurate height values for the unknown points.

Imagine you're on a hiking trip, and you know how high a particular rock formation is (Point A). You've also captured a picture of another rock formation (Point B) while standing in a different position. By discerning how much Parallax changes when you look at both formations from different angles, you can figure out how tall Point B is based on your knowledge of Point A's height.

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