4.12.4. Height determination

Let A and B are 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 L1 and L2 with B as air base distance and H as the flying height. Let h_a and h_b be the heights of these points with respect to a datum.

In stereo photogrammetry, we aim to determine the height of various points on the ground using aerial images taken from different perspectives. Here, we have two points, A and B, seen in stereo images. These points appear in two different images: one from the left photo and one from the right photo. The distance between the positions of these points in the photos, called the air base (B), along with the flying height (H) gives us critical information to calculate their heights (h_a and h_b). Essentially, by knowing the relative positions in both images, we can derive the height above a reference level, or datum.

Imagine standing on a hill and taking a photo of two people standing on lower ground. If you take one photo from directly above and another from further back, you can see how their heights vary based on their distance from you. Similarly, aerial images captured from a plane allow us to observe ground points from different angles, and using these images we can figure out how tall the points (like trees or buildings) actually are.

From L draw two lines parallel to L1 a' and L2b' to cut the photographic plane at a' and b'. If the average parallax bar readings at two points a and b are P_A and P_B, respectively, the difference in absolute parallax (∆p) of p_a and p_b can be related with the difference in parallax bar readings.

To determine the heights of the points A and B accurately, we utilize a concept called parallax. We draw parallel lines from our reference points (L1 and L2) to the photographic plane, creating new points a' and b'. The difference in position between these points across the two photos, known as absolute parallax, is directly linked to the readings taken from a parallax bar, which measures how the images of these points shift. The larger the difference in parallax, the greater the height difference between the two points.

Think of parallax like using a pair of binoculars to focus on a distant mountain. As you adjust the binoculars, the image of the mountain shifts relative to closer objects. In the context of aerial images, if one tree appears to shift significantly compared to another as you view two photos, it indicates that one tree is taller or further away. This shift helps us calculate their precise elevations.

Using the relationship in equation 4.23, the elevation of point B (h_b) can be computed. In a similar way, elevation of another unknown point C (h_c) can be computed using the relationship given below.

Once we establish the parallax readings, we can calculate the elevation of point B using a formula that incorporates the known height of point A and the observed parallax difference between points A and B. This relationship allows us to derive the height of an unknown point by leveraging our understanding of the shifts observed in the aerial photos. The method can be extended to other points like point C as well, ensuring we systematically calculate heights using a known reference.

Imagine if you have a known height of a fence in your yard. By observing how much higher or lower another object appears in the context of that fence from different angles, you can easily figure out its height relative to the fence. This method is similar to calculating unknown heights using known references in aerial photography.

This method, however, determines the approximate height of the points, so care must be taken to minimise the errors. The errors in the determination of height may be due to several reasons – locating and marking the flight line on photos, orienting the stereo-pair for parallax measurement, measurements in parallax and photo-distances, shrinkage and expansion of photographs, difference in flying height of stereo-photographs, tilt present on photos, and error in the height of known ground control point.

While calculating heights from stereo images, it is crucial to recognize that errors can arise from many sources. These can include inaccuracies in marking the flight path on the photos, misalignment of the images during stereo pair orientation, and even physical distortions of the photographs due to changes in their dimensions. Any error in these processes can lead to incorrect height determinations, so it's vital to minimize these errors to achieve reliable results.

Imagine baking a cake – if you mistakenly measure the ingredients or if the oven temperature isn't accurate, the final cake won't turn out as expected. Similarly, in photogrammetry, if we mishandle any part of the measurement process, our final calculations of ground heights will be off, affecting our overall results and reliability.

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