4.10. Relief Displacement of a Vertical Photograph

The relief displacement is present on the vertical photograph due to height of various objects. It is the displacement of the objects on a vertical aerial photograph from their true plan positions. Aerial photograph is based on the central or perspective projection, and all the objects on aerial photographs appear to be displaced from their true positions.

Relief displacement occurs in aerial photographs because of the varying heights of objects on the ground. When a photograph is taken from the air, the actual position of an object on the ground might differ from where it appears in the photo. This is because objects that are taller will be captured at a location further from the camera's central point due to perspective projection, causing an outward displacement. Conversely, lower areas, like depressions, will appear closer to the center of the photo.

Imagine taking a photo of a group of people standing on a sloped hill. The taller people standing at the back will seem further away from the camera than they really are, while the shorter people at the front may seem closer. This is similar to how objects appear in aerial photographs.

However, the objects near the principal point will be free from any relief displacement. Due to varying heights of different ground points, these points appear to be displaced on the photograph from their true geographic location.

The principal point is the central point of the aerial photograph, and it represents the point directly beneath the camera when the photo is taken. Objects located near this principal point do not show any relief displacement. As you move away from this point towards the edges of the photograph, you will notice that objects appear to be displaced either closer or further away based on their heights.

Think of standing at the center of a circle and looking out at people around you. The people standing right next to you (near the center) look like they are in their correct positions, while those further away at the edge seem distorted depending on their height.

The higher objects, such as tall buildings, trees, towers, hills etc., are displaced away (outward) from the principal point, while the valleys, depressions etc., are displaced (inward) towards the principal point.

As height increases, so does the distance from the principal point. For instance, if a tall building is photographed, it will appear farther from the center than it truly is, shifting the object away from the principal point. On the other hand, lower terrain features like valleys will appear to be pulled toward the center of the image, creating an inward displacement.

Imagine a toy building on top of a box. If you take a picture from above, the building looks further away from the center than the box does. If you then take a picture of a small hole in the ground, it will seem closer to the center of the photo. This demonstrates how height affects positioning in aerial photography.

The relief displacement is measured from the principal point of the photograph. It is always radial from the principal point, and therefore it is also known as the radial displacement.

To measure relief displacement accurately, distances are calculated starting from the principal point. This is termed 'radial' displacement because the measure extends outward in a straight line from the central point in all directions. This radial nature is critical for understanding how displacement affects various objects in the photograph.

Think of the principal point as the center of a dartboard. Rather than measuring how far the dart lands from the edge of the board, you measure from the center. This helps in assessing where each dart (object) lands relative to the center (principal point).

Let us establish a relationship for relief displacement. In Figure 4.13, let AA be a tower of height h above the ground. A photograph of the tower is taken from exposure station O. The aa' and a0' are the corresponding images of top and bottom of the tower on the photograph. The aa' distance (d) on the photograph is called the relief displacement as it is the horizontal displacement of tower on the photograph due to its height.

The relief displacement can be mathematically determined using the height of an object and its position in the photograph. By taking measurements and using them within certain established equations, one can compute the exact displacement for any tower or similar vertical object seen in a photograph.

Imagine you are trying to calculate how far a bird like a kite is flying above the ground. You observe its height and apply mathematical formulas to get its position relative to where it appears in your photo. This is similar to how relief displacement is computed in aerial photographs.

It is seen from equation 4.15 that the relief displacement (d) is directly proportional to radial distance of displaced image point from the principal point (r), and as (r) increases (d) also increases. It is therefore advisable that the objects situated at the edges of a photograph may not be selected for any measurement as it may have larger error which is required to be eliminated before use.

The equation indicates that as the radial distance from the principal point increases, so does the relief displacement. Therefore, any measurements taken from further away objects can be less accurate and may introduce significant errors. Selecting objects close to the principal point can yield more reliable results.

Like trying to read a sign far away versus one close to you; it's harder to accurately read those at a distance because of blurriness and distortion. Similarly, in aerial photography, it's better to focus on features nearer to the principal point for precise measurements.

Relief displacement is directly proportional to the height of the object, as (h) increases (d) also increases. Whereas, (d) is inversely proportional to the flying height, as (H) increases (d) decreases.

The relationship shows that taller objects will be displaced more in the photograph, leading to greater discrepancies in measurements. Conversely, if the flying height of the aircraft increases (the higher you are), the displacement will decrease, meaning objects will appear less distorted.

Consider a balloon floating high in the sky versus a toy on the ground. The balloon appears to sway with the wind at a greater rate compared to the grounded toy. This visualization helps understand how height affects aerial image displacement.

If the relief displacement is known, the height of an object can be computed as: dH/h = p; Equation 4.17 has been used to approximately compute the height of the object from a single vertical aerial photograph.

If you have measured the relief displacement in a photograph, you can use this relationship to find out the actual height of the object in question. This involves rearranging the equations so that height can be calculated based on the known values of displacement and other factors.

Think of making a shadow on the ground with a stick. If you know the length of the shadow and the angle of the sun, you can calculate how tall the stick is. Much like that calculation, relief displacement helps us to understand the height of objects from aerial photographs.

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