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Interactive Audio Lesson
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Introduction to Relief Displacement
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Today, we’re going to explore relief displacement in vertical photographs. Can anyone tell me why relief displacement happens in aerial images?
Is it because the heights of different objects aren’t taken into account?
Exactly! The height of an object will determine how much it appears displaced from its true position in an aerial photograph. Objects farther from the principal point, like tall buildings, get pushed outward.
So does that mean flat areas look accurate, but tall buildings don't?
Correct! The displacement is minimized at the principal point, making these areas more accurate. Let's remember this with the acronym P.A.R.T. — Principal point, Accurate, Radial, and Tall.
What happens to low objects, like valleys?
Great question! They actually appear to move inward towards the principal point. Always remember: high objects go out, low objects come in.
Got it! High out, low in!
Exactly! Now let’s move on to how we can measure this displacement accurately.
Mathematical Relationships
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To calculate relief displacement quantitatively, we rely on specific formulas. One fundamental equation relates relief displacement to the height of objects and flying height. Can anyone repeat its components?
We need to consider the focal length, the radial distance from the principal point, and object heights.
Correct again! The equation helps us understand that the relief displacement increases with height. Let’s summarize this concept: as height increases, displacement increases too.
So if I'm measuring taller buildings, I'd expect more error if I'm far from the principal point?
Exactly! Now, we can visualize this with a triangle analogy: the width of the triangle corresponds to height, and the distance from the principal point is the base. This helps illustrate the relationship visually.
Could you show us the formulas in action?
Absolutely! Let's take an example where we calculate displacement for a tower with a known height.
Measurement Techniques
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Now that we understand the math, let’s look at how to practically measure this displacement. Who knows what tools we might use?
A parallax bar, right?
Yes! The parallax bar helps us capture the difference in paths of images taken from different angles, which we can use to determine height. Remember, parallax is crucial!
Can you explain how we apply these measurements in real scenarios?
Sure! Let’s say we have two stereo photographs. By knowing the height of one known point, we calculate the heights for others. This is vital in mapping and urban planning.
So, accurate measurements help avoid errors in future decisions?
Absolutely! Always remember that accurate measurements lead to better decisions. Ready to explore some calculations?
Introduction & Overview
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Quick Overview
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This section discusses how relief displacement affects vertical aerial photographs, explaining how varying heights of objects lead to displacement from their true positions. It explores the mathematical relationships governing this phenomenon and emphasizes the implications for measurement accuracy in photogrammetry.
Detailed
Detailed Summary
Relief displacement refers to the phenomenon observed in vertical aerial photographs where the heights of various objects cause them to appear displaced from their actual geographical locations. Objects closer to the principal point of the photograph exhibit minimal relief displacement, while taller objects like buildings and trees are pushed outward from this point, and lower features such as valleys are drawn inward.
Key Points Covered:
- Definition and Importance: Relief displacement occurs due to the central projection nature of aerial photographs and is crucial for understanding measurement errors in photogrammetry.
- Displacement Direction: High structures are displaced radially outward, whereas lower structures are displaced inward towards the principal point.
- Measurement and Mathematical Relationships: The section introduces several equations that quantify relief displacement based on the height of objects and the focal length of the camera, guiding how to calculate distances accurately.
- Avoiding Measurement Errors: It details the relationship between relief displacement and factors like object height and flying height, advising against measuring near the photograph's edges due to larger potential errors.
- Application: By knowing the relief displacement, one can compute the height of objects using photographic parallax, highlighting the significance in practical applications like mapping.
This section is essential for anyone involved in aerial photography or photogrammetry, providing foundational knowledge on how to interpret aerial images accurately.
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Audio Book
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Introduction to Relief Displacement
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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.
Detailed Explanation
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.
Examples & Analogies
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.
Principal Point and Object Displacement
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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.
Detailed Explanation
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.
Examples & Analogies
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.
Displacement Direction
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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.
Detailed Explanation
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.
Examples & Analogies
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.
Measuring Relief Displacement
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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.
Detailed Explanation
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.
Examples & Analogies
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).
Mathematical Relationship of Relief Displacement
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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.
Detailed Explanation
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.
Examples & Analogies
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.
Factors Influencing Relief Displacement
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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.
Detailed Explanation
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.
Examples & Analogies
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.
Impact of Object Height and Flying Height
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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.
Detailed Explanation
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.
Examples & Analogies
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.
Measurement and Calculations
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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.
Detailed Explanation
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.
Examples & Analogies
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.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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Relief Displacement: The displacement observed in vertical photographs due to object heights affecting their position.
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Radial Direction: The direction of displacement is radial from the principal point.
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Measuring Techniques: Tools such as parallax bars are essential for accurate height measurements.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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An example of a tall skyscraper will show greater relief displacement than a flat field in an aerial photograph.
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If a valley appears displaced inward while a mountain is pushed outward, it highlights the principles of relief displacement.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
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Tall buildings reach to the sky, displace outwards, oh my! Valleys dip and come in close, remember that, it helps you the most.
📖 Fascinating Stories
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Imagine an aerial photographer flying at 1000 meters. He snaps a picture of a city skyline—tall skyscrapers push outward while the tiny park below leans inward. This image helps him understand displacement better.
🧠 Other Memory Gems
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Use 'H.O.P.' to remember: Height Outwards, Principle (point) is flat.
🎯 Super Acronyms
R.A.P. for Relief Displacement
- Radial
- Accurate (for measurements)
- Principal Point.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
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Term: Relief Displacement
Definition:
The apparent movement of objects in vertical aerial photographs due to differences in height affecting their perceived location.
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Term: Principal Point
Definition:
The point in a photograph where perspective projection occurs, having the least displacement.
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Term: Radial Displacement
Definition:
The direction of displacement (outward or inward) from the principal point based on an object's height.
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Term: Parallax
Definition:
The apparent displacement of an object viewed from different positions, used to calculate the height of objects in photogrammetry.
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Term: Flying Height
Definition:
The height at which the aerial photograph is taken above the ground level, impacting displacement measurements.