4.12.4 - Height determination
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Interactive Audio Lesson
Listen to a student-teacher conversation explaining the topic in a relatable way.
Introduction to Height Measurement
🔒 Unlock Audio Lesson
Sign up and enroll to listen to this audio lesson
Today we're going to discuss how we determine the height of objects using vertical aerial photographs. This method is vital in various fields like mapping and surveying.
Why is knowing the height of an object important?
Great question! Knowing the height helps in understanding topography and geographic features, which is essential for tasks like urban planning.
How do we actually measure height from these photographs?
We use stereo pairs of photographs taken from different perspectives to analyze differences in parallax, a method we'll closely examine.
Understanding Parallax and Its Measurement
🔒 Unlock Audio Lesson
Sign up and enroll to listen to this audio lesson
Parallax is the apparent shift in position of an object viewed from two different angles. Can one of you explain why this shift is important for our calculations?
It's important because it helps us determine how far away an object is in relation to the camera!
Exactly! Knowing the parallax allows us to establish the height using the relationships defined in our equations.
What kind of equations do we use for that?
We use equations that relate parallax to height. For instance, we can establish that .23 relates height differences to parallax readings directly.
Practical Application of Height Measurement
🔒 Unlock Audio Lesson
Sign up and enroll to listen to this audio lesson
Now let's talk about the practical application. When using a parallax bar, we first explicitly determine the positions of points on both photographs. How do we achieve that?
Maybe by aligning the floating marks on the parallax bar with the points on the stereo images!
That's correct! Once they align, we can measure the parallax difference, which gives us the required data to calculate heights.
What are some common errors we should watch out for during measurements?
Excellent inquiry. Errors can arise from various factors such as incorrectly locating the flight lines or inaccuracies in photo distances.
Understanding the Relationship Between Elements in Height Calculation
🔒 Unlock Audio Lesson
Sign up and enroll to listen to this audio lesson
Let’s summarize the relationships. The air base distance and flying height are crucial variables. Who can explain how they relate to parallax measurements?
The larger the distance of the air base, the greater the parallax, meaning we can measure height differences more accurately!
Exactly! Thus, maximizing our air base can help improve measurement accuracy.
Are there practical limits to how far apart we can take the photos?
Yes, and they depend on factors such as flying height and landscape features. These limits ensure we capture accurate images without excessive distortion.
Error Analysis in Height Determination
🔒 Unlock Audio Lesson
Sign up and enroll to listen to this audio lesson
Now let's delve into errors in height determination. What are some common pitfalls we've discussed so far?
Incorrect flight line positions and orientation issues are big ones!
Absolutely! Additionally, any errors in the known control points can significantly affect our height calculations.
How do we minimize these errors in practice?
We ensure diligent pre-flight planning, correct orientation, and multiple observations to gather averaged data.
Introduction & Overview
Read summaries of the section's main ideas at different levels of detail.
Quick Overview
Standard
The section elaborates on how height can be estimated from vertical aerial photographs by analyzing parallax differences between points on stereo images. It introduces key concepts such as parallax measurement, the use of a parallax bar, and the relationship between absolute parallax and height estimation.
Detailed
Height Determination from Vertical Aerial Photographs
In this section, the process of determining height from vertical aerial photographs is thoroughly examined, particularly the use of stereo-pairs and parallax measurements. The section begins by introducing points A and B, defined by their corresponding images on left and right photos. The relationship between the air base distance (B), flying height (H), and the elevations of the points is established through similar triangles based on the positions of these points on the photographs.
Key equations, such as the absolute parallax equation (∆p = pb - pa), are defined to calculate the difference between parallax readings at two locations. These readings help to form the basis for calculating height differences, as the difference in parallax is directly correlated with the elevations of the points in question.
The significance of having at least one known height is emphasized, as it allows for the estimation of unknown heights through established relationships (e.g., having the elevation of point A leads to the calculation of height at point B). Various sources of error in height determination, such as measurement inaccuracies, photographic distortions, and flight height variations, are also discussed, highlighting the necessity for careful implementation of methodology to ensure accurate height data acquisition.
Audio Book
Dive deep into the subject with an immersive audiobook experience.
Introduction to Height Determination
Chapter 1 of 4
🔒 Unlock Audio Chapter
Sign up and enroll to access the full audio experience
Chapter Content
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.
Detailed Explanation
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.
Examples & Analogies
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.
Analysis of Parallax
Chapter 2 of 4
🔒 Unlock Audio Chapter
Sign up and enroll to access the full audio experience
Chapter Content
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.
Detailed Explanation
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.
Examples & Analogies
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.
Calculating Height Differences
Chapter 3 of 4
🔒 Unlock Audio Chapter
Sign up and enroll to access the full audio experience
Chapter Content
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.
Detailed Explanation
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.
Examples & Analogies
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.
Error Minimization in Height Determination
Chapter 4 of 4
🔒 Unlock Audio Chapter
Sign up and enroll to access the full audio experience
Chapter Content
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.
Detailed Explanation
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.
Examples & Analogies
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.
Key Concepts
-
Parallax Measurement: The technique of determining height by measuring the apparent shift of objects between photographs taken from differing angles.
-
Stereo Images: Photographs captured from slightly different perspectives to facilitate three-dimensional measurements.
-
Height Calculation: The process of estimating the height of an object based on parallax differences measured in aerial photographs.
Examples & Applications
When measuring the height of a building, the photos taken from different angles will show the top of the building displaced more than the base due to parallax.
Using a known elevation at point A, the height at point B can be determined using the relationship of parallax difference established through equations discussed.
Memory Aids
Interactive tools to help you remember key concepts
Rhymes
Parallax can give a height clue, with images from different views, measure difference, watch it shift, to know the height is a great gift.
Stories
Imagine a bird flying above buildings, it sees them from different angles. By measuring how far they seem to shift, it can tell which is taller—this is how we measure heights in aerial photography!
Memory Tools
Remember PARA - 'Parallax Analysis for Real Aerial' to recall that parallax is essential for aerial height measurements.
Acronyms
HARP
Height And Reference Parallax – to remind us of the relationship between height and parallax measurements.
Flash Cards
Glossary
- Parallax
The apparent shift in position of an object viewed from two different angles, crucial for height measurement in aerial photography.
- Stereopair
A pair of aerial photographs taken from slightly different angles used for three-dimensional measurements.
- Parallax Bar
A device used to measure the difference of parallax between two points on stereo photographs to determine height.
- Flight Line
The path taken by the aircraft while capturing photographs, affecting alignment and accuracy in aerial photography.
Reference links
Supplementary resources to enhance your learning experience.