Analytical aerial triangulation - 4.14.1.3 | 4. Graphical Radial Triangulation | Surveying and Geomatics
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Introduction to Analytical Aerial Triangulation

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0:00
Teacher
Teacher

Today, we're diving into analytical aerial triangulation. Can anyone tell me why establishing Ground Control Points, or GCPs, is crucial in this process?

Student 1
Student 1

They help us align the photographs correctly to reflect actual terrain?

Teacher
Teacher

Exactly! GCPs provide reference that helps in accurately positioning the images. Now, let's explore how we mark these points on photographs. What do you think comes next after identifying the GCPs?

Student 2
Student 2

I believe we find the principal point for each photo?

Teacher
Teacher

Correct! The principal point is the foundation for other calculations. This leads us to the concept of minor control points. Can anyone define what MCPs are?

Student 3
Student 3

Are they points near the principal point to help in triangulation?

Teacher
Teacher

Exactly! They fulfill certain geometric conditions. Remember, MCPs are typically placed symmetrically around the principal point.

Teacher
Teacher

In summary, we discussed GCPs and MCPs as essential components in establishing a triangulated model. These points ensure that our aerial photographs can be accurately represented in three dimensions.

Graphical Radial Triangulation

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Teacher
Teacher

Let’s move on to the practical aspects of graphical radial triangulation. After identifying our GCPs, what’s the first step?

Scaling and Common Scale Adjustment

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Teacher
Teacher

In aerial photography, we need to adjust for scale differences due to varying elevations. Why is it necessary to bring photographs to a common scale?

Student 4
Student 4

To ensure all photographs reflect the same proportionality for accurate mapping?

Teacher
Teacher

Exactly! The common scale helps prevent distorted representations in your final maps. What method do we use to bring different scales together?

Student 2
Student 2

We perform a graphical triangulation by plotting known control data.

Teacher
Teacher

Correct. And we often start with selecting minor control points in the middle of the strip to avoid errors. Can anyone suggest why we’d start in the middle instead of the ends?

Student 1
Student 1

To minimize the cumulative azimuthal errors that might accumulate towards the edges of the photographs?

Teacher
Teacher

Exactly! Great observation. Let's summarize today’s learning. We covered the significance of consistent scaling and how to achieve it by using graphical triangulation methods with control points.

Introduction & Overview

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Quick Overview

This section covers the process of analytical aerial triangulation, including importance, techniques, and methods for achieving accurate aerial photography.

Standard

Analytical aerial triangulation is a crucial method in photogrammetry that integrates multiple photographic images to achieve accurate three-dimensional coordinates of terrain. This section discusses the graphical method of triangulation, block triangulation, and various triangulation methods, emphasizing the use of ground control points and scaling techniques.

Detailed

Detailed Summary

Analytical aerial triangulation is essential in photogrammetry, mainly for its capability to connect multiple photographs into a coherent model of the terrain. It begins with establishing Ground Control Points (GCPs) on photographs, marking them for reference in triangulation. The method involves identifying the principal points of photographs and selecting minor control points (MCPs) that hold specific geometric relationships to the principal point. Subsequently, lateral control points (LCPs) are identified between adjacent strips to ensure smooth connections.

A key aspect of analytical triangulation is the varying scales due to terrain elevation differences. Thus, bringing the photographs to a common scale using graphical triangulation is essential. The process requires careful plotting and scaling to ensure the accuracy of the final map.

The section also discusses the analytical and block triangulation approaches, underscoring the use of software algorithms for bundle adjustments in triangulation. The collinearity conditions formed through the relationship of object and image points provide a basis for calculating unknown coordinates. Finally, the importance of using multiple ground control points is highlighted to mitigate errors and improve the accuracy of the triangulation process.

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Graphical Radial Triangulation Steps

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Graphical radial triangulation is performed with simple instruments, such as mirror stereoscope, a ruler, a pencil and a tracing sheet. The steps are given below:
1. The photographs are laid out in strips and all GCPs are identified on the photographs and their numbers marked on the photographs.
2. The principal point is obtained for each photograph. The principal points are then stereoscopically transferred to the adjoining photographs as conjugate principal points.
3. Now two points, called minor control points (MCPs), also called pass points or wing points, are selected on both sides of the principal point of photo, fulfilling the following conditions:
a. The two points should be as nearly at the same elevation as the principal point.
b. The points should be at a distance from the principal point, which is equal to twice the mean base of the adjoining photographs.
c. The points should lie approximately on the bisector of the base angle on either side, and d. The point should serve as lateral point as well.
4. The MCPs are selected and transferred stereoscopically to adjoining photographs.
5. The lateral control points (LCPs) are selected in the centre of lateral overlaps of adjacent strips to serve as connecting points between different the strips. These LCPs are selected at least at the beginning and the end of the strip and on every third photo of the strip. These are then stereoscopically transferred to photographs of adjoining strips.
6. The radial directions from the principal point to all minor control, lateral control and ground control points appearing on the photograph are drawn, through the points.

Detailed Explanation

In graphical radial triangulation, we begin by laying out photographs in strips and identifying Ground Control Points (GCPs), which are key reference points. Next, we determine the principal point for each photograph, which is essentially the focal center. This principal point is then transferred between photographs for consistency. We also establish two MCPs near this principal point, ensuring they are nearly the same height as the principal and spaced according to certain criteria. Additionally, we select LCPs that connect adjacent strips. Finally, we draw radial lines from the principal point to all control points on each photo, which aids in creating accurate spatial relationships between the images.

Examples & Analogies

Imagine you're piecing together a big puzzle. Each photograph represents a puzzle piece. Just as you would start by identifying the corner pieces (the GCPs), you need to identify these key points on your images. The principal point acts like the center of the puzzle, guiding where other pieces should go. When you choose your points carefully, like ensuring they are at the same height and properly spaced, it's similar to ensuring your puzzle pieces fit together nicely. Drawing lines to connect points is like marking paths between similar pieces to help complete the picture.

Adjusting Photographs to a Common Scale

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Due to elevation differences of terrain and variations in the flying height of aircraft, the scale of photographs generally varies considerably. The photographs of a strip are required to be brought to a common scale through graphical triangulation. The plot of the strip where all the photographs, having uniform scale, are fixed in their correct relative position is called as MCP.

Detailed Explanation

Different elevations of terrain and flying heights can cause variations in the scale of aerial photographs, making it essential to standardize them to a common scale. This is done through graphical triangulation, which helps to align the photographs uniformly. The resulting plot, which maintains this consistency across all images, is known as the Minor Control Plot (MCP). This process ensures that measurements taken from the photographs remain accurate and representative of the actual distances.

Examples & Analogies

Think of it as adjusting the volume on several different audio speakers. Each speaker might have varying output levels, similar to how photographs might have different scales due to elevation. To create a balanced sound (or accurate representation), you adjust each speaker until they all operate at the same level. In aerial photography, this adjustment is crucial for ensuring that when you look at the combined images, everything fits together harmoniously.

MCP and Scaling Process

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Each strip is plotted on a transparent sheet to facilitate the drawing. The photographs are laid out in their correct relative directions so that the plotting is carried out in the right direction. With the first photograph in position below the tracing sheet, principal point base is transferred. The base line is extended up to the edge of the photograph on either side. The position of principal points of the first photograph and one of the two adjacent photographs is then transferred on the tracing sheet. The radial directions to all the points appearing on the photograph are also drawn.

Detailed Explanation

Once the photographs are arranged correctly, each strip is plotted on a transparent sheet, which allows for easier and more accurate drawing of reference lines. The process begins with placing the first photograph and transferring the principal point to the tracing sheet. This establishes a base line that will be extended further to include adjacent photographs. By doing this, you ensure that all parts of the photographs are represented accurately and in their true orientation before further measurements and adjustments are made.

Examples & Analogies

Envision laying a piece of fabric down to cut a pattern; you want the fabric to lay flat without wrinkles to ensure that your cutting is precise. In this case, laying down each photograph on the transparent sheet is akin to making sure that fabric is smooth and correctly oriented. Just as the pattern pieces must align with the fabric, the photographs must line up accurately before any adjustments or cutting (measuring) take place.

Using Bundle Adjustments

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The scaling is then carried out by plotting the actual distance AB between the two ground control points, between which the scaling is to be done, on a straight line drawn on a separate sheet. A semicircle is drawn taking B′ as centre and distance BB′ as radius. The scaled position of any other point C′ on minor control plot is obtained by coinciding A′ with A and C′ falling on the line AB.

Detailed Explanation

To scale the photographs accurately, you first determine the actual distance between two known ground control points (A and B). A straight line represents this, and a semicircle is drawn from one of these points to help locate other points on the plot. By aligning points correctly, you ensure that all features in the photo match their real-world locations accurately. This process is crucial in ensuring that the scaled positions of points derived from the minor control plots are consistent with ground reality.

Examples & Analogies

Consider trying to create a scale model of a building. You'd start with measurements of the foundation (the distance AB), and then use those dimensions to map out the entire structure accurately. Just like you’d use a compass to ensure your angles are right, the semicircle helps maintain the correct relationship between points in the photography process, ensuring every feature is proportionally accurate as you work from a small model to reality.

Final Adjustments and Error Minimization

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After scaling all the points of minor control plots, these points are pricked through the tracing sheet. The positions of principal points, minor control points and lateral control points of all the strips are likewise pricked on the graph sheet and adjusted so that all ground control points fall over their plotted positions and lateral control points give positions of least error.

Detailed Explanation

Once all points are scaled, they are marked (or pricked) through the tracing sheet, creating reference points on the graph sheet. This helps to closely align every control point on the maps to their actual positions. The adjustments made ensure minimal errors between the measurements taken in the photographs and the actual ground locations, making the outputs more reliable and accurate for analysis and mapping.

Examples & Analogies

It's similar to creating a pointillist painting where each dot (control point) has to be carefully placed to create an overall image. Just like in painting, you may step back to see how well the image comes together, you need to make sure each of those points is accurately placed to reflect what you see in real life. This fine-tuning ensures that when you look at the final output, it reflects the actual landscape correctly, without significant discrepancies.

Definitions & Key Concepts

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Key Concepts

  • Ground Control Points: Essential for establishing accurate positions in aerial triangulation.

  • Minor Control Points: Critical for the triangulation process and are selected based on specific elevation conditions.

  • Lateral Control Points: Used to maintain connections between overlapping photographs in adjacent strips.

  • Graphical Triangulation: A technique to align images for uniform scale in photogrammetry.

  • Bundle Adjustment: An advanced algorithm for refining the accuracy of multiple images.

Examples & Real-Life Applications

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Examples

  • The selection of GCPs across different elevations ensures more accurate photographs in varied terrains.

  • Using MCPs allows for precise triangulation along the principal point, improving mapping accuracy.

Memory Aids

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🎵 Rhymes Time

  • GCPs, MCPs, points of reference, ensure accuracy in the aerial presence.

📖 Fascinating Stories

  • Imagine a pilot flying over a landscape, using GCPs like treasure maps to align the photos correctly on the ground.

🧠 Other Memory Gems

  • GCP - Ground Connectivity Precision.

🎯 Super Acronyms

MCP - Minor Control Point, My Coordinates Protected.

Flash Cards

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Glossary of Terms

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  • Term: Ground Control Points (GCPs)

    Definition:

    Reference points in photographs used to accurately position images.

  • Term: Minor Control Points (MCPs)

    Definition:

    Points selected near the principal point to assist in triangulation.

  • Term: Lateral Control Points (LCPs)

    Definition:

    Points used to connect overlapping regions of adjacent photographic strips.

  • Term: Graphical Triangulation

    Definition:

    A method used to align photographs to a common scale and position.

  • Term: Bundle Adjustment

    Definition:

    An algorithm that adjusts multiple photographic images simultaneously to determine 3D coordinates.