4.14.3. Bundle adjustment

When working with software, the “bundle adjustment” algorithm will be necessary for triangulation. The name is derived from the ‘bundle of light rays’ that pass through each exposure station. Using algorithm, all photos are adjusted simultaneously to create an intersection of all light rays at each pass point and ground control points.

The term 'bundle adjustment' refers to the computational process used in photogrammetry where multiple photographs are adjusted together. This adjustment is necessary to accurately align the photographs so that they reflect the real positions of the points on the ground. Each photo's perspective can be thought of as a 'light ray bundle' whose intersection points with ground control points helps determine the correct spatial arrangement of these photos.

Imagine you and your friends are taking a group photo from different angles. If you wanted to combine these photos into a single image where everyone's positions were perfectly aligned, you would need to adjust the angles and positions of each photo. The bundle adjustment is like that adjustment process, ensuring that all the different angles come together in harmony.

A bundle of rays that originates from an object point and passes through the projective centre to the image points forms the basic computational unit of aerial triangulation.

In aerial triangulation, the fundamental unit of measurement is the bundle of rays that come from a specific point on the ground and travel through the camera's lens to create an image on the photograph. This relationship helps in understanding how to relate the 2D points in photos to their 3D locations in real space.

Think of a spotlight shining on a statue. The light (or rays) travels from the spotlight to the statue, creating an illuminated image on the wall behind it. Similarly, the camera captures the rays that illuminate objects on the ground, and by studying these paths, we can understand where each object is in the physical space.

Bundle block adjustment means the simultaneous least squares adjustment of all bundles from all the exposure stations, which implicitly includes the simultaneous recovery of the exterior orientation elements of all photographs and the positions of the object points.

Bundle block adjustment involves using mathematical techniques to minimize errors across all photographs at once. Instead of adjusting each photo individually, this method calculates the most probable positions of all object points and the orientations of all photographs simultaneously. This simultaneous processing enhances accuracy and reduces discrepancies.

Imagine a group project where each team member has to write a piece of text that fits together in a book. If everyone works in isolation, the final product may have inconsistencies. Now, if they all sit down together to write and edit their segments in real-time, the outcome is much more cohesive and accurate. Bundle block adjustment is like this collaborative effort aiming for the best overall result.

The fundamental equation of aerial triangulation is the collinearity equation which states that an object point, its homologous image point and the perspective centre, are collinear.

The collinearity equation is crucial for determining the relationship between an object in 3D space and its 2D representation in photographs. It states that for an object point (like a tree), the corresponding image point (how that tree appears in a photograph) and the camera's perspective center all lie on the same straight line. This principle helps in accurately calculating the spatial coordinates.

Picture a straight road disappearing into the horizon. If you stand at a point on the road, the road directly in front of you, the point where the road meets your view (like a tree), and your position create a straight line. This collinearity ensures everything aligns properly, just as it does in photography.

There are 6 unknowns in the collinearity equations, namely, the exterior orientation parameters. The principal point coordinates and camera constant are considered to be known for the basic bundle approach.

In the context of the collinearity equations, there are six unknown variables that need to be solved for, which include the exterior orientation parameters crucial for understanding the camera's position and angle when the photograph was taken. While some factors like principal point coordinates and camera constants are known, solving for the other variables is essential for accurate photo positioning.

Think of planning a treasure hunt. You know some vital clues (like the starting point and some distance), but you still need to find the right paths to take to reach the treasure. Each of the six unknowns needs to be calculated for you to find the most accurate route to the treasure locations represented in the photographs.

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