1. Pergeseran Relief & Triangulasi Udara
Dwi Arini-2015

2. Relief Displacement H’ = H – hA’
H (not shown) = Flying height above datum.
d = distance from bottom to top of object on image.
r = radial distance for principal point to top of object.
h = height of object from bottom to top. ‘
hA’
Datum

3. Relief Displacement Similar Triangles: (1) From scale equations: (2)
(3)

4. Relief Displacement Substitute 2 and 3 into 1:
Relief displacement increases linearly with the distance from the center of the photo.
Relief displacement increases linearly with the height of the object.
Relief displacement increases inversely with the flying height above the bottom of the object.

5. Relief Displacement
It is actually relief displacement that causes scale variations.
Cannot mosaic photos of same object taken at different photo centers even if H’ is constant.
Direction of displacement will be different on different photos.

6. Height of Object rearranged yields
Can get height of object by measuring displacement.
Example: H = 4500ft (above datum); Base of tower at 500 ft elevation; Radial distance from pp to top of tower = 3.00 inches; Displacement = inches.

7. } Errors } Systematic Errors
Determination of height of tower subject to:
Photo not exactly vertical.
Shrinkage / expansion of photo.
Uncertainty in d.
Uncertainty in r.
Uncertainty in H’.
} Systematic Errors }
Random Errors
Systematic errors obey known physical laws and can be corrected (e.g., corrections for shrinkage / expansion).
Random errors behave according to the laws of probability.

8. Random Errors
Normally-distributed random errors have a 68% chance of falling within one standard deviation (±) of the peak of the curve.
We can determine the impact of random errors in functions of variables using “error propagation”.

9. Random Errors In the relief displacement problem:
If we know we can determine
Can isolate each variable (d, r, H’) and see how changes affect hT.
Use partial derivatives:

10. Random Errors Effect of dd: Effect of dH’: Effect of dr:
If dd = ”
Effect of dH’:
If dH’ = +50 ft
Effect of dr:
If dr = in

11. Random Errors Combined Uncertainty
If Sd = ±0.001”; SH’ = ±50’; Sr = ±0.05”,
What is the uncertainty in hT?

12. Aerial Triangulation
Remember the exterior orientation. For both images forming the model we used some ground control points (GCPs) to establish the orientation via a resection in space. To do this we needed at least (!) 3 well distributed points forming a triangle.

13. Aerial Triangulation
Now imagine the case that we have much more than two images, let's say a block formed of 3 strips each containing 7 images as we will use in this example, and we have no signalised points but only a topographic map, scale 1:50,000. Greater parts of our area are covered with forest, so we can only find a few points which we can exactly identify. It may happen that for some images we are not even able to find the minimum of 3 points.

14. Aerial Triangulation
This may serve as a first motivation for that what we want to do now: The idea is to measure points in the images from which we do not know their object coordinates but which will be used to connect the images together. These are called connection points or tie points. In addition, we will measure GCPs wherever we will find some. Then, we will start an adjustment process to transform all measured points (observations) to the control points

15. Aerial Triangulation
In this way we will only need a minimum of 3 GCPs for the whole block – it is not necessary to have GCPs in each image. On the other hand, a standard rule is to have one GCP in every 3rd model at least near the borders of the block, and if necessary additional height control points inside of the block

16. Aerial Triangulation

17. Aerial Triangulation
All images of a block are connected together using corresponding points, “gluing” them to a mosaic which is then transformed to the GCPs. Of course this twodimensional scheme is not exactly what an aerial triangulation will do – nevertheless, it is very useful to understand the rules we must fulfil in our work. The aerial triangulation, today usually carried out in form of a bundle block adjustment can be seen as a method to solve an equation system, containing all measured image co-ordinates as well as the GCP terrain co-ordinates.

18. Aerial Triangulation
Remark: After the interior orientation of all images (next step), we will take a look into the principles of manual aerial triangulation measurement (ATM) and carry out an example. This is a good possibility to understand the way how ATM works, and is necessary for the measurement of ground control points. Nowadays usually automatic approaches are used, as well. But even for understanding the problems or errors occurring in the automatic processing it is valuable to know the basics of manual ATM.

19. Aerial Triangulation
“Glue” the images together to a block...

20. Aerial Triangulation
Then transform the block to the ground control points

21. Aerial Triangulation
In any model, at least 6 well-distributed object points must be measured. It is an old and good tradition to do this in a distribution like a 6 on a dice, the points are then called Gruber points in honour of Otto von Gruber, an Austrian photogrammetrist. Neighbouring models must have at least 2 common points. In standard, we will use 3 of the Gruber points (the left 3 for the left model, the right 3 for the right model). Neighbouring strips are connected together with at least one common point per model.

22. Aerial Triangulation
As a standard, we will use 2 of the Gruber points (the upper 2 for the upper strip, the lower 2 for the lower strip). Each object point must have a unique number. In particular this means that a point has the same number in any image in which it appears. On the other hand, different object points have different numbers

23. Principles of point transfer within a block
Aerial Triangulation
Principles of point transfer within a block