The last of the primary parameters is the mesh size. The elevations of the interest points are determined by the correlation process. From the elevations of the interest points, the elevations of the grid points are interpolated. The determination of the grid points is, therefore, a purely mathematical process which is done on the basis of the elevations of the interest points and has nothing to do with the correlation proc-ess itself. The basis (the elevations of the interest points) for the determination of the elevations of the grid points remains unchanged for all mesh sizes.
This means that there should not be any appreciable difference in accuracy, regardless of which mesh size is chosen, taking into consideration the scale and resolution of the images. A grid with mesh size 5 x 5m will reproduce the terrain with more information, while a grid with mesh size 25 x 25m reproduces the terrain more softly. On the other hand, the individual grid points in the 25 x 25m grid are determined with a greater degree of accuracy, as more interest points will be included in the determination of these grid points than by mesh size 5 x 5m.
Diagram 7.2: The accuracy with regard to image resolution.
The influece of resolution
0 0.2 0.4 0.6 0.8 1 1.2
15 µm 30 µm 60 µm
Resolution
Accuracy (m)
1:5,000_5 m 1:5,000_12.5 m 1:5,000_25 m 1:15,000_5 m 1:15,000_12.5 m 1:15,000_25 m 1:25,000_5 m 1:25,000_12.5 m 1:25,000_25 m
7 The investigation
In diagram 7.3 the accuracy for the individual mesh sizes is shown. The missing columns in the diagram represent the three grids which could not be calculated. It can be seen that the mesh size has only a small influence, there is only a faint rise when the larger mesh size is chosen. Only two results deviate from this tendency. It is those for 1:15,000, 30µm and 5 x 5 m, and 1:25,000, 60µm and 12.5 x 12.5 m, where the results are poorer than the tendency.
7.4.1 Summation of mesh size
The mesh size does not have a significant influence. However, there is a small reduction in accuracy us-ing a large mesh size. This conforms with expectations. A small mesh size reproduces the terrain with a greater degree of detail than a large mesh size. A grid with large mesh size reproduces the terrain more softly, while the accuracy must be expected to be a little poorer than when using a small mesh size.
7.4.2 Common conclusion
Looking at the results shown in diagram 7.1 and 7.2 where images with different scales and resolution are shown, it can be concluded that the best results are achieved by using a large scale and a small resolu-tion. The results are linear as expected, and they group themselves according to resolution, see diagram 7.1 or according to scale, see diagram 7.2.
The calculations for 1:15,000, 30µm and 5 x 5m and those for 1:25,000, 60µm and 12.5 x 12.5m deviate from the tendency. These two results correspond to these two calculations which ran slower compared to the remaining calculations. This leads to an investigation into whether there is a limit to how few pixels on the ground may by found per mesh size for a calculation to run without hitch.
It is seen again that the scale has an influence, as a better accuracy is achieved by using a small scale and a low resolution than a large scale and a low resolution.
7.4.3 The pixel size on the ground
Approximately the same accuracy is achieved by using a large scale and a low resolution as by using a smaller scale and a higher resolution, for example 1:15,000 and 30µm, and 1:25,000 and 15µm . This suggests that the scale of the images and their resolution should be regarded each on its own, but that the parameters are influenced by each other. This means that it is not the specific scale and resolution of the individual images which are important, but how great an area the individual pixel covers on the
The influence of mesh size
0 0.2 0.4 0.6 0.8 1 1.2
15 µm 1:5000
30 µm 1:5000
60 µm 1:5000
15 µm 1:15.000
30 µm 1:15.000
60 µm 1:15.000
15 µm 1:25.000
30 µm 1:25.000
60 µm 1:25.000 Resolution
Scale
Accuracy (m)
5 m 12.5 m 25 m
Diagram 7.3: Accuracy with regard to resolution and scale.
In table 7.7 the results achieved in relation to the pixel size on the ground are shown.
Scale Resolution Pixel size on the ground (m2)
Accuracy by mesh size
5 x 5 m 12.5 x 12.5 m 25 x 25 m 1:5,000
15µm 0.075 0.11 m 0.12 m 0.18 m
30µm 0.15 0.13 m 0.17 m 0.22 m
60µm 0.30 0.24 m 0.22 m 0.31 m
1:15,000
15µm 0.225 0.32 m 0.33 m 0.36 m
30µm 0.45 0.53 m 0.51 m 0.57 m
60µm 0.90 / 0.71 m 0.80 m
1:25,000
15µm 0.375 0.53 m 0.55 m 0.59 m
30µm 0.75 / 0.72 m 0.78 m
60µm 1.50 / 1.06 m 0.93 m
Table 7.7: The results as a function of the pixel size on the ground and the mesh size.
7.4.4 The number of pixels per mesh size
When the investigations are evaluated as to scale, resolution and mesh size, it turns out that there is a connection between the three primary parameters. For instance, it makes no sense to determine an ele-vation model with the mesh size 5 x 5 m, if a pixel size on the ground covers, for example, 3 x 3m.
The number of pixel sizes on the ground per mesh size is determined thus:
(7.1)
where: number_pixels =the number of pixels on the ground per mesh g = the mesh size (grid)
µ = the resolution of the images m = the scale of the images
In tables 7.8 – 7.10, the number of pixels on the ground per mesh is shown. The number is calculated for each scale. The relation is indicated with the colours green, yellow and red. In tables 7.8 – 7.10, the cal-culations which have gone well are marked with green. The calcal-culations marked with yellow have been done without warning from Match-T that the results deviate from the tendency. It was marked, however, that the calculation, itself, ran slower than expected. Calculations which could not be done are marked with red.
Image scale 1:5,000
Resolution 5 x 5 m 12.5 x 12.5 m 25 x 25 m
15µm ~ 67 x 67 ~ 167 x 167 ~ 333 x 333
30µm ~ 33 x 33 ~ 83 x 83 ~ 167 x 167
60µm ~ 17 x 17 ~ 42 x 42 ~ 83 x 83
Table 7.8: Number of pixels per mesh by different resolutions and mesh sizes in scale 1:5,000.
2
M
* µ pixels g of
number
=
7 The investigation
Image scale 1:15,000
Resolution 5 x 5 m 12.5 x 12.5 m 25 x 25 m
15µm ~ 22 x 22 ~ 56 x 56 ~ 111 x 111
30µm ~ 11 x 11 ~ 28 x 28 ~ 56 x 56
60µm ~ 6 x 6 ~ 14 x 14 ~ 28 x 28
Table 7.9: Number of pixels per mesh by different resolutions and mesh sizes in scale 1:15,000.
Image scale 1:25,000
Resolution 5 x 5 m 12.5 x 12.5 m 25 x 25 m
15µm ~ 13 x 13 ~ 33 x 33 ~ 67 x 67
30µm ~ 7 x 7 ~ 17 x 17 ~ 33 x 33
60µm ~ 3 x 3 ~ 8 x 8 ~ 17 x 17
Table 7.10: Number of pixels per mesh by different resolutions and mesh sizes in scale 1:25,000.
It will be seen from tables 7.8 – 7.10 that if the number of pixels per mesh size is greater than approx. 13 x 13 pixels, the calculation runs without problems. If the number of pixels per mesh size lies between approx. 8 x 8 pixels, and approx. 11 x 11 pixels, a calculation can be done, but the result deviates from the tendency. If the number of pixels is lower than approx. 8 x 8 pixels per mesh size, a calculation can-not be done. This phenomenon is also confirmed in the sources, where it is mentioned [Inpho, 1994] that a calculation can be expected to run slower if there are less than 30 x 30 pixels per mesh. It is also men-tioned by [Baltsavias, 1999] that it is recommended that there are 10 x 10 to 15 x 15 pixels per mesh.
This investigation shows that there should be at least 13 x 13 pixels per mesh size for a calculation to run smoothly, which falls within the recommendation from [Baltsavias, 1999] of 102 – 152 pixels. If the mini-mum of approx. 13 x 13 pixels per mesh size is used, a calculation will run smoothly. However, it is rec-ommend here that 15 x 15 pixels per mesh size is chosen, so that it is certain that a calculation can be done, see table 7.11.
Scale Pixel size (µm) Minimum mesh size (m)
1:5,000 15 x 15µm 1.125 x 1.125
1:5,000 30 x 30µm 2.25 x 2.25
1:5,000 60 x 60µm 4.5 x 4.5
1:15,000 15 x 15µm 3.375 x 3.375
1:15,000 30 x 30µm 6.75 x 6.75
1:15,000 60 x 60µm 13.5 x 13.5
1:25,000 15 x 15µm 6.625 x 6.625
1:25,000 30 x 30µm 11.25 x 11.25
1:25,000 60 x 60µm 22.5 x 22.5
Table 7.11: Minimum mesh size considering scale resolution.
The presumption is that with 15 x 15 pixels, Match-T can determine enough interest points to determine the grid points. A closer investigation of this is not possible, as the information concerning the accurate location and elevation of the interest points appear as a binary file. This file has not been accessible in this project. Therefore, it has not been possible to make a closer analysis of, for instance, the lack of in-terest points for the determination of a small mesh size as opposed to the resolution. The investigation done in this project has shown a tendency as regards which minimum mesh size can be expected to be serviceable with a certain scale and resolution.
If this knowledge is used on any given combination of scale, resolution and mesh size, it can be checked whether the calculation will run correctly, using formula 7.1. It must be noted, however, that even if the number of pixels per mesh size is over 15 x 15, this is no guarantee of a good result, but only of a smooth run of the calculation itself.