When creating a DEM by triangulation, the algorithm sometimes produces cylindrically shaped artefacts along the triangle axes between measured points and towards the edges. The actual anchor points are perfectly represented by the grid.
My example consists of precisely surveyed surface of a road with 3-point crossprofiles of ca. 6m length, the crossprofiles are every ca. 10m.
The objective is to compare against a surface measured by Laserscanning. So I created a 10 cm grid from both the Laserscan and the anchor point data, and then subtracted one from the other. The triangular shaped artefacts come out in the grid difference. Also the resampling high-pass filter or a hillshading shows these artefacts in the triangulated grid. These aretefacts have an amplitude of some centimeters, and do not appear everywhere. I tried other gridding methods, each of them shows their distinctive artefacts such that I could not create a sufficiently accurate result (ie., triangulation worked best so far).
Anyone an idea or suggestion on how to solve this problem? Also, is there a way to edit the delauney triangles (i.e., for a curvy road, one needs triangulation for the road surface only, and not for the space in between)?
A brief remark, I noticed that the natural neighbour gridding without extrapolation returns the same result as the triangulation (within numerical accuracy).
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I'm sorry, but I don't understand what you mean by "cylindrically shaped artefacts along the triangle axes" and it is difficult to interpret the image of the difference grid you posted. But I think the tools work correctly, both tools you tried use different triangulation algorithms but produce the same result. So most likely you observe something like an interference pattern caused by a minimal shift between the two datasets you use as input.
Best regards,
Volker
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The image shows the triangulated Grid (10 cm) after highpass filtering. The input points are the black squares, representing a road (3 squares = width of the road). For the upper right and lower left parts, trinagulation worked fine, indicated by a lack of (highpass) structure in between the points (just gray colours). In the central part, there are blue or red lines between some of the ajacent points. These correspond to an apparent topography of some centimeters, and are in my opinion an artefact of the triangulation. Funny enough, the problem does not occur between the central points (where there is also an axis of a delauney triangle).
The funny thing is, that the grid points close to the input point show correct values.
Maybe another question in relation to this, that would solve this problem. Is it possible to calculate the difference between a densely sampled dataset (grid or point cloud from Lidar) and sparsely sampled input dataset (e.g. theoretic points), directly (based on local interpolation)? I want to end up with a densely sampled dataset representing the features of the point cloud, in comparison to the given surface (given surface may be incorrect or not show local features, but is assumed to be like a triangulated mostly flat surface).
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Ok, so it is simply an issue of (linear) interpolation which shows up as soon as the grid points are located further away from a measured point.
Regarding your other question: sorry, no, such tools are not available in SAGA. We have such tools in our commercial point cloud add-on to SAGA, including a tool which can measure the distance between each point (of a high density point cloud) and a (local) triangulation of another (e.g. low density) point cloud.
Best regards,
Volker
www.laserdata.at
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Were there any improvements relating to this artefact-issue implemented in recent Saga Versions? Or any workaround suggestions (i.e., difference between sparsely and densely spaced data in surveying-type environment) ?
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Hello
When creating a DEM by triangulation, the algorithm sometimes produces cylindrically shaped artefacts along the triangle axes between measured points and towards the edges. The actual anchor points are perfectly represented by the grid.
My example consists of precisely surveyed surface of a road with 3-point crossprofiles of ca. 6m length, the crossprofiles are every ca. 10m.
The objective is to compare against a surface measured by Laserscanning. So I created a 10 cm grid from both the Laserscan and the anchor point data, and then subtracted one from the other. The triangular shaped artefacts come out in the grid difference. Also the resampling high-pass filter or a hillshading shows these artefacts in the triangulated grid. These aretefacts have an amplitude of some centimeters, and do not appear everywhere. I tried other gridding methods, each of them shows their distinctive artefacts such that I could not create a sufficiently accurate result (ie., triangulation worked best so far).
Anyone an idea or suggestion on how to solve this problem? Also, is there a way to edit the delauney triangles (i.e., for a curvy road, one needs triangulation for the road surface only, and not for the space in between)?
Thanks!
Last edit: E S 2018-11-12
A brief remark, I noticed that the natural neighbour gridding without extrapolation returns the same result as the triangulation (within numerical accuracy).
I still did not solve this problem with Saga. Can anyone at least comment if that problem is known, or if I do something wrong.
Hi,
I'm sorry, but I don't understand what you mean by "cylindrically shaped artefacts along the triangle axes" and it is difficult to interpret the image of the difference grid you posted. But I think the tools work correctly, both tools you tried use different triangulation algorithms but produce the same result. So most likely you observe something like an interference pattern caused by a minimal shift between the two datasets you use as input.
Best regards,
Volker
The image shows the triangulated Grid (10 cm) after highpass filtering. The input points are the black squares, representing a road (3 squares = width of the road). For the upper right and lower left parts, trinagulation worked fine, indicated by a lack of (highpass) structure in between the points (just gray colours). In the central part, there are blue or red lines between some of the ajacent points. These correspond to an apparent topography of some centimeters, and are in my opinion an artefact of the triangulation. Funny enough, the problem does not occur between the central points (where there is also an axis of a delauney triangle).
The funny thing is, that the grid points close to the input point show correct values.
Maybe another question in relation to this, that would solve this problem. Is it possible to calculate the difference between a densely sampled dataset (grid or point cloud from Lidar) and sparsely sampled input dataset (e.g. theoretic points), directly (based on local interpolation)? I want to end up with a densely sampled dataset representing the features of the point cloud, in comparison to the given surface (given surface may be incorrect or not show local features, but is assumed to be like a triangulated mostly flat surface).
Ok, so it is simply an issue of (linear) interpolation which shows up as soon as the grid points are located further away from a measured point.
Regarding your other question: sorry, no, such tools are not available in SAGA. We have such tools in our commercial point cloud add-on to SAGA, including a tool which can measure the distance between each point (of a high density point cloud) and a (local) triangulation of another (e.g. low density) point cloud.
Best regards,
Volker
www.laserdata.at
Were there any improvements relating to this artefact-issue implemented in recent Saga Versions? Or any workaround suggestions (i.e., difference between sparsely and densely spaced data in surveying-type environment) ?
AFAIK there has nothing changed.