问题
I have two sets of points, one from an analysis and another that I will use for the results of post-processing on the analysis data.
The analysis data, in black, is scattered.
The points used for results are red.
Here are the two sets on the same plot:
The problem I have is this: I will be interpolating onto the red points, but as you can see there are red points which fall inside areas of the black data set that are in voids. Interpolation causes there to be non-zero values at those points but it is essential that these values be zero in the final data set.
I have been thinking of several strategies for getting those values to zero. Here are several in no particular order:
- Find a convex hull whose vertices only contain black data points and which contains only red data points inside the convex set. Also, the area of this hull should be maximized while still meeting the two criteria.
This has proven to be fairly difficult to implement, mostly due to having to select which black data points should be excluded from the iterative search for a convex hull.
Add an extra dimension to the data sets with a single value, like 1 or 0, so both can be part of the same data set yet still distinguishable. Use a kNN (nearest neighbor) algorithm to choose only red points in the voids. The basic idea is that red points in voids will have nearest n(6?) nearest neighbors which are in their own set. Red data points that are separated by a void boundary only will have a different amount, and lastly, the red points at least one step removed from a boundary will have a almost all black data set neighbors. The existing algorithms I have seen for this approach return indices or array masks, both of which will be a good solution. I have not yet tried implementing this yet.
Manually extract boundary points from the SolidWorks model that was used to create the black data set. No on so many levels. This would have to be done manually, z-level by z-level, and the pictures I have shown only represent a small portion of the actual, full set.
Manually create masks by making several refinements to a subset of red data points that I visually confirm to be of interest. Also, no. Not unless I have run out of options.
If this is a problem with a clear solution, then I am not seeing it. I'm hoping that proposed solution 2 will be the one, because that actually looks like it would be the most fun to implement and see in action. Either way, like the title says, I'm still looking for direction on strategies to solve this problem. About the only thing I'm sure of is that Python is the right tool.
EDIT: The analysis data contains x, y, z, and 3 electric field component values, Ex, Ey, and Ez. The voids in the black data set are inside of metal and hence have no change in electric potential, or put another way, the electric field values are all exactly zero.
This image shows a single z-layer using linear interpolation of the Ex component with scipy's griddata. The black oval is a rough indicator of the void boundary for that central racetrack shaped void. You can see that there is red and blue (for + and - E field in the x direction) inside the oval. It should be zero (lt. green in this plot). The finished data is going to be used to track a beam of charged particles and so if a path of one of the particles actually crossed into the void the software that does the tracking can only tell if the electric potential remains constant, i.e. it knows that the path goes through solid metal and it discards that path.
If electric field exists in the void the particle tracking software doesn't know that some structure is there and bad things happen.
回答1:
You might be able to solve this with the big-data technique called "Support Vector Machine". Assign the 0 and 1 classifications as you mentioned, and then run this through the libsvm algorithm. You should be able to use this model to classify and identify the points you need to zero out, and do so programmatically.
I realize that there is a learning curve for SVM and the libsvm implementation. If this is outside your effort budget, my apologies.
来源：https://stackoverflow.com/questions/32511114/strategy-for-isolating-3d-data-points