I'm looking for a way to interpolate 2D fields that are arranged on a list, making the shape data = [11,2016,2016]
Up to the moment I've managed to stack the 2D plots over the Z axis and create an interactive plot, but i want to create a plot of the volume and thought that an interpolation through the 11 steps would work, I'd like to get only one 2D array at the end to plot.
Any suggestions about how to perform this? can I make it on one single operation or am I obliged to perform step by step interpolations between each step?
edit: a picture showing the image that i'm able to generate now and can maybe explain better my problem.
I'm a wee bit stuck.
I have a 3D point cloud (an array of (n,3) vertices), in which I am trying to generate a 3D triangular mesh from. So far I have had no luck.
The format my data comes in:
(x,y) values in regularly spaced (z) intervals. Think of the data as closed loop planar contours stored slice by slice in the z direction.
The vertices in my data must be absolute positions for the mesh triangles (i.e. I don't want them to be smoothed out such that the volume begins to change shape, but linear interpolation between the layers is fine).
Illustration:
Z=2. : ..x-------x... <- Contour 2
Z=1.5: ...\......|... <- Join the two contours into a mesh.
Z=1. : .....x----x... <- Contour 1
Repeat for n slices, end up with an enclosed 3D triangular mesh.
Things I have tried:
Using Open3D:
The rolling ball (pivot) method can only get 75% of the mesh completed and leaves large areas incomplete (despite a range of ball sizes). It has particular problems at the top and bottom slices where there tends to be large gaps in the middle (i.e. a flat face).
The Poisson reconstruction method smooths out the volume too much and I no longer have an accurate representation of the volume. This occurs at all depths from 3-12.
CGAL:
I cannot get this to work for the life of me. SWIG is not very good, the implementation of CGAL using SWIG is also not very good.
There are two PyBind implementations of CGAL however they have not incorporated the 3D triangulation libraries from CGAL.
Explored other modules like PyMesh, TriMesh, TetGen, Scikit-Geometry, Shapely etc. etc. I may have missed the answer somewhere along the line.
Given that my data is a list of closed-loop planar contours, it seems as though there must be some simple solution to just "joining" adjacent slice contours into one big 3d mesh. Kind of like you would in blender.
There are non-python solutions (like MeshLab) that may well solve these problems, but I require a python solution. Does anyone have any ideas? I've had a bit of a look into VTK and ITK but haven't found exactly what I'm looking for as of yet.
I'm also starting to consider that maybe I can interpolate intermediate contours between slices, and fill the contours on the top and bottom with vertices to make the data a bit more "pivot ball" method friendly.
Thank you in advance for any help, it is appreciated.
If there is a good way of doing this that isn't coded yet, I promise to code it and make it available for people in my situation :)
Actually there are two ways of having meshlab functionality in python:
The first is MeshLabXML (https://github.com/3DLIRIOUS/MeshLabXML ) a third party, is a Python scripting interface to meshlab scripting interface
the second is PyMeshLab (https://github.com/cnr-isti-vclab/PyMeshLab ) an ongoing effort done by the MeshLab authors, (currently in alpha stage) to have a direct Python bindings to all the meshlab filters
There is a very neat paper titled "Technical Note: an algorithm and software for conversion of radiotherapy contour‐sequence data to ready‐to‐print 3D structures" in the Journal of Medical Physics that describes this problem quite nicely. No python packages are required, however it is more easily implemented with numpy. No need for any 3D packages.
A useful excerpt is provided:
...
The number of slices (2D contours) constituting the specified structure is determined.
The number of points in each slice is determined.
Cartesian coordinates of each of the points in each slice are extracted and stored within dedicated data structures...
Numbers of points in each slice (curve) are re‐arranged in such a way, that the starting points (points with indices 0) are the closest points between the subsequent slices. Renumeration starts at point 0, slice 0 (slice with the lowest z coordinate).
Orientation (i.e., the direction determined by the increasing indices of points with relation to the interior/exterior of the curve) of each curve is determined. If differences between slices are found, numbering of points in non‐matching curves (and thus, orientation) is reversed.
The lateral surface of the considered structure is discretized. Points at the neighboring layers are arranged into threes, constituting triangular facets for the STL file. For each triangle the closest points with the subsequent indices from each layer are connected.
Lower and upper base surfaces of the considered structure are discretized. The program iterates over every subsequent three points on the curve and checks if they belong to a convex part of the edge. If yes, they are connected into a facet, and the middle point is removed from further iterations.
So basically it's a problem of aligning datasets in each slice to the nearest value of each slice. Then aligning the orientation of each contour. Then joining the points between two layers based on distance.
The paper also provides code to do this (for a DICOM file), however I re-wrote it myself and it works a charm.
I hope this helps others! Make sure you credit the author's in any work you do that uses this.
A recent feature of pymadcad can do things like this, not sure through if it fits your exact expectation in term of "pivot ball" or such things, checkout the doc for blending
Starting from a list of outlines, it can generate blended surfaces to join them:
For your purpose, I guess the best is one of:
blendpair(line1, line2)
junction(*lines)
I am currently working on a summer research project and we have generated 360 slices of a tumor. I now need to compile (if that's the right word) these images into one large 3D image. Is there a way to do this with either a python module or an outside source? I would prefer to use a free software if that is possible.
Perhaps via matplotlib, but anyway may require preprocessing I suppose:
https://www.youtube.com/watch?v=5E5mVVsrwZw
In your case, the z axis (3rd dimension) should be specified by your vector of images. Nonetheless, before proceeding, I suppose you would need to extract the shapes of the object you want to reconstruct. For instance, if i take any image of the many 2D you have, I expect to find RGB value for each pixel, but then, for instance if you want to plot a skull like in the video link, as I understand you would need to extract the borders of your object and from each of its frame (2D shape) and then plot their serie. But anyway, the processing may depend on the encoding of the information you have. Perhaps is sufficient to simply plot the series of images.
Some useful link I found:
https://www.researchgate.net/post/How_to_reconstruct_3D_images_from_two_or_four_2D_images
Python: 3D contour from a 2D image - pylab and contourf
I have a specific problem that maybe can help me with. I have, currently, 3 arrays of data and I want to make a 2D histogram of the first two while using the third array as values that get summed up in each particular bin. I also want to include a color bar that shows the scale of different colors you see in the histogram.
As a start I looked into using matplotlib.pyplot.hexbin to do this and it seems to work fine but I don't want to have hexagons as the shape of my bins. Is somebody able to point me to some resources on how to do this?
I am trying to display some timeseries data in 3D using colormapped values using VTK.
I have a single array of 3D positions for two different kinds of objects, say cones and spheres. These positions are interspersed. I also have a 2D array with timeseries data for these objects. n-th entry in position array correponds to n-th row in timeseries array. (all these are numpy arrays).
Now I want an animated display (using python-vtk) of the cones and the spheres with their colors varying according to the entries in the timeseries array. Currently I made it work by splitting each of the arrays into two - one for cones and one for spheres. But ideally I would like to just pipe cone entries of the position array through a coneGlyph and sphere entries through a sphere glyph and set the timeseries values for all the positions directly. What is the way to do that, if possible at all?
I bypassed the issue by storing the indices of the two kinds of objects (i.e., cone_indices and sphere_indices). I also create to vtkPoints objects with the cone positions and the sphere positions. These are used to create the vtkPolyData for the respective classes. In the update method of the timer class, I use these index-arrays to pick up the data for that time point for each type and assign the scalar values to the point data.
conePoints.GetPointData().SetScalars(coneData)
spherePoints.GetPointData().SetScalars(sphereData)
numpy's array lookup using an index-array is fast enough.