We have multiple CT-scans in the format of TIF image stacks. To get the mean curvature we first transform the stack to a triangular mesh (using Marching Cubes). To make the triangles in this mesh more equilateral we apply isotropic explicit remeshing to the mesh. Of this remeshed mesh we get the mean curvature using VTK.
However, the problem is this gives an inaccurate estimation, which can be seen for the sphere in the attachment (mean curvature in a sphere should be 1/radius for all vertices).
Getting the mean curvature from an image stack seems like a very common procedure in image processing, therefore I was wondering if anybody would know how to get an accurate estimation of the (mean) curvature if possible. Thanks in advance
Maybe fit a local multivariate polynomial to the data, e.g. using a Savtizky-Golay filter. Then compute the (2nd) partial derivatives of the fit.
I would try following:
- Skip the remeshing. Better results?
- Check the triangle orientation. Maybe VTK expects the triangles oriented the same.
Can you upload the DICOM CT of that ball. I can take a look. Probably the VTK implementation is based on local vertex 'umbrella' operators as described by Meyer & Desbrun:
http://www.geometry.caltech.edu/pubs/DMSB_III.pdf
I wrote an independent implementation...
Lambert Zijp I tried it without remeshing, but the result looks even more unnatural.
I do not have a DICOM file, but a TIF image stack (see attachment). The original micro-CT scans I have are also in this format. To all the image stacks I apply Gaussian Smoothing prior to the mesh generation (see attachment g_3) to get the resulting mesh to be more smooth. The resulting mesh without smoothing (for the ball) is in the attachments. As you'd expect the corresponding mean curvatures yield even higher errors.
So basically, I have a TIF image stack containing a micro-CT scan. I want to visualize the mean curvature of the object in the scan, but since the object is discretized by voxels I get some errors.
Hi Steven,
Your 'no smoothing' marching cubes rendering looks very familiar...
My suggestion that wrongly oriented triangles might have caused the problem, is not the case. The effect is caused by your artificial binary sphere. Marching cubes interpolates, but if the volume only contains 0 or 255, there is not so much to interpolate!
You could solve the problem by creating a sphere taking into account partial volume effects. The voxels at the edge of the sphere then have values proportional to the amount of each voxel that actually resides inside the sphere.
A more dirty but quicker solution is to make the sigma and kernel-size of the Gaussian blur much much much larger.
If you scan a real ball-phantom in the micro-CT, you would not have this problem: you get partial volume effects for free! :-)
By the way, the kernel of the Gaussian should be spherical as well. The implementation you use cuts corners in this respect. Here is img_0152.tif, thresholded at 255. It should be spherical.
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