I am curious, at this point, to compare approaches: Delaunay triangulation, 3D alpha shape, Voxel Grid and Marching Cubes.
Which of these approaches is most used?
I think triangulation is still the most flexible approach. But as always it is a matter of the results you want to achieve.
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Delaunay triangulation, the advantages of Delaunay mesh model is all triangles in the mesh model are as equiangular as possible, create non-overlapping triangles, the minimum interior angles of all triangles are maximized and the maximum angles are minimized.
It's a validation of the Dealunay method, but what about voxel gride, 3 alpha shape, marching cubes ...
Marching cubes approach is often used when you need the results fast. It is possible to run it in real-time for quite big volumes on decent consumer-grade hardware.
If you do need better results there are many better methods. On top of the ones mentioned, a very popular method is "Multi-level partition of unity implicits" [1] which was originally developed for point cloud data reconstruction but works well on volumes also.
Most recently there are many deep approaches tackling the problem as well. The downside is their specialisation for very specific use-cases.
[1] https://dl.acm.org/citation.cfm?id=882293
Delaunay triangulation, Marching cubes are 3D reconstruction techniques for meshing any 3D images, 3D images are composed of group of voxels called voxel grid.
Does this mean that Delaunay triangulation and Marching cubes make voxel grid?
What is the difference between Delaunay triangulation and Marching cubes?
They do not make a voxel grid. They output the mesh representation of the surface described by selected points in data. Marching cubes [1, 2] was designed to work on data presented on regular 3D grids, Delaunay triangulation [3] works on any kind of point cloud data (no necessarily on a regular 3D grid).
If the data is on regular grid, Marching cubes will work much faster than Delaunay triangulation. If your data is not in the form of regular grid and you would still like to run Marching cubes on it, you have to resample the data to do so.
[1] https://dl.acm.org/citation.cfm?id=37422
[2] https://en.wikipedia.org/wiki/Marching_cubes
[3] https://en.wikipedia.org/wiki/Delaunay_triangulation
What can you tell me about 3D alpha shape?
Is there any review article on this area ?
CT,MRI and PET scanners generate 3D images which contains voxel grid by using different meshing techniques we can extract surface of an object form 3D images.
Two classes of surface representations: parametric representations and implicit representations. Conversion from an implicit to parametric representation called iso-surface extraction the standard method for iso-surface extraction was marching cubes, however the complicated shape and topology cannot reconstructed correctly using MC, it generates badly shaped triangles and sharp features in data are not preserved.
An Alternative to MC was 3D Delaunay triangulation it will refine and filter the mesh. the output of surface mesh have well shaped triangles and faithful approximation to the original surface in term of both topology and geometry.
What is difference between parametric representations and implicit representations?
What is iso-surface extraction exactly? Is there any definition for that?
Please read this book " Polygon Mesh Processing By Mario Botsch, Leif Kobbelt, Mark Pauly, Pierre "
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