MeshLab Stuff: July 2010

In the pipeline of processing 3D data, after you have aligned and merged your range maps, you ofter require to get a nice clean textured mesh. In the last release of MeshLab we included our state-of-the-art parametrization/remeshing algorithm based on abstract parametrization. Now some a two-part tutorial on his practical usage.
Let's start from a medium complexity mesh of a skull (kindly provided and scanned for the VCG Lab by Marco Callieri). You can see it depicted in the two small figures on the right.
The mesh of the skull is composed by 1.000.000 triangles, it has a meaningful per-vertex color (recovered from a set of photos) and, as it often happens, it is topologically dirty.

First of all it is non 2-manifold (there are 7 edges where more than two face are incident) than there are many small holes and handles that make difficult any kind of parametrization.

So the first step is to build a watertight, coarser but topologically sound model. Poisson surface reconstruction is a perfect filter for this task. A reconstruction at depth 9 is usually good, that generates a mesh of 1.3M of faces. For this kind of processing a quite faithful geometric representation is not needed, but it is strongly needed that the overall topology is the right one. In this case some portions of the skull are remarkably thin and at low resolutions the poisson surface reconstruction can create unwanted holes.

After that a further simplification step is needed to bring the model size to a number reasonable for the Isoparametrization engine. Remember that the when building an abstract parametrization you do not need the full accuracy model but just a model that shares the overall shape and the same topology. For the purpose of the parametrization small details have a very small influence on the overall quality of the parametrization. Side figure depict the watertight Poisson reconstructed surface, note how the nostril cavity was filled (as expected because it was a hole with boundary).

So simplify it our watertight skull up to 50000 triangles. Take care to check Normal Preservation and Topology preservation Flag. The second one is particularly important, infact the basic edge collapse simplification algorithms can during simplification change the topology of the mesh, and while this is usually a nice feature (it allows for example the closure of very small holes) when you start from a mesh that is surely clean (a 2-manifold watertight model) it is better to be sure that such properties are preserved.

After that you can start with creating the Abstract Isoparametrization, a technique we introduced in:

Nico Pietroni, Marco Tarini, Paolo Cignoni
Almost isometric mesh parameterization through abstract domains
IEEE Transaction on Visualization and Computer Graphics, Volume 16, Number 4, page 621-635 - July/August 2010

Without going into details, that you will find in the above paper, the main idea is rather simple. Usually textures are defined in a dominion that is just the (0,0)-(1,1) square on the plane. In our approach as a domain of the parametrization we use a different 2-dimensional domain, the surface of a very coarse simplicial complex that has the same topology of the original mesh and it is composed by just a few hundred triangles. Such an approach is interesting because this abstract parametrization can be used for a number of things, like for example remeshing, texturing, tangent space smoothing etc.

To build the abstract isoparametrization just start the corresponding filter called "Isoparametrization", (default params are ok, you can lower convergence precision to a '1' to speedup a bit and try to change a bit the targeted size of the abstract domain). It is a bit slow so wait some minutes for the processing. At the end of the process, you do not see anything directly but the structure is attached to the mesh and you can use it in the other filters. If you want re-use it for a later use you have to save both the processed mesh and as a separate step the isoparametrization using the "Isoparametrization Save Abstract Domain Filter".

The created isoparametrization can be used to build a standard parametrization over any mesh that is reasonably close to the original one.
In our example we take a simplified version of the original mesh, composed by just 10000 triangles ("Skull_10k.ply"). We transfer over this simplifed mesh the just build isoparametrization
and then using the filter "Iso Parametrization transfer between meshes", setting as source mesh the one with the abstract parametrization (skull_60k_isoparam.ply) and skull_10k.ply as target.

Now we can transform the transferred isoparametrization into a standard atlased parametrization using the "Isoparametrization Build Atlased Mesh" filter. The two image on the right seems equal but you can see that in the lower one the triangles of the mesh have been cut along the triangles of the abstract parametrization in order to get proper atlas regions. At this point your mesh has a standard texture parametrization and it is ready for use it for a variety of operation.

The First thing that we can do is just to transfer the color of the original 1M vertexes color onto a texture according this parametrization. This can be done by using the filter "Transfer color to texture (between 2 meshes)", choose a reasonable texture size (2048x2048 is good) and you will obtain a simplified textured mesh that looks strikingly similar to the original heavy 1M tri model (try to compare the first and last snapshots).