How to remove internal faces with MeshLab

A very common situation that often arise the cleaning of a model with a detailed interior in which you are not interested in (and you want to remove it once for ever!). For example consider this nice LEGO model: 200k faces. Most of the faces are hidden inside the model, used to describe the internal pieces and pegs: not very useful in most cases. We can remove them with MeshLab.

After starting the filter color->vertex ambient occlusion over the mesh (and after waiting a few seconds) we have computed both a per-vertex gray color and stored for each vertex an attribute with a occlusion value. Side note: MeshLab has a general purpose per vertex and per face scalar quantity that are used and interchanged by many different algorithms with a variety of different semantic; we call this scalar quantity "quality" for no good reason (lazyness), it is a generic scalar quantity, it could be occlusion value (like in this case), a geodesic distance from border, gaussian curvature.

Second note: Ambient occlusion greatly enhance the perception of 3D shapes! Nowadays everyone recognizes it, but a few years ago not a lot of people was really aware of that (I am a proud user of AO since 2001 for nice renderings of Cultural Heritage stuff :) and, more recently, for nice renderings of molecules ).

Back to the topic of removal of internal faces.

We now can exploit this per-vertex occlusion value to select all the faces that have all their three vertices with a very low occlusion value. That means that we remove all the faces that has no visible vertices. This is not an perfect solution, there are easy counter-examples where this approach could remove visible faces (but with hidden vertices): in most cases it works wells but a bit of caution is always recommended.
In the side figure you can see the select by vertex quality filter in action with the all the selected internal faces: 130k faces out of 200k were totally internal and can be safely removed leaving just 70k faces.

On the subtle art of mesh cleaning

Most mesh processing algorithms usually require nice two-manifold, watertight, intersection free, well-shaped, clean meshes. Obviously in the real world this does not happen with a great frequency (apart in scientific papers). Common meshes are the most horrible mix of all the possible almost catastrophic degenerate situations.

MeshLab can help the tedious tasks of cleaning meshes in a variety of ways. Let's start with some simple examples involving vertices.

1. Unreferenced Vertices. Very common issue. Your mesh has some vertices that are not referenced by any triangle. A variety of cause can create these situations (algorithms deleting faces in a non careful way can create them). This situation can be more dangerous than it seems, because they can bring in trash uninitialized data in algorithms that initialize vertex data performing face-based traversal (e.g. normals computations...).
   An easy way to look at the presence of these vertices is simply switching to a point based rendering mode (evenually turning the lighting off, because, by default, unreferenced vertices have null normals). As always happens, sometime this situation is not an error but could be a feature (think to point clouds).
2. Duplicated vertices. Adjacent triangles does not share the vertices with the same coordinates. Sometimes it is an issue that come directly from some file formats (STL for example store triangles duplicating each vertex). This situation is easy to be detected:
   
   1. Smooth shading is the same of flat shading: the duplicated vertices do not allow the averagin of normals between adjacent faces that is necessary for smooth shading.
      
   2. Poor man version of Euler Characteristic does not work: instead of having:
      
      [face number] ~ 2 * [vertex number]
      
      you have:
      
      [face number] ~ 1/3 * [vertex number]
      
   Again this could be a feature and not an error. Sometimes, duplicating vertices can be used to impose sharp angles when you do not have simple techniques to store multiple normals for the same vertex.
   

The above cases can be cured, if necessary, by invoking in MeshLab the two filters, Remove Unreferenced Vertices and Remove Duplicated Vertices in the menu named: Filters->Cleaning and Repairing.