The Head: Mesh Creation

Description:

So far we have a cloud of 3D points which have to be connected somehow in order to look like a surface. This is known as mesh creation and this is how I do it:

• Go over all the points and try to get rid of the noisy ones, by approximating them with an average of their neighbors. It is clear that not all the points will have a valid number of neighbors. The number of valid neighbors is a parameter in the program that I can change. I found that a good value would be 4 (out of 8 neighbors). I also tried 5 or 6 but I got big holes in the mesh.
• The next step is to go over all the points and smooth the mesh. That is, for each point, look at the number of its valid neighbors that are at a certain distance from it (make this a parameter, too) and replace the current value with a weighted average between the current point and its valid neighbors. Yeah, you are right, the weight associated with the points will also be a parameter in the program. I found that a very good value for the weight of the current point would be 0.3, which surprised me. Of course, the weight of the valid neighbors would be 0.7. That was found to be a very important step! It improved the quality of the mesh considerably.
• The final step is to generate triangles. Take four neighboring points at a time and create two triangles using the shortest diagonal if the points are considered close to each other. If there are only three points and if they are close to each other, then connect them. If there are only two or less valid points, then don't do anything.

Code:

• C++ program

Results:

• JPEG image
  
• JPEG image (different view, with texture)
  
• VRML file without texture
  
• VRML file with texture

Comments:

Trying to fix the holes in the mesh helps a lot. Also, the low-pass filter improves the quality of the mesh considerably. The disadvantage of this method is the size of the resulting file, but it can be converted into a binary format, using ivcat.

I would post more VRML files to show my experiments with different parameters in the mesh program, but the UGCS disk quota is limited so I cannot keep too many files around. Anyway, this is the best mesh I could get.