Reducing a population of points in the 3D plot

I have an 3D image with a population of vertices with X,Y,Z coordinates placed in the volume. The number of vertices can be very very large. I am looking for a way to mathematically reduce the number of vertices, based on their proximity to each other. I would like to have spots separated by a maximum distance between spots. This distance is maybe can be the size of a single voxel in the image.

Any ideas will be appreciated.

[Satyajeet Sasmal]

Would you like to reduce the number of tesselations? If so, please look at the link below:

http://www.mathworks.com/help/matlab/ref/reducepatch.html

It reduces the number of patches in your 3D image, thereby reducing the number of vertices for the image.