Simplifying surfaces

Hi all,

I apologise if this is an obvious one.  I've been getting on quite well with GH, but this problem has so far eluded me.  I trying to think of a way to simplify surfaces.  For example, if you have a surface with lots of cut outs around it's edge, is it possible to remove these cut outs and hence simplify it? 

For example, has anyone got any ideas as to how I can make the surface on the left more like that on the right?

I've been going down the route of meshing the surface and trying to cull the vertices, but so far this hasn't achieved anything.

Any ideas would be much appreciated,

Dan