Split a polygon based on density of points in ArcGIS 10.1

Question

I have two layers:

1. Polygon layer representing administrative boundaries

2. Polygon layer representing topography (i.e. a map)

In some of the administrative areas, the buildings (shown in the map) are grouped in one area while the rest of the area is something else. I would like to split the administrative area into two, one containing all the buildings and another containing no buildings. See diagram.

I created a union between my two layers and then dissolved to create a third layer which identified the "building/not building" for each administrative area, this is close to what I want except that it doesn't create a single cut, but creates a complex shape that wraps around each building and go along roads etc.

I have a few thousand polygons like this so I would like to be able to cut them automatically.

Answer 1

What I worked out was:

1. Create a multipart feature made up of all the buildings in each area.
2. Buffer around these features and dissolve to create blobs around the buildings
3. Union with the original boundaries
4. each blob now has two boundary id values (its originating area, and its location)
5. Delete blobs were the boundary id values are not equal

This method was about 90% effective