Spatial statistics tools : clustering analysis on raster data

I've an apparently simple problem, but i can't find a clear methodology to use.

I'm tasked to delimit "urban areas" by vector convex polygons, using the Gridded Population of the World dataset from CIESIN

This dataset provides population density values over the entire world, as a raster file. The problem is, as you have already guessed, that the density values are very changing, and the definition of "urban" is quite relative.

I've tried to use a classical approach and calculated the slopes as if the density values were altitudes, but the slopes values were also very disparate and spatially complex, intricates.

I've looked into spatial clustering algorithms, LISA tools (Local Indocators of Spatial Association), with ArcGIS and GeoDa, but I'm quite lost among very specific tools. Some of the methods are working only on vector shapes, so a reclassification and a vectorization are needed (long computation).

Can you help me refining the set of methods and tools to use ? Thanks !

Answer

I did some work on this for my MSc http://ian01.geog.psu.edu/papers/mscthesis.pdf - basically I worked on gradient changes but the discussion may help you with this.