Hello,
Kelvin Probe Microscopes measure the "work function" of a materials surface. There are two ways (yielding two different resolutions, but let's forget about the tunneling method) to measure the work function of a surface: The lower resolution, phenomenologically classical method relies on the electrons overcoming the work function of a surface prior to conducting to the probe. The work function of a material will change with inhomogeneities in the material (different phases etc..). So back to your question. Remember that potentials are relative quantities. There isn't a "positive region" just a region where the work function is higher than the surrounding regions.
Hope this helps.
Regards
Modey3