I have created a polygon layer from rasters, and only have a single classification ID (and calculated acres) for each polygon.  I would like to "dissolve" all touching features into larger, individual polygons.  The 3 areas circled in red (below) contain green polygons/pixels that only touch on the points of the squares.  Intuitively (from an end user perspective) all of the green polygons within a circled area should be connected and treated as a single polygon because there are no "breaks" where the features/cells do not touch.

What would be the best method to accomplish "joining" or "dissolving" all of these features using ArcGIS.  I have ArcInfo and Spatial Analyst extension.  If there is a better methodology for doing this in Spatial Analyst, I can pre-process the polygons that way, too.

![Raster to Polygon][1]


  [1]: https://i.sstatic.net/cfKoe.jpg