Coloring an image with two Color schemes based on a Range

I would like to color an image generated from some data, using two color schemes based on two ranges of the data. This is my attempt:

Image[RandomReal[1, {10, 10}], 
      ColorFunction -> (Piecewise[{{ColorData["AlpineColors"][#],  0 < # < .5}, 
                                   {ColorData["SouthwestColors"][#], .5 < # < 1}}] &)]]