color – How to make a smooth highly contrasted image from a Blurr, without affecting the sides?

I’m generating a random texture using the code above, by blurring random tiles:

randomTiles = 
  Table[{RandomReal[], RandomReal[], RandomInteger[{1, 2}]}, {n, 1, 
    1500}];

Sharpen[Blur[ListDensityPlot[
   randomTiles,
   ColorFunction -> "IslandColors",
   InterpolationOrder -> 0,
   Frame -> False,
   ImageSize -> {500, 500}
   ], 10], 2]

Preview of what this code is doing:

enter image description here

Currently, the Blurr is also changing the sides of the picture, and the Sharpen isn’t doing what I need. So here’s what I would like to achieve:

  1. Transfomring the image without any blurr or other effects to the sides, which need to stay sharp. Croping the picture should be avoided, if possible.

  2. Tranforming the blurred texture to a very sharped and contrasted texture, with smooth edges everywhere, so I get two colors regions only without any gradient.

How can I do this?