How to make a smooth highly contrasted image from a Blur, 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:

Currently, the Blur 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. Transforming the image without any blur or other effects to the sides, which need to stay sharp. Cropping the picture should be avoided, if possible.

2. Transforming the blurred texture to a very sharpened and contrasting texture, with smooth edges everywhere, so I get two color regions only without any gradient.

How can I do this?

Colorize[Binarize[
  Blur[ListDensityPlot[randomTiles, ColorFunction -> "IslandColors", 
    InterpolationOrder -> 0, Frame -> False, PlotRangePadding -> 0, 
    ImageSize -> {500, 500}], 10], .6 ], 
    ColorRules -> {0 -> Orange, 1 -> Green}]