Color interpolation/smoothing in discrete-colored height map

Question

I am currently trying to smooth a height-map of a 2D world. I have multiple images of different 2D worlds, so it's something I'm not going to do manually but rather create a script.

Sample of a heightmap:

As you can see, colors do not blend. I'm looking to blend every space to the color of their neighbours so the slope of the height map is smooth.

What have I tried?

• Applying a blur filter, but it's not enough and gives bad quality results.

• Applying small noise filters but it's not even close to what I need.

So far...

Here is what happens if I apply the height-map as it is without interpolating the color with it's neighbours.

The result is flat surfaces, instead of slopes/mountain. Hope to make my goal clear.

I believe that interpolating the heights with their neighbours and adding random noise on the surfaces will result in a good quality height-map.

I appreciate your help.

Bonus

Do you have any idea how would I create a simulated normal map from the result of this smooth height-map?

Answer 1

You could try resizing your image down and then back up again to take advantage of interpolation, e.g. for 5% of original size:

magick U0kEbl.png.jpeg -set option:geom "%G" -resize "5%" -resize '%[geom]!' result.png

Here are results for 3%, 5% and 8% of original size: