On 31/07/17, at 13:10, Sven Littkowski wrote:
> The challenge is, how to change - probably in Photoshop, the inside of
> each pie-shaped section into its average color. Is there any
> Photoshop-Plugin that can give the average color of a selected section?

Can you try Gimp?

I found this script 
<https://chiselapp.com/user/saulgoode/repository/script-fu/wiki?name=sg-mean-fill>, 
tried it, and got the attached images.

-- 
light_source{9+9*x,1}camera{orthographic look_at(1-y)/4angle 30location
9/4-z*4}light_source{-9*z,1}union{box{.9-z.1+x clipped_by{plane{2+y-4*x
0}}}box{z-y-.1z+.1}box{-.1x+.1}box{.1z-.1}pigment{rgb<.8,0,1>}}//Jellby

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Preview of image 'screenshot_20170801_103849.jpg'

Preview of image 'screenshot_20170801_104000.jpg'

Preview of image 'screenshot_20170801_104012.png'