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This is the explanation about the border average in gimp doc.All the vocabulary used is easy, but I don't understand real meaning of none of them. What is the thickness here? What is bucket size and number here?

1) The width of pixels considered along the border

2) As I understand it, the script works with the idea that a plain average wouldn't work. It tries to find an average with is a better match for some part of the edge, so it distributes the colors of the pixels in N buckets, finds which is the biggest bucket, and computes the average of that (which is why in the example picture the average is close to the color fo the sky).