What transformations to make black text on a white background from this picture without filling?

Question

GIMP

Picture

That is, you need to remove the color and lightening so that the text inside is absolutely black, and the background around it is absolutely white (or transparent).
But you need to leave a smooth transition where the border of the text and background is. Without this transition, as it were, everything is obvious. But how to save this transition? If you hard colorize and then blur, then the letters "e" will turn out to be slightly different sizes.
Is there any universal way without taking into account the shape of the image and the distribution of colors on the background?

Answer 1

If fast, then draw the same gradient. "Subtract" it from the original image.
After leveling the background, do binarization.