Thinning by morphological operators

Since the backgrounds of our sample images are white (256 in gray-scale), we used dilation operator, which dilates the background and thins the image.
  , where b is the structuring element.
To prevent values greater than 255, which appear as the result of dilation operator above, we made a kind of normalization by multiplying each gray value by the coefficient (255/maximum gray value) if maximum gray value is greater than 255.  Here is the structuring element :

 Pivot element is the one in the center (darkest one).

Samples

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