how can I obtain the coordinates of the polygon border pixels

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Hello,
For example, there is an image on which I have a set of points and the vertices of the convex hull of these points. We can know the vertices coordinates easily, but how can I obtain the pixels' coordinates on the lines (border) of the convex hull. Any idea would be appreciated. I don't want to use the line equation such as y = kx+b, because we are not sure how many lines are there.
Thanks.
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Guillaume
Guillaume 2014-12-8
Considering that a line is an infinite number of points of no size and real coordinates and that a pixel has a size and integer coordinates, what criteria do you use to define that a pixel in on the border?

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