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Rosenfeld Digitization

Notes:

It is not necessary to explain for this public what it means to digitize a subset of R^2. I would only like to recall Rosenfeld’s idea. To digitize a subset of R^2, we do the following:

first we put one-by-one crosses in all the grid points.
** Here is an example of such a cross in the origin.
** These two points belong to the cross, these two do not.
A grid point belongs to the digitization of an object if the object and the the grid point’s cross have some points in common, so
** their intersection is not empty.
** We can think of such a square as a PIXEL, it gives a good picture of what digitization of an object means.

I will talk about a slight modification of this idea and I will call it “R’-digitization”. The modification is moving the crosses half a unit downwards. It is only a small technical detail, but it makes the calculations and formulations easier.

It is only important to remember that the R’-digitization of a straight line y=ax always includes the pixel(1,1). In the digitization of positive half lines it is the first pixel of the digitization.