I'm not certain what you're trying to say. When you talk about "the function," I'm assuming you're referring to the nearest unused colour function, which, while it is a one-to-one mapping is also a) a function from colour 3space to colour 3space (input is a targeted RGB point, output is a valid, unused RGB point) and b) it is also dependent on the state of the colour space i.e. the function is of the form (r0, g0, b0, colourspace) -> (r, g, b) + the colour space is modified to indicate that (r, g, b) has been used.

All of the dealings with the X, Y space (the image) are separate from the colour searching algorithm. There is a function to approximate the target colour of an unfilled pixel in X, Y by averaging the values of its neighbours, but that value is then used as input to the above-described search function.

I could simply be misunderstanding what you're trying to say.