> As part of a vectorization engine you need to trace the outline of all pixels of the same color in a bitmap. What other choice to you have than to think of pixels as squares with four sides?

I think that’s a bad example. For vector tracing, you want the ability to trace using lines and curves at any angle, not alongside the pixel boundaries, so you want to see the image as a function from ℝ² to RGB space for which you have samples at grid positions. Target then is to find a shape that covers the part of ℝ² that satisfies a discriminator function (e.g. “red component at least 0.8, green and blue components at most 0.1) decently well, balancing the simplicity of the shape (in terms of number of control points or something like that) with the quality of the cover.