Despite what the writeup says, you don't need to view pixels as little squares to make sense of this algorithm. It's a filter just like any other. You can evaluate its quality by examining its frequency response.
The 2D frequency response is poor because treating pixels as 'little squares' essentially substitutes Manhattan distance for Euclidean distance between pixel positions.
You have reasonable behavior along the orthogonal dimensions, but you're introducing a sqrt(2) stretch factor along diagonals.
I think you're missing my point. Although the "little squares" are used as a justification for the algorithm, the application of it is not dependent on that view. You're doing a convolution of points against a filter formula, just as you would with bicubic or Lanczos.
The stretch factor along diagonals will be the same for any separable filter will it not?
Yes, any separable filter causes grid artifacts that can be partially ameliorated by using a radial filter.
My own pipe-dream is that we would use a triangular grid (if you like, the Voronoi cells here are hexagonal pixels) for intermediate image representations. This is more spatially efficient and has nicer 2-dimensionnal frequency response than a square grid, and displays are so heterogeneous nowadays that we need to do some amount of resampling for output pretty much all the time anyway, and our GPUs are getting fast enough that resampling at high quality from a hexagon grid to a square grid for output should add only relatively cheap overhead.
Okay, sure. Go ahead and make a white paper about your analysis of the frequency response of this method for some particular scale of resizing (it ends up somewhere between a box filter and a bilinear filter), and you’ll see that it ends up doing a significantly worse job than the Lanczos filter. You’ll get less detail resolved and more aliasing artifacts.
