6 ms·

Probably not faster. Definitely better quality. As Alvy Ray Smith said, a pixel is not a little square, http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf http:/

• mark-r 9y ago
  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.
  • jacobolus 9y ago
    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.
    • mark-r 9y ago
      I agree completely by the way.
  • smallnamespace 9y ago
    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.
    • mark-r 9y ago
      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?
      • jacobolus 9y ago
        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.
• wtallis 9y ago
  That memo needs to die. There are better ways to make the few of its points that are still valid, without making assumptions and assertions that are frequently invalid with today's technology. Pixels are often not representative of little squares (rectangles). However, they are more likely to be representative of little rectangles now than they were in 1995, now that most photographs are captured on Bayer arrays of square sensors, most computer-generated images are rendered as an average of point samples weighted according to estimated coverage of a square pixel, and everything is displayed on LCD or OLED panels with square pixels comprised of rectangular subpixels. If you take a random JPEG or PNG off the Internet, interpreting the pixel data as point samples will usually be less accurate than interpreting them as integrated over a rectangle. Interpreting the data as integrated over a gaussian distribution is also less realistic than the rectangle interpretation. Doing image processing in a point sample or gaussian context is certainly useful, but it's definitely not more fundamentally right than the little square model. Historically, that context was at best a neutral choice that was equally unrealistic no matter what kind of hardware you were working with, but mathematically convenient. The paper's arguments about coordinate systems (whether the y-coordinate should grow toward the top of the screen or the bottom, and whether pixels should be centered on half-integer points) are also a waste of time for the modern reader.
  • jacobolus 9y ago
    The better alternatives are all like 50-page papers with worse titles and a lot of math. If you know a nice 5–10-page “modern” summary of how to treat filters for image resampling aimed at a non-specialist audience, please link away. I’ll agree that treating pixels as Gaussians is not especially great. In practice most images go through multiple layers of processing, physical sensor and display pixels come in all kinds of wacky shapes (and as you point out have channels offset by different amounts, etc.). It’s usually better to treat pixels as point samples for generic intermediate processing because you have no idea what kind of source an image comes from, and you have no idea what someone down the line is going to do with your image before sending a final signal to the display hardware. Creating synthetic images by integrating over little rectangles produces markedly inferior results to applying some real resampling filter to the samples, but gets done by computer games etc. because it’s computationally cheap, with the hope that there are enough pixels moving fast enough that someone won’t notice the artifacts.
• deleted 9y ago
  [deleted]
• a_e_k 9y ago
  I'd say usually better quality rather than definitely better quality. While the Lanczos filter is always superior to the box filter in theory, there are some case in practice where the box filter may be better. If you're downsampling a line-art image, for example, you may actually be better off with some variation of the box filter. The negative lobes on the Lanczos filter can induce objectionable ringing because line-art tends to be full of what are basically step functions. It's a similar issue as with strong mosquito artifacts on JPEG compressed line-art. A filter function that is everywhere non-negative, such as the box filter or a Gaussian can't suffer from this problem. Of the two, the box filter will give you sharper results but of course it doesn't antialias as well, either.