Editing Spatial anti-aliasing (section)

==Example of an image with extreme pseudo-random aliasing==
Because [[fractals]] have unlimited detail and no noise other than arithmetic round-off error, they illustrate aliasing more clearly than do photographs or other measured data. The [[Mandelbrot set#Escape time algorithm|escape times]], which are converted to colours at the exact centres of the pixels, go to infinity at the border of the set, so colours from centres near borders are unpredictable, due to aliasing. This example has edges in about half of its pixels, so it shows much aliasing. The first image is uploaded at its original sampling rate. (Since most modern software anti-aliases, one may have to download the full-size version to see all of the aliasing.) The second image is calculated at five times the sampling rate and [[downsampling|down-sampled]] with anti-aliasing. Assuming that one would really like something like the average colour over each pixel, this one is getting closer. It is clearly more orderly than the first.

In order to properly compare these images, viewing them at full-scale is necessary.
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Image:Mandelbrot_"Turbine"_desk_shape.jpg|1. As calculated with the program "MandelZot"
Image:Mandelbrot_Turbine_big_all_samples.jpg|2. Anti-aliased by blurring and down-sampling by a factor of five
Image:Mandelbrot_Budding_turbines.jpg|3. Edge points interpolated, then anti-aliased and down-sampled
Image:Mandelbrot_Turbine_Chaff.jpg|4. An enhancement of the points removed from the previous image
Image:Mandelbrot Budding Turbines downsampled.jpg|5. Down-sampled again, without anti-aliasing
</gallery>

It happens that, in this case, there is additional information that can be used. By re-calculating with a "distance estimator" algorithm, points were identified that are very close to the edge of the set, so that unusually fine detail is aliased in from the rapidly changing escape times near the edge of the set. The colours derived from these calculated points have been identified as unusually unrepresentative of their pixels. The set changes more rapidly there, so a single point sample is less representative of the whole pixel. Those points were replaced, in the third image, by interpolating the points around them. This reduces the noisiness of the image but has the side effect of brightening the colours. So this image is not exactly the same that would be obtained with an even larger set of calculated points. To show what was discarded, the rejected points, blended into a grey background, are shown in the fourth image.

Finally, "Budding Turbines" is so regular that systematic (Moiré) aliasing can clearly be seen near the main "turbine axis" when it is downsized by taking the nearest pixel. The aliasing in the first image appears random because it comes from all levels of detail, below the pixel size. When the lower level aliasing is suppressed, to make the third image and then that is down-sampled once more, without anti-aliasing, to make the fifth image, the order on the scale of the third image appears as systematic aliasing in the fifth image.

Pure down-sampling of an image has the following effect (viewing at full-scale is recommended):

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File:Mandelbrot-spiral-original.png|1) A picture of a particular spiral feature of the [[Mandelbrot set]]
File:Mandelbrot-spiral-antialiased-4-samples.png|2) 4 samples per pixel
File:Mandelbrot-spiral-antialiased-25-samples.png|3) 25 samples per pixel
File:Mandelbrot-spiral-antialiased-400-samples.png|4) 400 samples per pixel
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