Bart,
Maybe I misunderstand what you are looking for. I did a downsample with artifacts eliminated.
Hi Arthur,
The ultimate goal with down-sampling is to produce an image that looks identical, but only smaller than the original. Of course the highest (e.g. single pixel micro contrast) spatial frequencies will have to be sacrificed, because we have fewer pixels, but preferably not much more than those. We would hope for a smaller image, also with detail all the way to the corners, but without aliasing artifacts. That is unfortunately impossible, therefore we try to achieve a balance, keeping as much detail with as few disturbing artifacts as possible.
In a regular square pixel grid, the diagonal resolution is potentially up to 41% higher than in the horizontal/vertical directions. If we do not want to lose that when we down-sample, we must use good filters to both maintain that resolution, and minimize artifacts at the same time.
To illustrate that, here is a so-called Fast Fourier Transform (FFT) of the original image, a transformation from the spatial domain in to a frequency domain, which will allow us a better analytical view of the spatial frequency content (low frequencies in the center, high frequencies in the corners, in a radial progression, brighter is more detail, darker is less detail):
As you can see, the original has a somewhat square region in the middle, where the lowest spatial frequencies are represented in the center at a more or less uniform amplitude (all those details are equally well resolved). Towards the edges and specifically the corners, the further away from the center of the FFT, the higher/highest spatial frequencies are shown. Beyond a certain radius they are somewhat compromised, because the details get so small that they cannot be accurately resolved. The FFT representation (actually a Log Power spectrum) is very sensitive to small deviations which are visually exaggerated for easier viewing.
So, ideally our down-sampled version should look similar, only a smaller.
Here is an ImageMagick EWA down-sampled example, and its FFT:
The FFT shows detail virtually all the way to the (highest spatial frequency) corners, with very minimal artifacting (just a bit at the horizontal/vertical edges).
For comparison, the FFT of your
http://farm8.staticflickr.com/7300/11179981655_325c1eaa9f_o.jpg looks like this:
The darker edges and corners indicate lower amplitude high spatial frequencies, less micro detail (but obviously also less risk of artifacts).
Cheers,
Bart
