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SizeFixer Super-resolution and the MTF

The original image shown in Figure 1 above was taken with a 22M pixel Imacon 528c digital back (photo used with permission). Roll over with your mouse to see the "MTF" - the log Fourier spectrum of the horizontal image line through the centre of the photograph. The "DC" value is in the centre of the graph which shows the classic near-linear fall off of an in-focus lens as we go to higher spatial frequencies. We also see a sudden cut-off at the Nyquist frequency (I have shown the scale going to higher spatial frequencies to allow easy comparison with later results. The aim now is to compare what happens to this MTF when we use Photoshop Bicubic (Smoother) and SizeFixer super-resolution to upsize this photograph by 200% (quadrupling the number of pixels to 88 Mpixels). All log spectrum plots in what follows are from the same horizontal image line through the centre of the image. Each image has been treated in exactly the same way (Blackman windowing, FFT, rotated to centre and with spectrum as Log[1+Abs[ F(u) ]] ).

Figure 2 shows the original MTF and the MTF of the 200% upsized result using the method of Photoshop bicubic smoother (I have marked the original Nyquist frequency as pulses either side of the main peak). The two major differences are the upsized MTF moves upwards a little and the spectrum extends out to the new Nyquist frequency consistent with the 200% increase in size of the image line. The spectrum moving upwards is just a scaling effect that could be normalised out but it shows that the total count in the image line increases (we have twice as many pixels with the same average value as the original). The second difference is more interesting. The MTF form has changed only by extending out to the limit imposed by the new sampling. The central MTF triangle remains where it was, but is now supperimposed on a noise pedestal that extends out to higher frequencies. There is no signal between the original Nyquist frequency and the new Nyquist frequency - just noise.

Figure 3. Photoshop MTF and SizeFixer MTF.

Figure 3 shows the Photoshop bicubic smoother MTF and the SizeFixer super-resolution MTF for 200% upsizing. Both have the classic MTF shape of a near in-focus lens, a triangle superimposed on a noise pedestal. What is immediately apparent is that for SizeFixer the "base of the triangle" is broader, clearly extending beyond the original Nyquist frequency (again marked with pulses either side of the central "DC" spike).

There is in fact more information in the SizeFixer result than the original image. Where does this extra information come? To use the super-resolution in SizeFixer we have to have a reasonably good model of the camera MTF. All real cameras have an MTF and for a good camera and lens system this is dominated by the physics of the system and not its design/manufacturing imperfections. The non-linear (but formally very correct) processing in SizeFixer uses the camera MTF to upsize a photograph. The result, as we have seen, is that the frequency content of the result is extended beyond the original Nyquist frequency.

Starting from either a Photoshop or SizeFixer result we can apply further processing. Typically this is sharpening with USM (unsharp masking). The effect of this sharpening is to increase the contrast of high frequencies and, of course, to amplify the noise at the higher frequencies where there is little image information. There is a trade-off between how much sharpening you can apply before the noise amplification becomes apparent. Without super-resolution there is no information above the original Nyquist frequency just noise, all you can do with USM is to amplify this noise. With super-resolution there is information above the original Nyquist frequency that can be exploited by further enhancement of the image. One thing is certain, no amount of sharpening with USM will make the Photoshop bicubic result look like a SizeFixer result.

Find out more about SizeFixer here.