[opendtv] Re: Math of oversampling
- From: "Don Munsil" <don@xxxxxxxxxx>
- To: <opendtv@xxxxxxxxxxxxx>
- Date: Thu, 28 Apr 2005 17:25:31 -0700
From: "Jeroen Stessen" <jeroen.stessen@xxxxxxxxxxx>
> You can't judge a filter like that... You should judge the
> flatness of the passband and the deepness of the stopband,
> which can only be done in the frequency domain. Even a tiny
> variation in the time or place domain can give a huge
> difference in the stopband. A good filter should be designed
> by looking in the frequency domain in the first place. By just
> windowing some "perfect" filter in the time domain, especially
> if the window length is too short, you get inferior filters.
I disagree almost completely. I don't want to start a huge argument, but I
feel pretty strongly about this, having spent an inordinately long time
researching and implementing an image scaling engine.
Evaluating image scaling filters in the frequency domain is basically
worthless. I mean that without any hyperbole at all - the frequency response
of a digital image resizing filter does not predict in any meaningful way
how well it performs, either aesthetically or as a model of how real-world
image gathering works.
If we imagine scaling to be a physical simulation of swapping one image
sensor for another image sensor with more or fewer pixels, it's clear that
any interpolation or resampling operation is not in any way modeling this.
Fundamental to any resampling mathematics is the treatment of a pixel as a
point sample, and pixels are clearly not point samples. (There are a few
researchers who have looked at iterative methods of constructing models of
likely distributions of photons across pixel sites, and then "repacking"
them into new rectangles representing the new virtual CCD sensors, but such
methods are (so far) computationally expensive and don't necessarily produce
any more pleasing results than traditional interpolation methods.)
That's not to say that interpolation and resampling strategies are worthless
for scaling; they work quite well. It's just that we shouldn't imagine that
they represent some kind of "correct" interpretation of image scaling.
Moreover, the filters with the very best frequency response are absolutely
terrible for scaling, and the better the frequency response the worse the
performance. One of the primary artifacts of very long filters is excessive
ringing, and the longer the filter the further the ringing extends from an
edge. This ringing is not a real-world image phenomenon. You don't start to
see little halos around objects as you move closer to them or further away.
The primary reason frequency response is irrelevant to digital scaling is
because we do not evaluate images in frequency space. The eye measures light
amplitude directly at randomly scattered sites on the retina. There is no
direct measurement of "spacial frequency". This is in contrast to the ear,
which is a physical frequency analyzer. Thus for audio, frequency response
of resampling filters is essential, and measuring the frequency response
tells you how well the filter will perform. For images this is just not
true.
There is a pervasive assumption in image processing (implicit in many of the
standard texts) that image resampling is essentially identical to audio
resampling, just in two dimensions instead of one. It's not.
In practice, a good video scaling filter will have a relatively
decent-looking frequency response, but that's a side effect, not a goal.
Improving the frequency response will more than likely reduce the final
image quality, not improve it.
Best,
Don
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