[opendtv] Re: 20060117 Mark's (Almost) Monday Memo
- From: Tom Barry <trbarry@xxxxxxxxxxx>
- To: opendtv@xxxxxxxxxxxxx
- Date: Sat, 21 Jan 2006 13:24:10 -0500
Craig Birkmaier wrote:
> This should make it obvious that we are nowhere close to theoretical
> limits on compression efficiency. If you were to look at this as a
> typical logarithmic function we are still in the "learning curve" -
> the flat part where there are still large opportunities to improve.
> As we approach the inflection point, the gains in efficiency will
> grow smaller and smaller, but it is unlikely that we will every reach
> any theoretical limits that may exist.
I agree with all the above. But, that said, I think MPEG-2 may already
be approaching a limit on what can be done if we only recognize the
movement of unchanged fixed size square blocks. I think various forms
of object based compression will allow us to recognize and thus predict
the existence and complex behavior of much more sophisticated objects.
After all, humans can do it. Imagine a basketball scene where you are
looking at the back of a players head as he rotates toward you. You
would predict shortly being able to perceive his eyes and other facial
features. But information is really a measure of how much you are about
to be surprised by something. It takes very few bits just to confirm
something you already considered very probable.
Real time video compression will also be able to do this someday, based
upon a better model of visual reality and a recognition of real world
objects.
In the mean time maybe we can at least develop some better motion
compensation methods that recognize something other than moving squares.
AVC even takes some small steps in that direction.
- Tom
> At 3:01 PM -0500 1/20/06, Manfredi, Albert E wrote:
>
>>Except that I *think* what John really wondered is whether
>>there is a Shannon's Law equivalent for codecs. That is, a
>>theoretical limit to how much a given image (or audio
>>stream) can be compressed. This is independent of Moore's
>>Law, other than the presumed requirement of more computing
>>power needed as compresssion increases.
>
>
> Is there a Shannon's Law that tells us how much information a frame
> of any given size can contain?
>
> Perhaps.
>
> Shannon can help us predict the highest frequency that can be
> represented (without aliasing) for any given raster size. So in
> theory we could create some diabolical image that totally saturates
> the spectra that can be represented in a single frame.
>
> But this is just for one frame. Shannon tells us noting about the
> next frame, except that it can contain no more information than the
> previous "diabolical" frame. But the next frame can be equally
> challenging, but totally different. From a compression perspective
> this is truly diabolical - that is there is no relationship from one
> frame to the next, thus very little opportunity to take advantage of
> interframe entropy coding.
>
> A good example of this, that is sometimes used to test compression
> algorithms, is NOISE.
>
> Good luck trying to compress this, as it has virtually 100% entropy.
>
> Entropy coding takes advantage of the reality that there is
> "typically" a strong correlation between adjacent picture elements in
> a frame, and a strong correlation between the information in adjacent
> frames. The degree to which this can be used to compress the
> information is influenced by entropy (noise and sampling errors) and
> the correlation between areas of a frame and the information in a
> series of frames (e.g. a GOP).
>
> In other words, there is no correct answer to Bert's question. Any
> limits will change dynamically based on the ability of the
> compression algorithm to deal with specific types of image pathology.
> MPEG-2 falls apart when we do something as simple as dissolving
> between two different images, or an image and black; entropy goes
> through the roof and the encoder cannot compress these frames
> efficiently. MPEG-2 also falls apart on simple gradients; create a
> gradient from corner to corner of a frame and the DCT is useless. If
> you throw away even a single DCT coefficient in a block you will see
> quantization errors.
>
> As Tom alludes to, any theoretical limit on encoding efficiency must
> take into account the image pathology. I mentioned just a few of the
> more difficult problems in my original response to John's question.
> To achieve the theoretical limit of compression efficiency we must be
> able to predict anything that can possibly be represented within a
> frame, and in groups of frames.
>
> For practical reasons, like live TV, we must be able to do this in
> real time (understanding that non-real time encoding may be able to
> do a better job).
>
> This should make it obvious that we are nowhere close to theoretical
> limits on compression efficiency. If you were to look at this as a
> typical logarithmic function we are still in the "learning curve" -
> the flat part where there are still large opportunities to improve.
> As we approach the inflection point, the gains in efficiency will
> grow smaller and smaller, but it is unlikely that we will every reach
> any theoretical limits that may exist.
>
> Regards
> Craig
>
>
>
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