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Multidimensional Compression
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| Blake Shaw 2004-05-12, 9:28 pm |
| A black and white image can be seen as 2-dimensional data:
width x height
A grayscale image can be seen as 3-dimensional data:
width x height x color depth
A full color image can be seen as 4:
width x height x color depth x color channel
....and finally, video can be seen as 5:
width x height x color depth x color channel x time
I've just started looking into compression in the last couple of days,
but I was wondering if current compression algorithms take into account
the multidimensional redundancy that is present in a lot of data. Think
about it: a pixel's color depth in a video is going to be related not
only to the other pixels around it, but also the ones before and
after... and even the data from these other color channels.
Do current algorithms do a multidimensional analysis to find redundant
data? Is this even necessary or do general compression algorithms
already find the "chunks" of redundant data just fine?
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| Matt Mahoney 2004-05-12, 9:28 pm |
| "Blake Shaw" <mmxmm@mm.st> wrote in message
news:dN6dnawkwux-pwjdRVn-jw@comcast.com...
> A black and white image can be seen as 2-dimensional data:
> width x height
> A grayscale image can be seen as 3-dimensional data:
> width x height x color depth
> A full color image can be seen as 4:
> width x height x color depth x color channel
> ...and finally, video can be seen as 5:
> width x height x color depth x color channel x time
>
> I've just started looking into compression in the last couple of days,
> but I was wondering if current compression algorithms take into account
> the multidimensional redundancy that is present in a lot of data. Think
> about it: a pixel's color depth in a video is going to be related not
> only to the other pixels around it, but also the ones before and
> after... and even the data from these other color channels.
>
> Do current algorithms do a multidimensional analysis to find redundant
> data? Is this even necessary or do general compression algorithms
> already find the "chunks" of redundant data just fine?
Most good image compression algorithms already do this, although it may not
be explicit. For example, a DCT in JPEG exploits redundancy both
horizontally and vertically to produce coefficients that are mostly near 0
except near the DC term.
-- Matt Mahoney
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| Thomas Richter 2004-05-12, 9:28 pm |
| Hi,
> I've just started looking into compression in the last couple of days,
> but I was wondering if current compression algorithms take into account
> the multidimensional redundancy that is present in a lot of data. Think
> about it: a pixel's color depth in a video is going to be related not
> only to the other pixels around it, but also the ones before and
> after... and even the data from these other color channels.
> Do current algorithms do a multidimensional analysis to find redundant
> data? Is this even necessary or do general compression algorithms
> already find the "chunks" of redundant data just fine?
Yes, of course they do, just that the "decorrelation steps" for each
"dimension" have traditionally different names: For spatial decorrelation,
DCT or DWT are used. For correlation across color planes color
transformations (e.g. RGB->YCbCr) are used, for correlation in time
motion prediction and motion estimation are used. There are of course
new ideas for some decorrelation steps, e.g. to use wavelets in time
domain or image segmentation in space domain. A more general setup would
be that of "vector quantization" in the space domain that quantizes several
coefficients at once, etc, etc....
Thus, in general, a lot of "multidimensionality" is done, though the
steps highly depend on the dimension you want to decorrelate.
So long,
Thomas
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