how to prove that?

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how to prove that?
5 answers - 470 bytes -
suppose there is an 256x256 gray image, and it's entropy is H0
bits(This means, this image can be compressed to H0 bit without
distoration), if copy this image 3 times and put them together to form
a larger image with size 512x512, how to caculate the entropy of this
512x512 image? does it equal to H0?
here the entropy can also be treated as Kolmogorov-Complexcity. it
stands for the limitation of the image can be compressed.
No.1 | | 690 bytes | |

"xiaoxiao" <xiaoweihuacom@hotmail.comwrote in message
news:1155345084.681028.225550@
suppose there is an 256x256 gray image, and it's entropy is H0
bits(This means, this image can be compressed to H0 bit without
distoration), if copy this image 3 times and put them together to form
a larger image with size 512x512, how to caculate the entropy of this
512x512 image? does it equal to H0?
here the entropy can also be treated as Kolmogorov-Complexcity. it
stands for the limitation of the image can be compressed.

it should be the same, however, the actual compressed size may be at least a
little larger due to minor reasons
No.2 | | 801 bytes | |
cr88192 wrote:
"xiaoxiao" <xiaoweihuacom@hotmail.comwrote in message
news:1155345084.681028.225550@
suppose there is an 256x256 gray image, and it's entropy is H0
bits(This means, this image can be compressed to H0 bit without
distoration), if copy this image 3 times and put them together to form
a larger image with size 512x512, how to caculate the entropy of this
512x512 image? does it equal to H0?
here the entropy can also be treated as Kolmogorov-Complexcity. it
stands for the limitation of the image can be compressed.
--
it should be the same, however, the actual compressed size may be at least a
little larger due to minor reasons

by the size of the little program that makes 3 copies of your image.
-- Matt Mahoney
No.3 | | 1179 bytes | |
Matt Mahoney wrote:

cr88192 wrote:
>"xiaoxiao" <xiaoweihuacom@hotmail.comwrote in message
>news:1155345084.681028.225550@
>suppose there is an 256x256 gray image, and it's entropy is H0
>bits(This means, this image can be compressed to H0 bit without
>distoration), if copy this image 3 times and put them together to form
>a larger image with size 512x512, how to caculate the entropy of this
>512x512 image? does it equal to H0?
>here the entropy can also be treated as Kolmogorov-Complexcity. it
>stands for the limitation of the image can be compressed.
>>
>>
>it should be the same, however, the actual compressed size may be at
>least a little larger due to minor reasons
>
by the size of the little program that makes 3 copies of your image.

-- Matt Mahoney

Which would be then Kolmogorov-Complexity I think. If all the images
considered are generated by source that copies the image in the described
way then the entropy should equal to that of the source outputting the
original images.
No.4 | | 713 bytes | |
xiaoxiao wrote:
) suppose there is an 256x256 gray image, and it's entropy is H0
) bits(This means, this image can be compressed to H0 bit without
) distoration), if copy this image 3 times and put them together to form
) a larger image with size 512x512, how to caculate the entropy of this
) 512x512 image? does it equal to H0?
) here the entropy can also be treated as Kolmogorov-Complexcity. it
) stands for the limitation of the image can be compressed.

Entropy is not an absolute measure, it depends on the model that is
being used. Typically, it should not be much larger than H0, but
there are plenty of models for which it could be a lot larger.

SaSW, Willem
No.5 | | 736 bytes | |

Willem wrote:
xiaoxiao wrote:
) suppose there is an 256x256 gray image, and it's entropy is H0
) bits(This means, this image can be compressed to H0 bit without
) distoration), if copy this image 3 times and put them together to form
) a larger image with size 512x512, how to caculate the entropy of this
) 512x512 image? does it equal to H0?
) here the entropy can also be treated as Kolmogorov-Complexcity. it
) stands for the limitation of the image can be compressed.

Entropy is not an absolute measure, it depends on the model that is
being used. Typically, it should not be much larger than H0, but
there are plenty of models for which it could be a lot larger.
--
SaSW, Willem

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