How does a predictive coding aid in lossless compression?
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I'm working on this lab where we need to apply a lossless predictive coding to an image before compressing it (with Huffman, or some other lossless compression algorithm).
From the example seen below, it's pretty clear that by pre-processing the image with predictive coding, we've modified its histogram and concentrated all of its grey levels around 0. But why exactly does this aid compression?
Is there maybe a formula to determine the compression rate of Huffman, knowing the standard deviation and entropy of the original image? Otherwise, why would the compression ratio be any different; it's not like the range of values has changed between the original image and pre-processed image.
Thank you in advance,
Liam.
image-processing data-compression huffman-coding
asked Apr 3 at 20:40
Liam F-ALiam F-A
261
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add a comment |
$begingroup$
I'm working on this lab where we need to apply a lossless predictive coding to an image before compressing it (with Huffman, or some other lossless compression algorithm).
From the example seen below, it's pretty clear that by pre-processing the image with predictive coding, we've modified its histogram and concentrated all of its grey levels around 0. But why exactly does this aid compression?
Is there maybe a formula to determine the compression rate of Huffman, knowing the standard deviation and entropy of the original image? Otherwise, why would the compression ratio be any different; it's not like the range of values has changed between the original image and pre-processed image.
Thank you in advance,
Liam.
image-processing data-compression huffman-coding
asked Apr 3 at 20:40
Liam F-ALiam F-A
261
$endgroup$
add a comment |
$begingroup$
I'm working on this lab where we need to apply a lossless predictive coding to an image before compressing it (with Huffman, or some other lossless compression algorithm).
From the example seen below, it's pretty clear that by pre-processing the image with predictive coding, we've modified its histogram and concentrated all of its grey levels around 0. But why exactly does this aid compression?
Is there maybe a formula to determine the compression rate of Huffman, knowing the standard deviation and entropy of the original image? Otherwise, why would the compression ratio be any different; it's not like the range of values has changed between the original image and pre-processed image.
Thank you in advance,
Liam.
image-processing data-compression huffman-coding
asked Apr 3 at 20:40
Liam F-ALiam F-A
261
$endgroup$
I'm working on this lab where we need to apply a lossless predictive coding to an image before compressing it (with Huffman, or some other lossless compression algorithm).
From the example seen below, it's pretty clear that by pre-processing the image with predictive coding, we've modified its histogram and concentrated all of its grey levels around 0. But why exactly does this aid compression?
Is there maybe a formula to determine the compression rate of Huffman, knowing the standard deviation and entropy of the original image? Otherwise, why would the compression ratio be any different; it's not like the range of values has changed between the original image and pre-processed image.
Thank you in advance,
Liam.
image-processing data-compression huffman-coding
image-processing data-compression huffman-coding
asked Apr 3 at 20:40
Liam F-ALiam F-A
261
asked Apr 3 at 20:40
Liam F-ALiam F-A
261
asked Apr 3 at 20:40
Liam F-ALiam F-A
261
asked Apr 3 at 20:40
Liam F-ALiam F-A
261
asked Apr 3 at 20:40
Liam F-ALiam F-A
261
261
add a comment |
add a comment |
1 Answer
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Huffman coding, as usually applied, only considers the distribution of singletons. If $X$ is the distribution of a random singleton, then Huffman coding uses between $H(X)$ and $H(X)+1$ bits per singleton, where $H(cdot)$ is the (log 2) entropy function.
In contrast, predictive coding can take into account correlations across data points. As a simple example, consider the following sequence:
$$
0,1,2,ldots,255,0,1,2,ldots,255,ldots
$$
Huffman coding would use 8 bits per unit of data, whereas with predictive coding we could get potentially to $O(log n)$ bits for the entire sequence.
answered Apr 3 at 20:58
Yuval FilmusYuval Filmus
196k15184349
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$begingroup$
Huffman coding, as usually applied, only considers the distribution of singletons. If $X$ is the distribution of a random singleton, then Huffman coding uses between $H(X)$ and $H(X)+1$ bits per singleton, where $H(cdot)$ is the (log 2) entropy function.
In contrast, predictive coding can take into account correlations across data points. As a simple example, consider the following sequence:
$$
0,1,2,ldots,255,0,1,2,ldots,255,ldots
$$
Huffman coding would use 8 bits per unit of data, whereas with predictive coding we could get potentially to $O(log n)$ bits for the entire sequence.
answered Apr 3 at 20:58
Yuval FilmusYuval Filmus
196k15184349
$endgroup$
add a comment |
$begingroup$
Huffman coding, as usually applied, only considers the distribution of singletons. If $X$ is the distribution of a random singleton, then Huffman coding uses between $H(X)$ and $H(X)+1$ bits per singleton, where $H(cdot)$ is the (log 2) entropy function.
In contrast, predictive coding can take into account correlations across data points. As a simple example, consider the following sequence:
$$
0,1,2,ldots,255,0,1,2,ldots,255,ldots
$$
Huffman coding would use 8 bits per unit of data, whereas with predictive coding we could get potentially to $O(log n)$ bits for the entire sequence.
answered Apr 3 at 20:58
Yuval FilmusYuval Filmus
196k15184349
$endgroup$
add a comment |
$begingroup$
Huffman coding, as usually applied, only considers the distribution of singletons. If $X$ is the distribution of a random singleton, then Huffman coding uses between $H(X)$ and $H(X)+1$ bits per singleton, where $H(cdot)$ is the (log 2) entropy function.
In contrast, predictive coding can take into account correlations across data points. As a simple example, consider the following sequence:
$$
0,1,2,ldots,255,0,1,2,ldots,255,ldots
$$
Huffman coding would use 8 bits per unit of data, whereas with predictive coding we could get potentially to $O(log n)$ bits for the entire sequence.
answered Apr 3 at 20:58
Yuval FilmusYuval Filmus
196k15184349
$endgroup$
Huffman coding, as usually applied, only considers the distribution of singletons. If $X$ is the distribution of a random singleton, then Huffman coding uses between $H(X)$ and $H(X)+1$ bits per singleton, where $H(cdot)$ is the (log 2) entropy function.
In contrast, predictive coding can take into account correlations across data points. As a simple example, consider the following sequence:
$$
0,1,2,ldots,255,0,1,2,ldots,255,ldots
$$
Huffman coding would use 8 bits per unit of data, whereas with predictive coding we could get potentially to $O(log n)$ bits for the entire sequence.
answered Apr 3 at 20:58
Yuval FilmusYuval Filmus
196k15184349
answered Apr 3 at 20:58
Yuval FilmusYuval Filmus
196k15184349
answered Apr 3 at 20:58
Yuval FilmusYuval Filmus
196k15184349
answered Apr 3 at 20:58
Yuval FilmusYuval Filmus
196k15184349
196k15184349
add a comment |
add a comment |
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