Hi Everyone,

I am a Ph.D student working on some image processing tasks and I have run into an interesting problem that I thought someone on here might have an idea about. This paper discusses a method to compare two images based upon the amount they can be compressed. [edit] Sorry, since this is my first post, I can't post URLs. So search for;
ON THE CONTRIBUTION OF COMPRESSION TO VISUAL. PATTERN RECOGNITION. Gunther Heidemann

The formula is simply D_comp(I1, I2) = S(I1) + S(I2) - S(I12)

Basically, if I have two images, one.bmp (S(I1)) and two.bmp (S(I2)). If I compress each one, and also combine the two to make S(I12), and compress that, I can feed them into the formula and it tells me how similar they are. Sounds simple enough.

Then, in the description of the theory, it states that a large value for D_comp indicates that the two images are similar, and a value for zero is found when they're not similar. All good so far...(however I would have thought that if two images are identical, combining them would make D_comp closer to zero).

So I have implemented this as a quick test as follows;

Code:

cat one.bmp | gzip -c -9 > one_cat.gz
cat two.bmp | gzip -c -9 > two_cat.gz
cat one.bmp two.bmp | gzip -c -9 > bridges_cat.gz

so;

Code:

gzip -l one_cat.gz two_cat.gz bridges_cat.gz

gives me;

Code:

         compressed        uncompressed  ratio uncompressed_name
             937867             1440054  34.9% one_cat
             907797             1440054  37.0% two_cat
            1846241             2880108  35.9% bridges_cat
            3691905             5760216  35.9% (totals)

Therefore my D_comp value is 937867 + 907797 - 1846241 = -577

Note that this is a negative number, not mentioned in the paper, since I am guessing that there is an assumption that by combining two images S(I12), one would achieve a greater level of compression.

Here are the two images I have tried this on;
one.bmp = once again, I can't post the URL - brooklyn Bridge

two.bmp = once again, I can't post the URL - golden gate bridge

Since these were jpg files, I used image magik to convert them to BMP, so that they were the same byte size. Both images are 800x600 and as you can see from the gzip -l output, the uncompressed file sizes are the same.

So my question is, why would two files produce a smaller total amount of bytes when compressed, than when combined. I would have thought that the gzip algorithm would have been more efficient at compressing the joint image.

Also, when both images are the same;

Code:

cat one.bmp one.bmp | gzip -c -9 > same_cat.gz
gzip -l one_cat.gz same_cat.gz
         compressed        uncompressed  ratio uncompressed_name
             937867             1440054  34.9% one_cat
            1875794             2880108  34.9% same_cat
            2813661             4320162  34.9% (totals)

which results in a value of D_comp -60.

Appologies for the long post. Does anyone know why gzip might do this? Does it look normal? I was thinking it might be something to do with header information that it couldn't compress.

Kind regards,

Martin