{"id":1753,"date":"2016-04-14T14:14:52","date_gmt":"2016-04-14T18:14:52","guid":{"rendered":"https:\/\/blogs.mathworks.com\/steve\/?p=1753"},"modified":"2019-11-01T16:37:24","modified_gmt":"2019-11-01T20:37:24","slug":"jpeg2000-and-specifying-a-target-compression-ratio","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/steve\/2016\/04\/14\/jpeg2000-and-specifying-a-target-compression-ratio\/","title":{"rendered":"JPEG2000 and specifying a target compression ratio"},"content":{"rendered":"

I was looking at some documentation yesterday and saw something that I had forgotten. When you write a JPEG2000 image file using imwrite<\/tt><\/a>, you can specify a desired compression ratio.<\/p>

OK, that sounds fun. Let's try it with the peppers image.<\/p>

rgb = imread('peppers.png'<\/span>);\r\nimshow(rgb)\r\ntitle('Original image'<\/span>)\r\n<\/pre>\"\" 
Shall we start with a modest compression ratio of 10?<\/p>
imwrite(rgb,'peppers_10.j2k'<\/span>,'CompressionRatio'<\/span>,10);\r\nimshow('peppers_10.j2k'<\/span>)\r\ntitle('Target compression ratio: 10'<\/span>)\r\n<\/pre>\"\" 
That looks the same.<\/p>
Hold on, though. Let's make sure we agree on what compression ratio means. And while we're at it, let's check the output file to verify the actual ratio.<\/p>
The in-memory storage format for this image is 3 color values for each pixel, and each color value is stored using 1 byte. So the total number of in-memory bytes to represent the image is the number of rows times the number of columns times 3.<\/p>
size(rgb)\r\n<\/pre>
\r\nans =\r\n\r\n   384   512     3\r\n\r\n<\/pre>
num_mem_bytes = prod(ans)\r\n<\/pre>
\r\nnum_mem_bytes =\r\n\r\n      589824\r\n\r\n<\/pre>
Now let's figure out the size of the JPEG2000 file we just created.<\/p>
s = dir('peppers_10.j2k'<\/span>);\r\nnum_file_bytes = s.bytes\r\n<\/pre>
\r\nnum_file_bytes =\r\n\r\n       58384\r\n\r\n<\/pre>
The compression ratio is the ratio of those two numbers.<\/p>
r = num_mem_bytes \/ num_file_bytes\r\n<\/pre>
\r\nr =\r\n\r\n   10.1025\r\n\r\n<\/pre>
That's pretty close to the specified target.<\/p>
Let's compress the image by a factor of 20.<\/p>
imwrite(rgb,'peppers_20.j2k'<\/span>,'CompressionRatio'<\/span>,20)\r\nimshow('peppers_20.j2k'<\/span>)\r\ntitle('Target compression ratio: 20'<\/span>)\r\n<\/pre>\"\" 
I'm still seeing very little difference. Let's dial it all the way up to 100.<\/p>
imwrite(rgb,'peppers_100.j2k'<\/span>,'CompressionRatio'<\/span>,100)\r\nimshow('peppers_100.j2k'<\/span>)\r\ntitle('Target compression ratio: 100'<\/span>)\r\n<\/pre>\"\" 
Now that's getting pretty bad. Let's zoom into a region and compare more closely.<\/p>
subplot(1,2,1)\r\nimshow(rgb)\r\nxlim([310 440])\r\nylim([30 130])\r\ntitle('Original'<\/span>)\r\n\r\nsubplot(1,2,2)\r\nimshow('peppers_100.j2k'<\/span>)\r\nxlim([310 440])\r\nylim([30 130])\r\ntitle('Target compression ratio: 100'<\/span>)\r\n<\/pre>\"\" 
How extreme can we get? Let's try 1000.<\/p>
imwrite(rgb,'peppers_1000.j2k'<\/span>,'CompressionRatio'<\/span>,1000)\r\nclf\r\nimshow('peppers_1000.j2k'<\/span>)\r\ntitle('Target compression ratio: 1000'<\/span>)\r\n<\/pre>\"\" 
That's pretty ugly. But how big is the file? Did we get close to the target?<\/p>
s = dir('peppers_1000.j2k'<\/span>);\r\ns.bytes\r\n<\/pre>
\r\nans =\r\n\r\n   545\r\n\r\n<\/pre>
num_mem_bytes \/ s.bytes\r\n<\/pre>
\r\nans =\r\n\r\n   1.0822e+03\r\n\r\n<\/pre>
That last image is stored using just 545 bytes! That's a compression ratio of about 1082.<\/p>
I know JPEG2000 is used in some medical imaging systems, and I have also heard that the Library of Congress uses it.<\/p>
Do you use JPEG2000? If so, please leave a comment. I'd be interested to hear about your application.<\/p>