Jpeg Project Description

This is the description of my program - how to use it and how it works. Keep in mind that it works on both color and grayscale bitmaps. To use it, you need to install the numpy and Pillow libraries, and you need to run it on Python 3.6.

How to use

The program, jpeg_compressor.py, is a python program that runs with command line arguments. If you don’t want to deal with command line arguments, you can just pass the --interactive argument to have the program prompt you. You can run jpeg_compressor.py -h for all the arguments. The most important one is --action {compress,decompress,both}

If your action is "compress" or “both,” you need to have these options:

  --originalfile ORIGINALFILE

                        Filename for compressed file(either for storing the

                        compressed file or reading it.

  --compressedfile COMPRESSEDFILE

                        Filename for compressed file(either for storing the

                        compressed file or reading it.

  --blocksize BLOCKSIZE

                        Block size for image (for compression)

  --qualityfactor QUALITYFACTOR

                        Quality Factor (generally 30,40, 50)

  --compressionmethod {gzip,zlib,bzip,xz}

                        Compression Method

If your action is decompress, you only need to supply the "compressedfile" and “compressionmethod” arguments. For all actions, you can also supply this argument.

--verbose Prints Messages

If you want the program to annotate what it’s doing, plus tell you the compression ratios. For example:

python jpeg_compressor.py --action both --verbose --originalfile Kodak12gray.bmp --compressedfile file.gz --blocksize 8 --qualityfactor 50 --compressionmethod gzip

This command will first compress "Kodak12gray.bmp" into file.gz, with a blocksize of 8, quality factor of 50, and compress with gzip. It will then uncompress file.gz with gzip, and display the image. Because --verbose is turned on, the program will also print out what it’s doing.

An example of a decompress call to the above image:

python jpeg_compressor.py --action decompress --verbose --compressedfile file.gz --compressionmethod gzip

Notice how for the decompression, you just have to specify the filename and the compression method, since information like the block size is encoded in the image.

How the Program Works:

The code is fairly heavily commented, so I will just give a brief overview of how my program works. The main data structures used are the numpy matrices, and the PIL image format, which is used for reading and writing images.

To compress, the program first reads in the image as a numpy matrix, and then decides whether to send it to the color compressor or the grayscale compressor. These are the steps the compressor takes:

1. Read the image as a matrix

2. Crop the image to the block size

3. Level the matrix by subtracting 128

4. On each block of the matrix:

   1. Perform the DCT (generate DCT matrix, do dct_matrix * block * transform_dct_matrix)

   2. Quantize it (using the quantization matrix from the standard, modified with the quality factor).

   3. Get all of the items in the zig-zag order and add them to a list

   4. Add the DC component to a list of DC component

5. Add the DC components in front of the zig_zag list

6. Encode the height and width of the image into two bytes, using the formula:

high_byte = n/(block_size * 255)
low_byte = (n%(block_size * 255))/block_size

7. Add the width, height,quality factor, and block size to the zig zag list, so that it is encoded into the image (so the user doesn’t have to know these things).

8. Add a certain number m to each item in the list, so all of the bytes are above 0. Then, add m.

9. Compress the list of bytes using the lossless compression given by the user (gzip, bzip, zlib).

10. Save the compressed version as a file, and report statistics.

If the image is color, steps 2-4 are done on all 3 channels, and added to one long list of zags.

To view the compressed image:

1. Uncompress the file using the compression method given by the user.

2. Get the m, and subtract it from each item.

3. Get all of the relevant metadata (blocksize, quality factor, height, width), and use the height and width to find out if the image is color or b&w

4. Separate the DC components from the AC components

5. Create a new matrix that is height x width (if it is color, make height x width x 3)

6. For each section of the list that is block_size^2:

   1. Restore the original shape (undoing the zig-zag algorithm and adding the DC component for that block)

   2. Multiply by the quantization matrix

   3. Undo the DCT (dctmatrix transform * m * dctmatrix)

   4. Add it to the appropriate part of the new matrix

7. Re-level the matrix by adding 128

8. Display the image as a matrix

   1. If the image is a color image, it needs to be saturated (anything less than 0 = 0, anything greater than 255 = 255), and then turn it into an uint8 matrix

9. Display statistics (how long it took).

Note that for step 6, if the image is color, it will fill the blocks into all 3 channels.

One of the benefits of my style with lots of functions is that it is very easy to plug and change certain parts. For example, to add a new lossless compression, you just have to define the compress/uncompress functions, add it to the dictionary of compression methods, and add it as a command line argument. I added xz at the last minute due to a friend’s advice.

Some things I wish I did better:

• Be able to encode the DC differences as opposed to just the DC coefficients - when I did it, I just got a max-min greater than 256, so I couldn’t encode it as a byte.

• Avoid having to add that ‘m’ and subtract it later.

• Somehow encode the compression technique so that the user does not have to enter it. The problem with this is that the bytes become compressed, so I wouldn’t know what to decompress it with to get the data.

Example run:

>python jpeg_compressor.py --action both --verbose --originalfile Kodak12.bmp --compressedfile file.gz --blocksize 8 --qualityfactor 50 --compressionmethod gzip

Starting program with these arguments:

Namespace(action='both', blocksize=8, compressedfile='file.gz', compressionmethod='gzip', interactive=False, originalfile='Kodak12.bmp', qualityfactor=50, verbose=True)

Image is color image.

Opened color image Kodak12.bmp for compression, split into 3 channels

Leveled each block by subtracting 128

Performed DCT on each block of the image, and zig-zagged the blocks into a list

Encoded the width, height, block size, and compression method

Compressed Kodak12.bmp to file.gz using lossless compression method gzip

Block size 8 and quality factor 50

Took 4.33 seconds

Original file size: 1179704 bytes

New file size: 110256 bytes

Compression Ratio: 10.7

Decompressed file.gz using lossless decompression method gzip

This is a color photo

Restored each block by un-zigzagging, multiplying by the quantization matrix, and undoing the DCT

Re-leveled image by adding 128 to each pixel

Displaying Image (check your task bar)

Time taken: 3.76 seconds

Tables

The following is a result of my compression algorithm on the test images. For each one, I include the filename, original size (in bytes), compression ratio achieved with Pillow’s JPEG converter (with quality = 95 for PSNR 50, q=75 for 40, and q=35 for 30), and the compression ratio received with the blocksize and lossless compression technique. The block sizes I used were 8 and 16, and the lossless compressions I used were gzip, bzip, zlib, and xz.

PSNR = 50

Filename	Og. Size (bytes)	JPEG Compression ratio	Ratio (8/gzip)	16/gzip	8/bzip	16/bzip	8/zlib	16/zlib	8/xz	16/xz
Kodak08.bmp	1179704	5.089	4.945	4.992	5.983	6.406	4.787	4.729	8.492	9.039
Kodak08gray.bmp	394296	1.865	4.863	4.921	5.422	5.5	4.72	4.669	5.617	5.508
Kodak09.bmp	1179704	8.873	11.425	12.698	14.409	16.882	10.89	11.852	17.739	20.375
Kodak09gray.bmp	394296	3.181	11.181	12.337	12.779	14.323	10.67	11.536	13.013	14.12
Kodak12.bmp	1179704	9.005	10.699	11.914	13.83	16.278	10.178	11.064	17.028	19.782
Kodak12gray.bmp	394296	3.139	9.927	11.116	11.692	13.163	9.498	10.35	11.743	12.76
Kodak18.bmp	1179704	5.783	6.156	6.52	7.472	8.28	5.936	6.142	9.393	10.546
Kodak18gray.bmp	394296	2.341	6.481	6.997	7.591	8.122	6.256	6.617	7.677	7.982
Kodak21.bmp	1179704	6.964	7.844	8.083	9.798	10.679	7.555	7.609	13.156	14.344
Kodak21gray.bmp	394296	2.579	8.047	8.271	9.168	9.441	7.778	7.785	9.438	9.45
Kodak22.bmp	1179704	6.776	7.552	8.242	9.104	10.474	7.267	7.702	11.184	12.678
Kodak22gray.bmp	394296	2.598	7.629	8.416	8.927	9.819	7.35	7.849	9.155	9.502

PSNR = 40

Filename	Og. Size (bytes)	JPEG Compression ratio	Ratio (8/gzip)	16/gzip	8/bzip	16/bzip	8/zlib	16/zlib	8/xz	16/xz
Kodak08.bmp	1179704	11.588	5.588	5.75	6.852	7.503	5.391	5.425	9.742	10.497
Kodak08gray.bmp	394296	4.159	5.487	5.658	6.138	6.396	5.308	5.354	6.37	6.362
Kodak09.bmp	1179704	25.103	13.26	14.973	17	20.607	12.669	13.911	21.304	24.522
Kodak09gray.bmp	394296	8.978	12.891	14.509	14.942	17.181	12.319	13.534	15.077	16.651
Kodak12.bmp	1179704	23.742	12.697	14.424	16.808	20.084	12.038	13.329	19.98	23.848
Kodak12gray.bmp	394296	8.247	11.758	13.373	14.039	16.047	11.19	12.416	13.779	15.33
Kodak18.bmp	1179704	14.199	7.038	7.69	8.644	9.929	6.769	7.206	10.846	12.466
Kodak18gray.bmp	394296	5.643	7.42	8.197	8.732	9.639	7.152	7.711	8.836	9.411
Kodak21.bmp	1179704	18.035	9.017	9.436	11.482	12.805	8.674	8.851	15.46	17.001
Kodak21gray.bmp	394296	6.668	9.202	9.619	10.641	11.223	8.898	9.048	10.928	11.016
Kodak22.bmp	1179704	17.369	8.742	9.81	10.658	12.716	8.371	9.134	13.012	15.05
Kodak22gray.bmp	394296	6.567	8.861	10.007	10.383	11.942	8.497	9.334	10.593	11.398

PSNR = 30

Filename	Og. Size (bytes)	JPEG Compression ratio	Ratio (8/gzip)	16/gzip	8/bzip	16/bzip	8/zlib	16/zlib	8/xz	16/xz
Kodak08.bmp	1179704	20.975	6.523	6.888	8.164	9.252	6.264	6.482	11.641	12.694
Kodak08gray.bmp	394296	7.463	6.421	6.772	7.26	7.734	6.18	6.393	7.521	7.617
Kodak09.bmp	1179704	46.697	15.782	18.164	20.887	25.819	15.088	16.835	26.118	30.11
Kodak09gray.bmp	394296	17.338	15.289	17.578	17.994	21.355	14.694	16.329	18.174	20.337
Kodak12.bmp	1179704	45.594	15.865	18.317	21.881	26.292	14.932	16.883	24.406	29.797
Kodak12gray.bmp	394296	16.207	14.572	16.913	17.928	20.558	13.759	15.567	16.882	19.309
Kodak18.bmp	1179704	27.137	8.397	9.499	10.471	12.558	8.056	8.856	13.029	15.361
Kodak18gray.bmp	394296	10.709	8.858	10.11	10.597	12.161	8.529	9.473	10.608	11.641
Kodak21.bmp	1179704	33.775	10.741	11.464	13.93	15.998	10.337	10.706	18.817	20.759
Kodak21gray.bmp	394296	12.705	10.909	11.728	12.747	13.828	10.513	10.972	13.054	13.393
Kodak22.bmp	1179704	33.94	10.621	12.252	13.319	16.184	10.133	11.338	15.513	18.437
Kodak22gray.bmp	394296	12.866	10.763	12.441	12.922	15.111	10.296	11.547	12.724	14.189