Contents

1 MPEG-1

• El estándard MPEG-1 (formalmente llamado “Coding of moving pictures and associated audio for digital storage media at up to about $1.5$ Mbit/s” o “estándar ISO/IEC 11172”) define cómo debe descomprimirse un bit-stream MPEG-1, no cómo debe comprimirse (aunque sí que aporta una propuesta) [1].
• Otros parámetros importantes del estandar son:
  1. Horizontal picture size $\le 768$ points (best $352$).
  2. Vertical picture size $\le 576$ points (best $288$).
  3. Picture rate $=23.976$, $24$, $25$, $29.97$, $30$, $50$, $59.95$ y $60$ Hz.
  4. Bit rate $\le 1.856.000$ bps.
  5. Chrominance sub-sampling: Default 4:2:0 (Y,Cb,Cr).

2 Compression ratios

• An MPEG-1 (Moving Picture Experts Group) coder compress a PCM video sequence generating a output a PCM CD audio sequence bit-rate, which is:
  $$\left(16+16\right)\frac{\text{bits}}{\text{samples}}\times 44.100\frac{\text{samples}}{\text{segundo}}=1.411.200\frac{\text{bits}}{\text{second}}$$

  This means that, if a PCM video needs $184.320.000\frac{\text{bits}}{\text{second}}$ (see), the compression ratio ios about 180:1!

3 Redundancy removing

• In MPEG-1, the technique that removes the video redundancy is called hybrid video coding:
  1. Temporal redundancy is exploited thorough motion compensation, which is an specific version of temporal predictive encoding applied to sequences of images.
  2. Spatial redundancy is removed by means of quantization in the $8\times 8$-DCT domain (like in JPEG).
  3. The remaining statistical redundancy is eliminated using entropy coding.

4 The MPEG-1 compressor

5 The MPEG-1 decompressor

Notice that:

and that:

6 The ME (Motion Estimation) procedure

• Removes temporal redundancy. A predicted image can be encoded as the difference between it and another image called prediction image which is a motion compensated projection of one or more images named reference images. ME tries to generate residue images as close as possible to the null images.

• CPU expensive although it is useful if we “compress one time, decompress many”.
• Only performed by the compressor.

7 I, P and B pictures

• Depending on the way the predictions are built, in MPEG-1 we found the following types of encoded images:
  1. I-pictures (Intra-coded): when the encoded image it is encoded by itself (no ME needs to be performed).
  2. P-pictures (Predictive-coded): when the encoded image has been ME compensated using a previous (in time) I or P image.
  3. B-pictures (Bidirectionally predictive-coded): when the prediction image has been generated using two I or P images, one anterior and other posterior, in time. Notice that B-images never are used as reference images.

8 Display (time) and bit-stream orders

• When there are B-frames in a GOP, we can speak about to different image orders:
  1. Display order: Is the order used to show the images.
  2. Bit-stream order: Is the order in which the pictures are stored in the code-stream.
• Examples:

9 The GOP (Group Of Pictures) concept

• The IPPP... compression of the whole image sequence has two big drawbacks:
  1. The decompression of the $V_i$ image implies the decompression of the $i-1$ previous ones. This in unacceptable when we want to go directly to decompress only the $V_i$ picture.
  2. If a image of index $j<i$ has been lost or has some kind of error, the images $\left\{V_j,\cdots ,V_i\right\}$ are unusable.
• Notice that nothing changed if we use B-frames.
• For these reasons, the length (in images) of the compressed sequences need to be limited.

• In this context, the images that are compressed as a whole is called a GOP. Examples:
  0 0 0 0 0 0 0 0 0 0 1 1 1 1 1  
  0 1 2 3 4 5 6 7 8 9 0 1 2 3 4  
  -----------------------------> time  
  I  
  I P P  
  I B P B P  
  B B I B P B P  
  B B I B B P B B P B B P  
  B I B B B B P B I B B I I  
  I B B P B B P B B P B B P  
  B B I B B P B B P B B P B B P

10 Open and closed GOPs

• In a MPEG-1 sequence we can found:
  1. Closed GOPs: If the GOP does not need another GOP to be decompressed.
  2. Open GOPs: Otherwise. Open GOPs are very rare because they not allows the random access to a image of the sequence neither to keep the errors under control. Examples:

     I B B P B B P B B P B B P	(closed GOP)
     B B I B B P B B P B B P B B P	(open GOP)

11 The BC task

• The amount of information erased by the quantization step $\mathcal{𝒬}$ is controlled by the BC (Bit-rate Control) box. Under output bit-rate constraints, the quantization step $q$ is increased or decreased depending on the content of the images.

12 Motion fields encoding

• In MPEG-1 the motion vectors ($\left(x,y\right)$) are encoded using a static Huffman code.
• $x$ and $y$ follows a Laplace probability distribution.
• $0\le x,y<16$.

13 The MPEG-1’s data partitioning

• Each slice is encoded independently compressed and is labeled in the code-stream with a special code. This increases the error resilience of the code-stream.
• The minimal size of an slice is one macro-blocks and the maximal size is a picture.

14 Fast visualization

• In MPEG-1 there is an special type of images called D-pictures. In a D-picture there are only D-macro-blocks, which are I-macro-blocks that are only compressed using its DC DCT coefficient.
• D-macroblocks, i.e., D-pictures are decompressed very fast because the DC coefficients represent the averagle of each $8\times 8$-block, and therefore, the inverse DCT is not carried out.
• However, the I-pictures and the D-pictures are redundant. For this reason, the fast visualization is performed typically using I-pictures only.

Lab

• Let’s compress an image sequence and compute the PSNR[dB]/bit-rate figure-of-merit.
  1. Compress the akiyo sequence using FFMPEG:

     

  2. Compute the average bit-rate of the compressed sequence in bits/second (multiply the size of the compressed file by 8 and divide by the duration of the video).
  3. Decompress the sequence using:

     

  4. Use the snr command-line tool for compute the PSNR[dB] value of each image of the sequence. Example:
     snr \  
       --file_A=akiyo_352x288x300_30Hz.yuv \  
       --file_B=decompressed_akiyo.yuv \  
       --block_size=‘echo "352*288*3/2" | bc -l‘

  5. Plot the ratio PSNR[dB]/bit-rate, for each image of the sequence.
  6. Repeat the previous experiment for different quantization steps.

References