video compression

Video Compression
Djordje Mitrovic – University of Edinburgh

This document deals with the issues of video compression. The algorithm, which is used by the MPEG
standards, will be elucidated upon in order to explain video compression. Only visual compression will be
discussed (no audio compression). References and links to further readings will be provided in the text.

What is compression?
Compression is a reversible conversion (encoding) of data that contains fewer bits. This allows a more
efficient storage and transmission of the data. The inverse process is called decompression (decoding).
Software and hardware that can encode and decode are called decoders. Both combined form a codec
and should not be confused with the terms data container or compression algorithms.

Figure 1: Relation between codec, data containers and compression algorithms.

Lossless compression allows a 100% recovery of the original data. It is usually used for text or executable
files, where a loss of information is a major damage. These compression algorithms often use statistical
information to reduce redundancies. Huffman-Coding [1] and Run Length Encoding [2] are two popular
examples allowing high compression ratios depending on the data.

Using lossy compression does not allow an exact recovery of the original data. Nevertheless it can be
used for data, which is not very sensitive to losses and which contains a lot of redundancies, such as
images, video or sound. Lossy compression allows higher compression ratios than lossless compression.

Why is video compression used?
A simple calculation shows that an uncompressed video produces an enormous amount of data: a
resolution of 720x576 pixels (PAL), with a refresh rate of 25 fps and 8-bit colour depth, would require the
following bandwidth:

720 x 576 x 25 x 8 + 2 x (360 x 576 x 25 x 8) = 1.66 Mb/s (luminance + chrominance)

For High Definition Television (HDTV):

1920 x 1080 x 60 x 8 + 2 x (960 x 1080 x 60 x 8) = 1.99 Gb/s

Even with powerful computer systems (storage,
processor power, network bandwidth), such data amount
cause extreme high computational demands for
managing the data. Fortunately, digital video contains a
great deal of redundancy. Thus it is suitable for
compression, which can reduce these problems
significantly. Especially lossy compression techniques
deliver high compression ratios for video data. However,
one must keep in mind that there is always a trade-off
between data size (therefore computational time) and Uncompressed Compressed Image
quality. The higher the compression ratio, the lower the Image 72KB has only 28 KB, but
size and the lower the quality. The encoding and is has worse quality
decoding process itself also needs computational

resources, which have to be taken into consideration. It makes no sense, for example for a real-time
application with low bandwidth requirements, to compress the video with a computational expensive
algorithm which takes too long to encode and decode the data.

Image and Video Compression Standards
The following compression standards are the most known nowadays. Each of them is suited for specific
applications. Top entry is the lowest and last row is the most recent standard. The MPEG standards are
the most widely used ones, which will be explained in more details in the following sections.

Standard Application Bit Rate
JPEG Still image compression Variable
H.261 Video conferencing over ISDN P x 64 kb/s
MPEG-1 Video on digital storage media (CD-ROM) 1.5Mb/s
MPEG-2 Digital Television 2-20 Mb/s
H.263 Video telephony over PSTN 33.6-? kb/s
MPEG-4 Object-based coding, synthetic content, Variable
interactivity
JPEG-2000 Improved still image compression Variable
H.264/ Improved video compression 10’s to 100’s kb/s
MPEG-4 AVC

Adapted from [3]

The MPEG standards
MPEG stands for Moving Picture Coding Exports Group [4]. At the same time it describes a whole family
of international standards for the compression of audio-visual digital data. The most known are MPEG-1,
MPEG-2 and MPEG-4, which are also formally known as ISO/IEC-11172, ISO/IEC-13818 and ISO/IEC-
14496. More details about the MPEG standards can be found in [4],[5],[6]. The most important aspects
are summarised as follows:

The MPEG-1 Standard was published 1992 and its aim was it to provide VHS
quality with a bandwidth of 1,5 Mb/s, which allowed to play a video in real
time from a 1x CD-ROM. The frame rate in MPEG-1 is locked at 25 (PAL) fps
and 30 (NTSC) fps respectively. Further MPEG-1 was designed to allow a
fast forward and backward search and a synchronisation of audio and video.
A stable behaviour, in cases of data loss, as well as low computation times
for encoding and decoding was reached, which is important for symmetric
applications, like video telephony.

In 1994 MPEG-2 was released, which allowed a higher quality with a slightly
higher bandwidth. MPEG-2 is compatible to MPEG-1. Later it was also used
for High Definition Television (HDTV) and DVD, which made the MPEG-3 standard disappear completely.
The frame rate is locked at 25 (PAL) fps and 30 (NTSC) fps respectively, just as in MPEG-1. MPEG-2 is
more scalable than MPEG-1 and is able to play the same video in different resolutions and frame rates.

MPEG-4 was released 1998 and it provided lower bit rates (10Kb/s to 1Mb/s) with a good quality. It was a
major development from MPEG-2 and was designed for the use in interactive environments, such as
multimedia applications and video communication. It enhances the MPEG family with tools to lower the
bit-rate individually for certain applications. It is therefore more adaptive to the specific area of the video
usage. For multimedia producers, MPEG-4 offers a better reusability of the contents as well as a
copyright protection. The content of a frame can be grouped into object, which can be accessed
individually via the MPEG-4 Syntactic Description Language (MSDL). Most of the tools require immense
computational power (for encoding and decoding), which makes them impractical for most “normal, non-
professional user” applications or real time applications. The real-time tools in MPEG-4 are already
included in MPEG-1 and MPEG-2. More details about the MPEG-4 standard and its tool can be found in
[7].

The MPEG Compression
The MPEG compression algorithm encodes the data in 5 steps [6], [8]:

First a reduction of the resolution is done, which is followed by a motion compensation in order to reduce
temporal redundancy. The next steps are the Discrete Cosine Transformation (DCT) and a quantization
as it is used for the JPEG compression; this reduces the spatial redundancy (referring to human visual
perception). The final step is an entropy coding using the Run Length Encoding and the Huffman coding
algorithm.

Step 1: Reduction of the Resolution

The human eye has a lower sensibility to colour information than to dark-bright contrasts. A conversion
from RGB-colour-space into YUV colour components help to use this effect for compression. The
chrominance components U and V can be reduced (subsampling) to half of the pixels in horizontal
direction (4:2:2), or a half of the pixels in both the horizontal and vertical (4:2:0).

Figure 2: Depending on the subsampling, 2 or 4 pixel values of the chrominance channel can be
grouped together.

The subsampling reduces the data volume by 50% for the 4:2:0 and by 33% for the 4:2:2 subsampling:

| Y |=| U |=| V |

|Y | + 1 |U | + 1 |V | 1
4:2:0 = 4 4
=
|Y | + |U | + |V | 2

|Y | + 1 |U | + 1 |V | 2
4:2:0 = 2 2
=
|Y | + |U | + |V | 3

MPEG uses similar effects for the audio compression, which are not discussed at this point.

Step 2: Motion Estimation

An MPEG video can be understood as a sequence of frames. Because two successive frames of a video
sequence often have small differences (except in scene changes), the MPEG-standard offers a way of
reducing this temporal redundancy. It uses three types of frames:

I-frames (intra), P-frames (predicted) and B-frames (bidirectional).

The I-frames are “key-frames”, which have no reference to other frames and their compression is not that
high. The P-frames can be predicted from an earlier I-frame or P-frame. P-frames cannot be
reconstructed without their referencing frame, but they need less space than the I-frames, because only
the differences are stored. The B-frames are a two directional version of the P-frame, referring to both
directions (one forward frame and one backward frame). B-frames cannot be referenced by other P- or B-
frames, because they are interpolated from forward and backward frames. P-frames and B-frames are
called inter coded frames, whereas I-frames are known as intra coded frames.

Figure 3:. An MPEG frame sequence with two possible references: a P-frame referring to a I-frame
and a B-frame referring to two P-frames.

The usage of the particular frame type defines the quality and the compression ratio of the compressed
video. I-frames increase the quality (and size), whereas the usage of B-frames compresses better but
also produces poorer quality. The distance between two I-frames can be seen as a measure for the
quality of an MPEG-video. In practise following sequence showed to give good results for quality and
compression level: IBBPBBPBBPBBIBBP.

The references between the different types of frames are realised by a process called motion estimation
or motion compensation. The correlation between two frames in terms of motion is represented by a
motion vector. The resulting frame correlation, and therefore the pixel arithmetic difference, strongly
depends on how good the motion estimation algorithm is implemented. Good estimation results in higher
compression ratios and better quality of the coded video sequence. However, motion estimation is a
computational intensive operation, which is often not well suited for real time applications. Figure 4 shows
the steps involved in motion estimation, which will be explained as follows:

Frame Segmentation - The Actual frame is divided into non-
overlapping blocks (macro blocks) usually 8x8 or 16x16
pixels. The smaller the block sizes are chosen, the more
vectors need to be calculated; the block size therefore is a
critical factor in terms of time performance, but also in terms
of quality: if the blocks are too large, the motion matching is
most likely less correlated. If the blocks are too small, it is
probably, that the algorithm will try to match noise. MPEG
uses usually block sizes of 16x16 pixels.

Search Threshold - In order to minimise the number of
expensive motion estimation calculations, they are only
calculated if the difference between two blocks at the same
position is higher than a threshold, otherwise the whole block
is transmitted.

Block Matching - In general block matching tries, to “stitch
together” an actual predicted frame by using snippets (blocks)
from previous frames. The process of block matching is the
most time consuming one during encoding. In order to find a
matching block, each block of the current frame is compared
with a past frame within a search area. Only the luminance
information is used to compare the blocks, but obviously the
colour information will be included in the encoding. The
search area is a critical factor for the quality of the matching. It
is more likely that the algorithm finds a matching block, if it
searches a larger area. Obviously the number of search
operations increases quadratically, when extending the
search area. Therefore too large search areas slow down the Figure 4: Schematic process of
encoding process dramatically. To reduce these problems motion estimation. Adapted from [8]
often rectangular search areas are used, which take into

account, that horizontal movements are more likely than vertical ones. More details about block matching
algorithms can be found in [9], [10].

Prediction Error Coding - Video motions are often more complex, and a simple “shifting in 2D” is not a
perfectly suitable description of the motion in the actual scene, causing so called prediction errors [13].
The MPEG stream contains a matrix for compensating this error. After prediction the, the predicted and
the original frame are compared, and their differences are coded. Obviously less data is needed to store
only the differences (yellow and black regions in Figure 5).

Figure 5

Vector Coding - After determining the motion vectors and evaluating the correction, these can be
compressed. Large parts of MPEG videos consist of B- and P-frames as seen before, and most of them
have mainly stored motion vectors. Therefore an efficient compression of motion vector data, which has
usually high correlation, is desired. Details about motion vector compression can be found in [11].

Block Coding - see Discrete Cosine Transform (DCT) below.

Step 3: Discrete Cosine Transform (DCT)

DCT allows, similar to the Fast Fourier Transform (FFT), a representation of image data in terms of
frequency components. So the frame-blocks (8x8 or 16x16 pixels) can be represented as frequency
components. The transformation into the frequency domain is described by the following formula:

1 N −1 N −1
(2 x + 1)uπ (2 y + 1)vπ
F (u , v) = C (u )C (v)∑∑ f ( x, y ) ⋅ cos ⋅ cos
4 x =0 y =0 2N 2N

C (u ), C (v) = 1 / 2 for u , v = 0
C (u ), C (v) = 1, else
N = block size

The inverse DCT is defined as:

1 N −1 N −1 (2 y + 1)uπ (2 x + 1)vπ
f ( x, y ) = ∑ ∑ C (u)C (v) F (u, v) cos 16 cos 16
4 u =0 v =0

The DCT is unfortunately computational very expensive and its complexity increases disproportionately
2
( O ( N ) ). That is the reason why images compressed using DCT are divided into blocks. Another
disadvantage of DCT is its inability to decompose a broad signal into high and low frequencies at the
same time. Therefore the use of small blocks allows a description of high frequencies with less cosine-
terms.

Figure 6: Visualisation of 64 basis functions (cosine frequencies) of a DCT. Reproduced from [12]

The first entry (top left in Figure 6) is called the direct current-term, which is constant and describes the
average grey level of the block. The 63 remaining terms are called alternating-current terms. Up to this
point no compression of the block data has occurred. The data was only well-conditioned for a
compression, which is done by the next two steps.

Step 4: Quantization

During quantization, which is the primary source of data loss, the DCT terms are divided by a quantization
matrix, which takes into account human visual perception. The human eyes are more reactive to low
frequencies than to high ones. Higher frequencies end up with a zero entry after quantization and the
domain was reduced significantly.

FQUANTISED = F (u, v) DIV Q(u, v)

Where Q is the quantisation Matrix of dimension N. The way Q is chosen defines the final compression
level and therefore the quality. After Quantization the DC- and AC- terms are treated separately. As the
correlation between the adjacent blocks is high, only the differences between the DC-terms are stored,
instead of storing all values independently. The AC-terms are then stored in a zig-zag-path with
increasing frequency values. This representation is optimal for the next coding step, because same
values are stored next to each other; as mentioned most of the higher frequencies are zero after division
with Q.

Figure 7: Zig-zag-path for storing the frequencies. Reproduced from [13].

If the compression is too high, which means there are more zeros after quantization, artefacts are visible
(Figure 8). This happens because the blocks are compressed individually with no correlation to each
other. When dealing with video, this effect is even more visible, as the blocks are changing (over time)
individually in the worst case.

Figure 8: Block artefacts after DCT.

Step 5: Entropy Coding

The entropy coding takes two steps: Run Length Encoding (RLE ) [2] and Huffman coding [1]. These are
well known lossless compression methods, which can compress data, depending on its redundancy, by
an additional factor of 3 to 4.

All five Steps together

Figure 9: Illustration of the discussed 5 steps for a standard MPEG encoding.

As seen, MPEG video compression consists of multiple conversion and compression algorithms. At every
step other critical compression issues occur and always form a trade-off between quality, data volume
and computational complexity. However, the area of use of the video will finally decide which
compression standard will be used. Most of the other compression standards use similar methods to
achieve an optimal compression with best possible quality.

References
[1] HUFFMAN, D. A. (1951). A method for the construction of minimum redundancy codes. In the
Proceedings of the Institute of Radio Engineers 40, pp. 1098-1101.

[2] CAPON, J. (1959). A probabilistie model for run-length coding of pictures. IRE Trans. On Information
Theory, IT-5, (4), pp. 157-163.

[3] APOSTOLOPOULOS, J. G. (2004). Video Compression. Streaming Media Systems Group.
http://www.mit.edu/~6.344/Spring2004/video_compression_2004.pdf (3. Feb. 2006)

[4] The Moving Picture Experts Group home page. http://www.chiariglione.org/mpeg/ (3. Feb. 2006)

[5] CLARKE, R. J. Digital compression of still images and video. London: Academic press. 1995, pp. 285-
299

[6] Institut für Informatik – Universität Karlsruhe. http://www.irf.uka.de/seminare/redundanz/vortrag15/
(3. Feb. 2006)

[7] PEREIRA, F. The MPEG4 Standard: Evolution or Revolution
www.img.lx.it.pt/~fp/artigos/VLVB96.doc (3. Feb. 2006)
[8] MANNING, C. The digital video site.
http://www.newmediarepublic.com/dvideo/compression/adv08.html (3. Feb. 2006)

[9] SEFERIDIS, V. E. GHANBARI, M. (1993). General approach to block-matching motion estimation.
Optical Engineering, (32), pp. 1464-1474.

[10] GHARAVI, H. MILLIS, M. (1990). Block matching motion estimation algorithms-new results. IEEE
Transactions on Circuits and Systems, (37), pp. 649-651.

[11] CHOI, W. Y. PARK R. H. (1989). Motion vector coding with conditional transmission. Signal
Processing, (18). pp. 259-267.

[12] Institut für Informatik – Universität Karlsruhe.
http://goethe.ira.uka.de/seminare/redundanz/vortrag11/#DCT (3. Feb. 2006)

[13] Technische Universität Chemnitz – Fakultät für Informatik.
http://rnvs.informatik.tu-chemnitz.de/~jan/MPEG/HTML/mpeg_tech.html (3. Feb. 2006)

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