Digital image processing (6) -- image compression

一、Description of image compression

（一）、Image coding technology research background

1. Information transmission mode great changes have taken place in

1. The change of the communication mode

文字+语音 图像+文字+语音

2. The change of the communication object

人与人 人与机器,机器与机器

2. Image transmission and storage of information space

（1）Color video information

For the resolution of the television pictures640480的彩色图像,每秒30帧,The amount of data for a second：
6404802430=210.94M – So when I play,需要211MbpsThe communication circuit.
– 参考数据：Broadband network for2048K.
– 存储时,1张DVD可存4.7G,The only can hold22.8秒的数据.

（2）Facsimile data

–If only2值图像,以200dpiThe resolution of the transmission,一张A4The content of the paper the amount of data for：
165423371=3888768bit –按64KTelephone line transmission rate,You need to pass the time：59.3秒（At present four types of the fax machine15sIn transmitting a
页 ISO A4Wide file

Because of the communication mode and communication object change brings the biggest problem is：
–传输带宽、速度、Storage capacity limit.
• Give us a problem,Also give us a chance：

How to solve by means of the software hardware physical limits

Image communication system model

The principle of image redundancy lossless compression

从原来的1638=284bits 压缩为：(1+3)*8=32bits

（四）、 The necessity of image compression and compression

1. 图像压缩

• 图像压缩,本质上说,Is the source of image data according to certain rules of transformation and combination,So as to achieve with as little code as possible to represent the data information as much as possible.Compression coding to realize,Or the effect of compression encoding has,所以,Generally called the processing compression.

2. 压缩的必要性
   • A simulated image must pass a pulse code modulation（PCM—Pulse Code Modulation)To become a digital image.

（PCM-Pulse code modulation used for speech signals early）

二、Fidelity criterion of image compression and compression performance parameters of the

三、Statistical coding compression

（一）、 Summary of statistical coding

– According to the image pixel gray value of the probability distribution characteristics of compression coding called statistical coding.

– Entropy and average code word length
• 1）H(d) < R(d)时,Can design a certain average code word length shorter undistorted coding method.
• 2）The average code word length less thanH(d)The undistorted coding method does not exist.

– 熵编码
• The encoded image of the average length of code word as close as possible to the image entropyH.
• 基本思路是：Probability of grayscale with short code word,概率小的,用
长码字

（二）、 Statistical coding method

1. 行程编码(RLE编码)

• （1）基本原理

– By changing the description of the image way,来实现压缩.Will the yan in the line
Color the same value of adjacent pixels with a count and the color value instead of.

• （2）举例说明

aaaabbbccdeeeeefffffff (共22*8=176 bits)

4a3b2c1d5e7f (共12*8=96 bits)

• （3）应用分析
– Suitable for travel longer image,一般不单独使用.

2. Huffman 编码（熵编码）

–基本原理：
• In order to achieve greater compression ratio,提出了一种方法,Is to appear in the image frequency of pixel values for a short code,There will be a small frequency like value for a relatively long code.

Huffman, a|：

3. Shannon-Fano编码

算法：
• 1）Will be ordered according to the gray level probability increasing;
• 2）According to probability principle of similar or equal the sum of gray level set in two;
• 3）Apply the above segmentation criterion recursively to grayscale subset,Until only a grayscale eventually subset;
• 4）在分割过程中,To share the two subsets to give0和1

平均码长：

信息熵：

编码效率：

四、Predictive coding and transform coding compression

一. 预测编码

– 预测编码（Predictive Coding),是根据“过去”The moment of pixel values,Using a model,To predict the current pixel values,Predictive coding is usually not directly on the signal coding,But the prediction error coding.When forecasting more accurate,误差较小时,To achieve the purpose of coding compression.

– 原理：The margin of a discrete pixels of image of real value,Using the correlation of the adjacent pixels,Predict it's likely the next pixel value,To the poor,This difference in the nature of forecast,量化,编码,就可以达到压缩的目的.

Predictive coding schemes

预测器：

${\hat{f}}_n=F(f_{n-1},f_{n-2},...,f_{n-k})$

${\hat{f}}_n$ According to the brightness values of several pixels in front $f_{n-1},f_{n-2},...,f_{n-k}$

预测而得：$\Delta {}_n=f_n-{\hat{f}}_n$

量化器：对 $\Delta {}_n$ 进行舍入,The quantitative

编码器：Can use the mature coding technology,如Huffman编码等

解码器：The encoder counter

In the predictive coding,Differential pulse code modulation is the most commonly used（Differential Pulse Code Modulation, DPCM),

原理图如下所示：

The same as the prediction process and start receiving decoding,Used to predict
Is also the same,Closed end of the output signal is originated approximation,
The error is

注意：1）Multi-point prediction;

Each row of the first several pixels unpredictable,These pixels need coding in other way,This is the predictive coding needed additional operation

Prediction coefficients with different images and different,But for every image forecast calculation coefficient is too much trouble,也不现实,Refer to previous data choose to use.In the static image compression standard of international(JPEG)中,Front some form of this method and the coefficient of predicted a recommended value for reference.

（二）、 变换编码

原理：Image data after orthogonal transformation,Other is the independency of the transform coefficient has a certain,（例如,对于FT来说,Frequency coefficient of big's transform coefficients are concentrated in the low frequency part,Have very low amplitude and high frequency part,Thus the low frequency transform coefficient quantization、编码和传输,The high frequency part does not handle,So that we can achieve the purpose of image compression.

五、Image coding and compression standard

（一）、 图像编码标准：

– JBIG,H.26x,JPEG,MPEG等

（二）、 Static image format-JPEG

• 国际标准化组织（ID）和国际电报电话咨询委员会（CCITT）Jointly set up expert groupJPEG（Joint Photographic Experts Group）于1991年3月提出了ISO CDIO918The draft proposal:多灰度静止图像的数字压缩编码（通常简称为JPEG标准）.

This is a more suitable for color and monochrome grayscale or continuous tone static digital image compression standard.它包括基于DPCM（差分脉冲编码调制）、DCT（离散余弦变换）和HuffmanLossy compression algorithm two parts.

JPEG压缩编码算法的主要计算步骤如下：

1. 正向离散余弦变换(FDCT);
2. 量化(quantization);
3. Z字形编码(zigzag scan);
4. 使用差分脉冲编码调制(differential pulse code modulation,DPCM)The dc 系数(DC)进行编码;
5. 使用行程长度编码(run-length encoding,RLE) 对交流系数(AC)进行编码.
6. 熵编码(entropy coding).

JPEG压缩编码算法

（三）、 Activity image format-MPEG

MPEG（Moving Pictures Experts Group）是 ISO/IEC/JTC/SC2/WG11的一个小组.It work for theJPEG标准和CCITT专家组的H.261标准,于1990In forming a draft standard.

• MPEGThe standard is divided into two stages:第一个阶段（MPEG1）Is in view of the transfer rate of lMb/s到l.5Mb/s的普通电视质量的视频信号的压缩;
第二个阶段（MPEG-2）Target is the second30帧的720x572
分辨率的视频信号进行压缩;在扩展模式下,MPEG-2Can the resolution of1440Xl152高清晰度电视（HDTV）The signal compression

MPEG-3：原本针对于HDTV(1920×1080),后来被MPEG-2代替.

• ·MPEG-4：针对多媒体应用的图像编码标准.是为了播放流式媒体的高质量视频而专门设计的,It can use very narrow belt degree,通过帧重建技术,压缩和传输数据,以求使用最少的数据获得最佳的图像质量.

• ·MPEG-7：基于内容表示的标准,Applied to more
Media information search,过滤,组织和处理

小结

• The necessity of image coding： Coding purpose and principle of
• The classification of image coding： 统计编码、预测编码、Transform coding, etc.
• The fidelity of image coding standards： 客观（均方差、Signal-to-noise ratio (SNR) mean square 比）;主观.
• The performance of the encoding parameters：熵、平均码长、冗余度、编码效率.
• 统计编码：行程编码、霍夫曼编码
• 预测编码、变换编码
• Image coding international standards：JPEG、MPEG