JPG学习笔记2(附完整代码)

  我们已经从BMP图中拿到了需要压缩RGB的数据,我们需要对原数据从RGB域转变YCbCr域,之后对YCbCr数据进行下采样(down sampling)。对于不需要看文章的同学,这边直接给出源代码。https://github.com/Cheemion/JPEG_COMPRESS

                图片引用"Compressed Image File Formats JPEG, PNG, GIF, XBM, BMP - John Miano"[1]

1.RGB域和YCbCr域

RGB代表红绿蓝,通过3种颜色的叠加来得到我们看到的颜色。0-到255分别代表颜色从浅到深。

Y   =  0.299   * red + 0.587  *  green + 0.114  *  blue; Cb = -0.1687 * red - 0.3313 * green + 0.5    *    blue + 128; Cr  =  0.5       * red - 0.4187 * green -  0.0813 * blue + 128;

Y是RGB的加权平均值,称之为亮度(luminance)

Cb是B分量和亮度的差值, 称为Chrominance(Cb)

Cr是R分量和亮度的差值,称为Chrominance(Cr)

以下代码将RGB转为YCbCr。为什么将RGB转为YCbCr? 因为人眼对亮度(Y)的变化更敏感,所以我可以对Cr和Cb进行下采样(压缩,比如本来1个字节代表一个pixel的数据,压缩后用1个字节代表4个pixels的数据),尽可能保留完整的Y分量。通过这样子我们可以进一步的压缩数据。

void JPG::convertToYCbCr() {
    for(uint i = 0; i < height; i++) {
        for(uint j = 0; j < width; j++) {
            YCbCr temp = BMPData[i * width + j];
            BMPData[i * width + j].Y  =  0.299  * temp.red + 0.587 * temp.green  + 0.114  * temp.blue;
            BMPData[i * width + j].Cb = -0.1687 * temp.red - 0.3313 * temp.green + 0.5    * temp.blue + 128;
            BMPData[i * width + j].Cr =  0.5    * temp.red - 0.4187 * temp.green - 0.0813 * temp.blue + 128;
        }
    }
}

2.sampling(采样)

 采样通常是对连续信号进行采样,比如下图蓝色是连续信号x(t),红色是对信号进行采样后得到的信号x[n]=x(T*n), T是采样间隔,1/T是采样频率。

 而在JPEG中,我们是对已经离散的数据进行采样,并且JPEG中的采样数值是相对采样数值。相对于最高采样频率的采样数值。

如下左图

Y(luminance)分量的水平采样频率(H, Horizantal sampling frequency)和垂直采样频率(V, vertical sampling frequency)都是4,是最高的采样频率。最高的采样频率就相当于保留原图的Y分量,不进行下采样。

Cb分量的水平和垂直的采样频率都是2,等于最高采样频率的一半。所以水平每2个点采样一次,垂直每2个点采样一次。

Cr分量的水平和垂直采样频率都是1,等于最高采样频率的1/4。所以水平和垂直每4个点采样一个点。

3个分量的量叠加就得到了我们的像素的值。

  图片引用"Compressed Image File Formats JPEG, PNG, GIF, XBM, BMP - John Miano"[1]

2.YCbCr数据在JPEG中的存储

JPEG规定所有的数据都是以8*8的一个block(data unit)的形式进行离散余弦变化和存储的.可以把这8*8的block看成是最小存储单元。

MCU是Y,Cb,Cr的完整的block组成的能够完整还原一个范围的色彩的最小单元。啥意思?

假设我们的图片是10*10的大小.

若Y,Cb,Cr的水平和垂直的采样频率都为1,则原图由4个mcu(4种颜色分别代表一个MCU)组成(每个mcu包含1个y的block,一个cb的block,一个cr的block, 每个mcu的大小为8*8),边缘空白的地方可用0替代,也可以重复边缘的值。

左上角那块4*4的小block的值分别

pixel[0,0] = y[0,0] + cb[0,0] + cr[0,0]

pixel[0,1] = y[0,1] + cb[0,1] + cr[0,1]

pixel[1,0] = y[1,0] + cb[1,0] + cr[1,0]

pixel[1,1] = y[1,1] + cb[1,1] + cr[1,1]

若Y的水平和垂直采样频率为2, cb和cr的采样频率为1, 则原图由1个mcu组成(大小为16*16)。mcu中包含4个y的block(2*2),一个cb,一个cr。总共6个block,大小只占原来block的一半。

左上角那块4*4的小block的值分别

pixel[0,0] = y[0,0] + cb[0,0] + cr[0,0]

pixel[0,1] = y[0,1] + cb[0,0] + cr[0,0]

pixel[1,0] = y[1,0] + cb[0,0] + cr[0,0]

pixel[1,1] = y[1,1] + cb[0,0] + cr[0,0]

 

总结:mcu大小= 垂直最大采样值 * 水平最大采样值, 一个mcu包含y的水平采样值*y的垂直采样值个的y个block(y的水平采样为2,垂直为2,则一个muc有4个yblock)。其他分量同理

1.3定义JPG class代码

//定义Block
using
Block = int[64];
//定义YCbCr,同时这个结构用来展示存放rgb数据
struct YCbCr { union { double Y; double red; }; union { double Cb; double green; }; union { double Cr; double blue; }; };

 



struct
MCU { Block* y; Block* cb; Block* cr; };

//定义JPG类,用于压缩图片 class JPG { public:
//rgb转到YCbCr
void convertToYCbCr();
   //下采样
void subsampling();
//变化
void discreteCosineTransform();
//量化
void quantization();
//哈夫曼
void huffmanCoding();
//输出
void output(std::string path); public:
MCU
* data;
Block
* blocks;
//BMPData存放的是bmp图片的RGB数据 YCbCr
* BMPData; uint blockNum; //原图的像素 uint width; uint height; //mcu 有多少个 长度是多少 uint mcuWidth; uint mcuHeight; //一个完整的muc的水平和垂直像素个数 uint mcuVerticalPixelNum; uint mcuHorizontalPixelNum; //用于subsampling // only support 1 or 2 byte YVerticalSamplingFrequency; byte YHorizontalSamplingFrequency; byte CbVerticalSamplingFrequency; byte CbHorizontalSamplingFrequency; byte CrVerticalSamplingFrequency; byte CrHorizontalSamplingFrequency; byte maxVerticalSamplingFrequency; byte maxHorizontalSamplingFrequency; public:
JPG(uint width, uint height,const RGB* const rgbs, byte YVerticalSamplingFrequency, byte YHorizontalSamplingFrequency, byte CbVerticalSamplingFrequency, byte CbHorizontalSamplingFrequency, byte CrVerticalSamplingFrequency, byte CrHorizontalSamplingFrequency ) :width(width), height(height), YVerticalSamplingFrequency(YVerticalSamplingFrequency), YHorizontalSamplingFrequency(YHorizontalSamplingFrequency), CbVerticalSamplingFrequency(CbVerticalSamplingFrequency), CbHorizontalSamplingFrequency(CbHorizontalSamplingFrequency), CrVerticalSamplingFrequency(CrVerticalSamplingFrequency), CrHorizontalSamplingFrequency(CrHorizontalSamplingFrequency) { maxHorizontalSamplingFrequency = std::max({YHorizontalSamplingFrequency, CbHorizontalSamplingFrequency, CrHorizontalSamplingFrequency}); maxVerticalSamplingFrequency = std::max({YVerticalSamplingFrequency, CbVerticalSamplingFrequency, CrVerticalSamplingFrequency}); //mcu的个数 mcuWidth = (width + (maxHorizontalSamplingFrequency * 8 - 1)) / (maxHorizontalSamplingFrequency * 8); mcuHeight = (height + (maxVerticalSamplingFrequency * 8 - 1)) / (maxVerticalSamplingFrequency * 8); mcuVerticalPixelNum = maxVerticalSamplingFrequency * 8; mcuHorizontalPixelNum = maxHorizontalSamplingFrequency * 8; //总共多少个MCU data = new MCU[mcuWidth * mcuHeight]; //一个MCU有多少个Block blockNum = (YVerticalSamplingFrequency * YHorizontalSamplingFrequency + CbVerticalSamplingFrequency * CbHorizontalSamplingFrequency + CrHorizontalSamplingFrequency * CrVerticalSamplingFrequency); //分配block内存空间 blocks = new Block[mcuHeight * mcuHeight * blockNum]; //把内存映射到对于的结构中 for (uint i = 0; i < mcuHeight; i++) { for (uint j = 0; j < mcuWidth; j++) {
data[i
* mcuWidth + j].y = &blocks[(i * mcuWidth + j) * blockNum]; data[i * mcuWidth + j].cb = data[i * mcuWidth + j].y + YVerticalSamplingFrequency * YHorizontalSamplingFrequency; data[i * mcuWidth + j].cr = data[i * mcuWidth + j].cb + CbVerticalSamplingFrequency * CbHorizontalSamplingFrequency; } } //BMP数据用于存放,bmp的原图的数据 BMPData = new YCbCr[width * height];
//把bmp数据暂时存放在BMPdata中
for(uint i = 0; i < height; i++) { for(uint j = 0; j < width; j++) { BMPData[i * width + j].red = static_cast<double>(rgbs[i * width + j].red); BMPData[i * width + j].blue = static_cast<double>(rgbs[i * width + j].blue); BMPData[i * width + j].green = static_cast<double>(rgbs[i * width + j].green); } } } ~JPG() { delete[] data; delete[] blocks; delete[] BMPData; } };

 

 

1.6下采样代码

//这里直接把左上的点 当作subsampling的点了
//也可以取平均值
void JPG::subsampling() {
    //遍历mcu
    for (uint i = 0; i < mcuHeight; i++) {
        for (uint j = 0; j < mcuWidth; j++) {
//拿到mcu MCU
& currentMCU = data[i * mcuWidth + j];
//每个mcu起始的坐标点
uint heightOffset = i * maxVerticalSamplingFrequency * 8; uint widthOffset = j * maxHorizontalSamplingFrequency * 8; //iterate over 每一个component Y, cb cr for (uint componentID = 1; componentID <= 3; componentID++) { //遍历block, 从muc中拿block for(uint ii = 0, yOffSet = heightOffset; ii < getVerticalSamplingFrequency(componentID); ii++, yOffSet = yOffSet + 8) { for(uint jj = 0, xOffset = widthOffset; jj < getHorizontalSamplingFrequency(componentID); jj++, xOffset = xOffset + 8) {
//拿到具体的block对象 Block
& currentBlock = currentMCU[componentID][ii * getHorizontalSamplingFrequency(componentID) + jj]; //遍历Block every pixels 像素, 并且采样赋值 for(uint y = 0; y < 8; y++) { for(uint x = 0; x < 8; x++) {
//得到被采样的那个点的坐标
uint sampledY = yOffSet + y * maxVerticalSamplingFrequency / getVerticalSamplingFrequency(componentID); uint sampledX = xOffset + x * maxHorizontalSamplingFrequency / getHorizontalSamplingFrequency(componentID); //cannot find in original pictures; if(sampledX >= width || sampledY >= height) { currentBlock[y * 8 + x] = 0; } else { currentBlock[y * 8 + x] = BMPData[sampledY * width + sampledX][componentID]; } } } } } } } } }

完整代码  https://github.com/Cheemion/JPEG_COMPRESS/tree/main/Day2

完结

祝你开心每一天。

参考资料

[1]https://github.com/Cheemion/JPEG_COMPRESS/blob/main/resource/Compressed%20Image%20File%20Formats%20JPEG%2C%20PNG%2C%20GIF%2C%20XBM%2C%20BMP%20-%20John%20Miano.pdf

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