JPG学习笔记5（附完整代码）
JPG压缩的第4步是哈夫曼编码。下面主要介绍JPEG是如果进行哈夫曼编码的。
图片引用自"Compressed Image File Formats JPEG, PNG, GIF, XBM, BMP - John Miano"[1]
1.AC数据的哈夫曼Symbol.
对于AC数据而言，需要编码的前4位代表这个数据之前有多少个0，后4位代表当前值的Magnitude Value。
AC数据的编码是以ZigZag的顺序进行的。
如下图为例，从1开始前面有0个0， 数值大小为1, magnitude value为1，需要编码的symbol为0x01;
接着走到3处，前面有5个0，数值大小为3, magnitude value 为2，需要编码的symbol为0x52;
以此类推：
唯一有的2个额外的情况
0x00代表后面的数据都为0
0xF0代表16个0
总共的symbol数量 = (为0的个数)16 * 10(不同的maginitude) + 2 (特殊情况) = 162。
2.DC数据的哈夫曼Symbol
DC数据存的是difference，即当前Block的DC值减去上一个Block的DC值。
如下可知DC symbol总共有12个
3.JPEG默认哈夫曼编码
JPEG提供了默认的huffmanTable(emprically good)[2]，如下
引用"https://www.impulseadventure.com/photo/optimized-jpeg.html"
也可以自己根据图片生成huffmanCode,代码如下
void JPG::huffmanCoding() { /*****************************************创建yDC_Table*********************************************/ int lastYDC = 0; uint componentID = 1; //创建YDC_Table for (uint i = 0; i < mcuHeight; i++) { for (uint j = 0; j < mcuWidth; j++) { MCU& currentMCU = data[i * mcuWidth + j]; //iterate over 每一个component Y, cb cr //遍历block for(uint ii = 0; ii < getVerticalSamplingFrequency(componentID); ii++) { for(uint jj = 0; jj < getHorizontalSamplingFrequency(componentID); jj++) { Block& currentBlock = currentMCU[componentID][ii * getHorizontalSamplingFrequency(componentID) + jj]; int difference = currentBlock[0] - lastYDC; //DC分量是encode difference lastYDC = currentBlock[0]; byte symbol = getBinaryLengthByValue(difference); //Y的2进制的长度就是symbol的值 yDC.countOfSymbol[symbol]++; } } } } yDC.generateHuffmanCode(); /*****************************************创建 yAC_Table*********************************************/ for (uint i = 0; i < mcuHeight; i++) { for (uint j = 0; j < mcuWidth; j++) { MCU& currentMCU = data[i * mcuWidth + j]; //遍历block for(uint ii = 0; ii < getVerticalSamplingFrequency(componentID); ii++) { for(uint jj = 0; jj < getHorizontalSamplingFrequency(componentID); jj++) { Block& currentBlock = currentMCU[componentID][ii * getHorizontalSamplingFrequency(componentID) + jj]; uint numZero = 0; for(uint k = 1; k < 64; k++) { if(currentBlock[ZIG_ZAG[k]] == 0) { numZero++; if(numZero == 16) { if(isRemainingAllZero(currentBlock, k + 1)) { yAC.countOfSymbol[0x00]++; break; } else { yAC.countOfSymbol[0xF0]++;//16个0 numZero = 0; } } } else { byte lengthOfCoefficient = getBinaryLengthByValue(currentBlock[ZIG_ZAG[k]]); byte symbol = (numZero << 4) + lengthOfCoefficient; yAC.countOfSymbol[symbol]++; numZero = 0; } } } } } } yAC.generateHuffmanCode(); /*****************************************创建chromaDC_Table*********************************************/ int lastChromaDC = 0; for(uint componentID = 2; componentID <=3; componentID++) { for (uint i = 0; i < mcuHeight; i++) { for (uint j = 0; j < mcuWidth; j++) { MCU& currentMCU = data[i * mcuWidth + j]; //iterate over 每一个component Y, cb cr //遍历block for(uint ii = 0; ii < getVerticalSamplingFrequency(componentID); ii++) { for(uint jj = 0; jj < getHorizontalSamplingFrequency(componentID); jj++) { Block& currentBlock = currentMCU[componentID][ii * getHorizontalSamplingFrequency(componentID) + jj]; int difference = currentBlock[0] - lastChromaDC; //DC分量是encode difference lastChromaDC = currentBlock[0]; byte symbol = getBinaryLengthByValue(difference); //Y的2进制的长度就是symbol的值 chromaDC.countOfSymbol[symbol]++; } } } } } chromaDC.generateHuffmanCode(); /*****************************************创建chromaAC_Table*********************************************/ for(uint componentID = 2; componentID <=3; componentID++) { for (uint i = 0; i < mcuHeight; i++) { for (uint j = 0; j < mcuWidth; j++) { MCU& currentMCU = data[i * mcuWidth + j]; //遍历block for(uint ii = 0; ii < getVerticalSamplingFrequency(componentID); ii++) { for(uint jj = 0; jj < getHorizontalSamplingFrequency(componentID); jj++) { Block& currentBlock = currentMCU[componentID][ii * getHorizontalSamplingFrequency(componentID) + jj]; uint numZero = 0; for(uint k = 1; k < 64; k++) { if(currentBlock[ZIG_ZAG[k]] == 0) { numZero++; if(numZero == 16) { if(isRemainingAllZero(currentBlock, k + 1)) { chromaAC.countOfSymbol[0x00]++; break; } else { chromaAC.countOfSymbol[0xF0]++;//16个0 numZero = 0; } } } else { byte lengthOfCoefficient = getBinaryLengthByValue(currentBlock[ZIG_ZAG[k]]); byte symbol = (numZero << 4) + lengthOfCoefficient; chromaAC.countOfSymbol[symbol]++; numZero = 0; } } } } } } } chromaAC.generateHuffmanCode(); }
void generateHuffmanCode() { std::vector<LinkedSymbol> symbols; //遍历每个出现的symbol， add to vectors for(uint symbol = 0; symbol < 256; symbol++) { if(countOfSymbol[symbol] == 0) continue; Symbol* s = new Symbol(symbol, countOfSymbol[symbol], 0, nullptr); LinkedSymbol linkedSymbol; linkedSymbol.symbol = s; linkedSymbol.weight = s->weight; symbols.push_back(linkedSymbol); } // FF是一个不会出现的symbol,作为我们的dummy symbol 防止one bit stream 的出现 比如11111, 这样就可以防止compressdata中出现FF的可能 Symbol* dummySymbol = new Symbol(0xFF, 1, 0, nullptr); LinkedSymbol dymmyLinkedSymbol; dymmyLinkedSymbol.symbol = dummySymbol; dymmyLinkedSymbol.weight = dummySymbol->weight; symbols.push_back(dymmyLinkedSymbol); //合并的过程 while(symbols.size() != 1) { //leastWeight LinkedSymbol least = getLeastWeightLinkedSymbol(symbols); //second Least Weight LinkedSymbol second = getLeastWeightLinkedSymbol(symbols); //add two weights least.weight = least.weight + second.weight; //linked two linkedsymbols; Symbol* temp = second.symbol; while(temp->nextSymbol != nullptr) temp = temp->nextSymbol; temp->nextSymbol = least.symbol; least.symbol = second.symbol; //把每个symbol加1 codeLength,并且加入到 for(auto i = least.symbol; i != nullptr; i = i->nextSymbol) { i->codeLength++; } symbols.push_back(least); } //放入sortedSymbols for(Symbol* i = symbols[0].symbol; i != nullptr; i = i->nextSymbol) { sortedSymbol.push_back(*i); } //排序,并且把dummy symbol 放在最后面; std::sort(sortedSymbol.begin(), sortedSymbol.end(), comp); //释放内存 Symbol* temp = symbols[0].symbol; while(temp != nullptr) { auto t = temp->nextSymbol; delete temp; temp = t; } //长度为n的code的个数 //生成codeLengthCount for each codeLength; for (auto it = sortedSymbol.cbegin(); it != sortedSymbol.cend(); it++) { codeCountOfLength[it->codeLength]++; } //规定codeLength不能大于16, 套用书上的方法实现了一下 for(uint ii = 32; ii >= 17; ii--) { while(codeCountOfLength[ii] != 0) { uint jj = ii - 2; while(codeCountOfLength[jj] == 0) jj--; codeCountOfLength[ii] = codeCountOfLength[ii] - 2; codeCountOfLength[ii - 1] = codeCountOfLength[ii - 1] + 1; codeCountOfLength[jj + 1] = codeCountOfLength[jj + 1] + 2; codeCountOfLength[jj] = codeCountOfLength[jj] - 1; } } uint index = 1; //codeLength赋值回去 for (auto it = sortedSymbol.begin(); it != sortedSymbol.end(); it++) { if(codeCountOfLength[index] != 0) { it->codeLength = index; codeCountOfLength[index]--; } else { index++; it--; } } //生成huffmanCode for each symbol uint huffmanCode = 0; uint currentLength = 1; for (auto it = sortedSymbol.begin(); it != sortedSymbol.end(); it++) { if(currentLength == it->codeLength) { it->code = huffmanCode++; codeOfSymbol[it->symbol] = it->code; codeLengthOfSymbol[it->symbol] = it->codeLength; } else { huffmanCode = huffmanCode << 1; currentLength++; it--; } } }
全部代码在https://github.com/Cheemion/JPEG_COMPRESS/tree/main/Day5
完结
Thanks for reading.
>>>> （JPG学习笔记6）待续
参考资料
[2]https://www.impulseadventure.com/photo/optimized-jpeg.html
