介绍了如何利用得到的RGB信息重新对RGB图片进行编码，以及对其他图片如BMP所得到的RGB信息进行编码从而得到*.jpg文件。
1.转换色彩空间
我这里使用的RGB转YCbCr的公式如下：
double y = (0.299 * t.red + 0.587 * t.green + 0.114 * t.blue - 128); double cb = (-0.1687 * t.red - 0.3313 * t.green + 0.500 * t.blue); double cr = (0.500 * t.red - 0.4187 * t.green - 0.0813 * t.blue);
这里t的结构如下，如果要是还有Alpha这个值也可以添加进去
struct RGB{ uint8_t red; uint8_t green; uint8_t blue; };
2.离散余弦变化
使用矩阵乘法，转化那个DCT变换的公式，最后会得到 Y=AXA’ 这个公式A’是指A的转置，X是输入，Y是输出
矩阵A的获取方式如下：
double** JPEGData::createDCTAndIDCTArray(int row){ double** res=new double*[row]; for(int i=0;i<row;i++) res[i]=new double[row]; for(int i=0;i<row;i++){ for(int j=0;j<row;j++){ double t=0; if(i==0) t=sqrt(1.0/row); else t=sqrt(2.0/row); res[i][j]=t*cos(M_PI*(j+0.5)*i/row); } } return res; }
计算Y的方法如下：
void JPEGData::DCT(double** originMatrix){ //原理 Y=A*X*A' vector<vector<double>> temp(ROW,vector<double>(COL,0)); for(int i=0;i<ROW;i++){ for(int j=0;j<COL;j++){ double sum=0; for(int k=0;k<COL;k++){ sum+=DCTAndIDCTArray[i][k]*originMatrix[k][j]; } temp[i][j]=sum; } } for(int i=0;i<ROW;i++){ for(int j=0;j<COL;j++){ double sum=0; for(int k=0;k<COL;k++){ sum+=temp[i][k]*DCTAndIDCTArray[j][k]; } originMatrix[i][j]=sum; } } }
3.zigzag编码
此编码的目的是为了使更多的0聚到一起，从而压缩文件大小（我打断点发现我这里0里面经常会出现1）。编码方式是将88的矩阵变成164的矩阵。
4.量化
此步量化是对已经zigzag编码后的量化，就是对已经变成1×64的数组的变换，而对应的量化表如下，也是1×64的数组，对应项相乘即可
static uint8_t YQualityTable[64] = { 16, 11, 10, 16, 24, 40, 51, 61, 12, 12, 14, 19, 26, 58, 60, 55, 14, 13, 16, 24, 40, 57, 69, 56, 14, 17, 22, 29, 51, 87, 80, 62, 18, 22, 37, 56, 68, 109, 103, 77, 24, 35, 55, 64, 81, 104, 113, 92, 49, 64, 78, 87, 103, 121, 120, 101, 72, 92, 95, 98, 112, 100, 103, 99}; static uint8_t CQualityTable[64]={ 17, 18, 24, 47, 99, 99, 99, 99, 18, 21, 26, 66, 99, 99, 99, 99, 24, 26, 56, 99, 99, 99, 99, 99, 47, 66, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99 };
5.Huffman编码
（之前要差分编码和行程编码）
Huffman编码的直流和交流表如下：
static const uint8_t bits_dc_luminance[16] = {//亮度表 0, 1, 5, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0 }; static const uint8_t val_dc_luminance[] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 }; static const uint8_t bits_dc_chrominance[16] = {//色度表 0, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0 }; static const uint8_t val_dc_chrominance[] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 }; static const uint8_t bits_ac_luminance[16] = { 0, 2, 1, 3, 3, 2, 4, 3, 5, 5, 4, 4, 0, 0, 1, 0x7d }; static const uint8_t val_ac_luminance[] = { 0x01, 0x02, 0x03, 0x00, 0x04, 0x11, 0x05, 0x12, 0x21, 0x31, 0x41, 0x06, 0x13, 0x51, 0x61, 0x07, 0x22, 0x71, 0x14, 0x32, 0x81, 0x91, 0xa1, 0x08, 0x23, 0x42, 0xb1, 0xc1, 0x15, 0x52, 0xd1, 0xf0, 0x24, 0x33, 0x62, 0x72, 0x82, 0x09, 0x0a, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x3a, 0x43, 0x44, 0x45, 0x46, 0x47, 0x48, 0x49, 0x4a, 0x53, 0x54, 0x55, 0x56, 0x57, 0x58, 0x59, 0x5a, 0x63, 0x64, 0x65, 0x66, 0x67, 0x68, 0x69, 0x6a, 0x73, 0x74, 0x75, 0x76, 0x77, 0x78, 0x79, 0x7a, 0x83, 0x84, 0x85, 0x86, 0x87, 0x88, 0x89, 0x8a, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97, 0x98, 0x99, 0x9a, 0xa2, 0xa3, 0xa4, 0xa5, 0xa6, 0xa7, 0xa8, 0xa9, 0xaa, 0xb2, 0xb3, 0xb4, 0xb5, 0xb6, 0xb7, 0xb8, 0xb9, 0xba, 0xc2, 0xc3, 0xc4, 0xc5, 0xc6, 0xc7, 0xc8, 0xc9, 0xca, 0xd2, 0xd3, 0xd4, 0xd5, 0xd6, 0xd7, 0xd8, 0xd9, 0xda, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7, 0xe8, 0xe9, 0xea, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5, 0xf6, 0xf7, 0xf8, 0xf9, 0xfa }; static const uint8_t bits_ac_chrominance[16] = { 0, 2, 1, 2, 4, 4, 3, 4, 7, 5, 4, 4, 0, 1, 2, 0x77 }; static const uint8_t val_ac_chrominance[] = { 0x00, 0x01, 0x02, 0x03, 0x11, 0x04, 0x05, 0x21, 0x31, 0x06, 0x12, 0x41, 0x51, 0x07, 0x61, 0x71, 0x13, 0x22, 0x32, 0x81, 0x08, 0x14, 0x42, 0x91, 0xa1, 0xb1, 0xc1, 0x09, 0x23, 0x33, 0x52, 0xf0, 0x15, 0x62, 0x72, 0xd1, 0x0a, 0x16, 0x24, 0x34, 0xe1, 0x25, 0xf1, 0x17, 0x18, 0x19, 0x1a, 0x26, 0x27, 0x28, 0x29, 0x2a, 0x35, 0x36, 0x37, 0x38, 0x39, 0x3a, 0x43, 0x44, 0x45, 0x46, 0x47, 0x48, 0x49, 0x4a, 0x53, 0x54, 0x55, 0x56, 0x57, 0x58, 0x59, 0x5a, 0x63, 0x64, 0x65, 0x66, 0x67, 0x68, 0x69, 0x6a, 0x73, 0x74, 0x75, 0x76, 0x77, 0x78, 0x79, 0x7a, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87, 0x88, 0x89, 0x8a, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97, 0x98, 0x99, 0x9a, 0xa2, 0xa3, 0xa4, 0xa5, 0xa6, 0xa7, 0xa8, 0xa9, 0xaa, 0xb2, 0xb3, 0xb4, 0xb5, 0xb6, 0xb7, 0xb8, 0xb9, 0xba, 0xc2, 0xc3, 0xc4, 0xc5, 0xc6, 0xc7, 0xc8, 0xc9, 0xca, 0xd2, 0xd3, 0xd4, 0xd5, 0xd6, 0xd7, 0xd8, 0xd9, 0xda, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7, 0xe8, 0xe9, 0xea, 0xf2, 0xf3, 0xf4, 0xf5, 0xf6, 0xf7, 0xf8, 0xf9, 0xfa };
依据这几个表可以得出4个Huffman表，两个直流和两个交流表。
然后就要写数据了，真正压缩数据前面的部分我就不写了，看后面的代码吧，直接开始压缩数据如何编码。
到此步骤你已经得到了一个MCU的数据一次要写一个MCU，直流分量重置间隔默认为图片一行的MCU数量
这里要注意几点：
第一，要对直流分量进行差分编码，对交流分量进行形成编码
第二，如果写入的一个字节是0xFF，这是段标识所以要在此字节后面加入一个字节的0x00
第三，如果一行的MCU都写入完毕，接下来写入DRI，那就需要把上一个MCU没写入的部分写入，例如上一个MCU写入的字节多了两位11，那就写入一个字节0b11000000，然后写入两个字节的DRI标识
第四，写入的数据中有负数，比如写入-2，那对应就应该写入0b01，可使用如下方法得到对应的值
len = bitLength((int)abs(val)) pow(2, len) + val - 1
数据编码部分，要用写入数据有多少位查找对应的Huffman编码，先写入Huffman编码，再写入数据，直流交流均如此。
直流部分要使用差分编码，写入的数据是上一个DC值减去此DC值的差值
交流部分要使用行程编码，因为之前的操作大部分数据都变成0了，所以行程编码很合适，然后将有多少0和数据有多少位作为权重查找Huffman编码。
我将上述步骤都写到一起了，一次处理一个MCU并写入
bool JPEGData::writeJPEG(const char* filePath, int samp_factor[3][2], int quality_scale){ auto _rgb = getRGBMatrix(); max_h_samp_factor=0; max_v_samp_factor=0; for(int i=0;i<3;i++){ write_samp_factor[i][0]=samp_factor[i][0]; write_samp_factor[i][1]=samp_factor[i][1]; max_h_samp_factor=max(max_h_samp_factor,write_samp_factor[i][0]); max_v_samp_factor=max(max_v_samp_factor,write_samp_factor[i][1]); } initQualityTable(quality_scale); fstream file(filePath,ios::out|ios::binary); if(file.fail()) return false; try{ createDCEnHuffman(); createACEnHuffman(); writeTwoByte(file, (uint16_t)((FLAG << 8) + SOI)); // SOI for(int i=0;i<18;i++){ //APP writeByte(file, APP[i]); } JPEGQuality::write(file); // DQT writeTwoByte(file, (uint16_t)((FLAG << 8) + SOF0)); // SOF writeTwoByte(file, (uint16_t)0x0011); writeByte(file, (uint8_t)0x08); writeTwoByte(file, (uint16_t)height); writeTwoByte(file, (uint16_t)width); writeByte(file, (uint8_t)0x03); writeByte(file, (uint8_t)0x01); writeByte(file, (uint8_t)((samp_factor[0][0] << 4) | samp_factor[0][1])); writeByte(file, (uint8_t)0x00); writeByte(file, (uint8_t)0x02); writeByte(file, (uint8_t)((samp_factor[1][0] << 4) | samp_factor[1][1])); writeByte(file, (uint8_t)0x01); writeByte(file, (uint8_t)0x03); writeByte(file, (uint8_t)((samp_factor[2][0] << 4) | samp_factor[2][1])); writeByte(file, (uint8_t)0x01); JPEGHuffmanCode::write(file); // DHT writeTwoByte(file, (uint16_t)((FLAG << 8) + DRI)); // DRI writeTwoByte(file, (uint16_t)0x0004); writeTwoByte(file, (uint16_t)ceil(_rgb.col * 1.0 / (ROW * max_h_samp_factor))); writeTwoByte(file, (uint16_t)((FLAG<<8)+SOS)); // SOS writeTwoByte(file, (uint16_t)0x000C); writeByte(file, (uint8_t)0x03); writeByte(file, (uint8_t)0x01); writeByte(file, (uint8_t)0x00); writeByte(file, (uint8_t)0x02); writeByte(file, (uint8_t)0x11); writeByte(file, (uint8_t)0x03); writeByte(file, (uint8_t)0x11); writeByte(file, (uint8_t)0); writeByte(file, (uint8_t)0x3F); writeByte(file, (uint8_t)0); RGBToYCbCr(_rgb, file); writeTwoByte(file, (uint16_t)((FLAG << 8) + (uint8_t)JPEGPType::EOI)); // EOI } catch(...){ file.close(); return false; } file.close(); return true; } void JPEGData::RGBToYCbCr(Matrix<RGB> _rgb, fstream& file){ // vector<double*> res; int mcu_width = COL * max_h_samp_factor, mcu_height = ROW * max_v_samp_factor; int YUV[3] = {write_samp_factor[0][0] * write_samp_factor[0][1], write_samp_factor[1][0] * write_samp_factor[1][1], write_samp_factor[2][0] * write_samp_factor[2][1]}; int y_h_param = max_h_samp_factor * 1.0 / write_samp_factor[0][0], y_v_param = max_v_samp_factor * 1.0 / write_samp_factor[0][1], cb_h_param = max_h_samp_factor * 1.0 / write_samp_factor[1][0], cb_v_param = max_v_samp_factor * 1.0 / write_samp_factor[1][1], cr_h_param = max_h_samp_factor * 1.0 / write_samp_factor[2][0], cr_v_param = max_v_samp_factor * 1.0 / write_samp_factor[2][1]; double cb_h_samp_scale=write_samp_factor[1][0]*1.0/max_h_samp_factor, cb_v_samp_scale=write_samp_factor[1][1]*1.0/max_v_samp_factor, cr_h_samp_scale=write_samp_factor[2][0]*1.0/max_h_samp_factor, cr_v_samp_scale=write_samp_factor[2][1]*1.0/max_v_samp_factor; preDCValue[0] = preDCValue[1] = preDCValue[2] = 0; mcu_rows = ceil(_rgb.row * 1.0 / mcu_height); mcu_cols = ceil(_rgb.col * 1.0 / mcu_width); int DRI = mcu_cols, DriFLAG = 0xD0; for (int mcu_y = 0; mcu_y < mcu_rows; mcu_y++) { for (int mcu_x = 0; mcu_x < mcu_cols; mcu_x++) { double ***yuv = new double **[YUV[0] + YUV[1] + YUV[2]]; int count=0; for (int i = 0; i < 3; i++) { for (int j = 0; j < YUV[i]; j++) { yuv[count] = new double *[ROW]; for (int k = 0; k < ROW; k++) { yuv[count][k] = new double[COL]; memset(yuv[count][k], 0, sizeof(double) * COL); } count++; } } int row = mcu_y * mcu_height, col = mcu_x * mcu_width; // cout<<dec<<"("<<row<<","<<col<<") "; for (int i = 0; i < mcu_height; i++) { for (int j = 0; j < mcu_width; j++) { RGB t = _rgb.getValue(row + i, col + j); // 得到的是一整个mcu，但是要把它分成多个8*8矩阵 double y = YCbCrValueLimit(0.299 * t.red + 0.587 * t.green + 0.114 * t.blue - 128); double cb = YCbCrValueLimit(-0.1687 * t.red - 0.3313 * t.green + 0.500 * t.blue); double cr = YCbCrValueLimit(0.500 * t.red - 0.4187 * t.green - 0.0813 * t.blue); int yPos = (i / ROW) * max_h_samp_factor + (j / COL); int cbPos = YUV[0] + (int)((j / COL) * cb_v_samp_scale) + (int)((i / ROW) * cb_h_samp_scale); int crPos = YUV[0] + YUV[1] + (int)((j / COL) * cr_v_samp_scale) + (int)((i / ROW) * cr_h_samp_scale); if (i % y_v_param == 0 && j % y_h_param == 0) yuv[yPos][i % ROW][j % COL] = y; if (i % cb_v_param == 0 && j % cb_h_param == 0) yuv[cbPos][i / cb_v_param][j / cb_h_param] = cb; if (i % cr_v_param == 0 && j % cr_h_param == 0) yuv[crPos][i / cr_v_param][j / cr_h_param] = cr; // cout<<dec<<"("<<(int)y<<","<<(int)cb<<","<<(int)cr<<")"<<" "; } // cout<<endl; } // cout<<endl; int pos = 0; for (int i = 0; i < 3; i++) { int huffmanID = i == 0 ? 0 : 1; for (int j = 0; j < YUV[i]; j++, pos++) { DCT(yuv[pos]); double *temp = ZigZag(yuv[pos]); //encode DC temp[0] = round(temp[0] / (i == 0 ? YQualityTable[0] : CQualityTable[0])); //quality int dcDiff = temp[0] - preDCValue[i];// 进行差分编码 int lenDC=getBitLength((int)abs(dcDiff)); preDCValue[i] = temp[0]; if (dcDiff < 0) dcDiff = pow(2, lenDC) + dcDiff - 1; writeBit(file, lenDC, dcDiff, en_dc_huffman[huffmanID].table[lenDC]); //encode AC int endPos = 63; while(endPos>0&&temp[endPos]==0) endPos--; for(int k=1;k<=endPos;k++){ int zeroCount = 0; temp[k] = round(temp[k] / (i == 0 ? YQualityTable[k] : CQualityTable[k]));//quality while (k < endPos && temp[k] == 0) { temp[k + 1] = round(temp[k + 1] / (i == 0 ? YQualityTable[k + 1] : CQualityTable[k + 1])); zeroCount++; k++; } int lenAC = getBitLength((int)abs(temp[k])); if (temp[k] < 0) temp[k] = pow(2, lenAC) + temp[k] - 1; while(zeroCount>=16){ writeBitToFile(file,en_ac_huffman[huffmanID].table[0xf0].second, en_ac_huffman[huffmanID].table[0xf0].first); zeroCount -= 16; } writeBit(file, lenAC, temp[k], en_ac_huffman[huffmanID].table[(zeroCount << 4) | lenAC]); zeroCount = 0; } if(endPos!=63) writeBitToFile(file, en_ac_huffman[huffmanID].table[0x00].second, en_ac_huffman[huffmanID].table[0x00].first); } } FREE_LP_3(yuv, YUV[0] + YUV[1] + YUV[2], ROW) } // cout<<endl; if (bitCurPos != 0) writeByte(file, (uint8_t)curBitValue); bitCurPos = curBitValue = 0; preDCValue[0] = preDCValue[1] = preDCValue[2] = 0; writeTwoByte(file, (uint16_t)((FLAG << 8) + DriFLAG++)); if (DriFLAG > 0xD7) DriFLAG = 0xD0; } } void JPEGQuality::write(fstream &file){ writeByte(file, FLAG); writeByte(file, DQT); writeTwoByte(file, (uint16_t)0x0043); writeByte(file, (uint8_t)0x00); for(int i=0;i<64;i++){ writeByte(file, YQualityTable[i]); } writeByte(file, FLAG); writeByte(file, DQT); writeTwoByte(file, (uint16_t)0x0043); writeByte(file, (uint8_t)0x01); for(int i=0;i<64;i++){ writeByte(file, CQualityTable[i]); } } void JPEGHuffmanCode::write(fstream &file){ // Y dc writeByte(file, (uint8_t)FLAG); writeByte(file, (uint8_t)DHT); writeTwoByte(file, (uint16_t)0x001F); writeByte(file, (uint8_t)0x00); for(int i=0;i<16;i++) writeByte(file, bits_dc_luminance[i]); for(int i=0;i<12;i++) writeByte(file, val_dc_luminance[i]); // Y ac writeByte(file, (uint8_t)FLAG); writeByte(file, (uint8_t)DHT); writeTwoByte(file, (uint16_t)0x00B5); writeByte(file, (uint8_t)0x10); for(int i=0;i<16;i++) writeByte(file, bits_ac_luminance[i]); for(int i=0;i<162;i++) writeByte(file, val_ac_luminance[i]); // UV dc writeByte(file, (uint8_t)FLAG); writeByte(file, (uint8_t)DHT); writeTwoByte(file, (uint16_t)0x001F); writeByte(file, (uint8_t)0x01); for(int i=0;i<16;i++) writeByte(file, bits_dc_chrominance[i]); for(int i=0;i<12;i++) writeByte(file, val_dc_chrominance[i]); // UV ac writeByte(file, (uint8_t)FLAG); writeByte(file, (uint8_t)DHT); writeTwoByte(file, (uint16_t)0x00B5); writeByte(file, (uint8_t)0x11); for(int i=0;i<16;i++) writeByte(file, bits_ac_chrominance[i]); for(int i=0;i<162;i++) writeByte(file, val_ac_chrominance[i]); } static int bitCurPos = 0; // 当前字节在哪个bit位 static int curBitValue = 0; // 当前值是多少 void writeBitToFile(fstream& file,int len,int realData){ while (len > (8 - bitCurPos)) { int rightMoveBit = len + bitCurPos - 8; int bitValue = realData >> rightMoveBit; curBitValue |= bitValue; writeByte(file, (uint8_t)curBitValue); if (curBitValue == 0xFF) writeByte(file, (uint8_t)0); realData -= bitValue << rightMoveBit; len -= 8 - bitCurPos; curBitValue = bitCurPos = 0; } curBitValue |= realData << (8 - bitCurPos - len); bitCurPos += len; if (bitCurPos >= 8) { writeByte(file, (uint8_t)curBitValue); if (curBitValue == 0xFF) writeByte(file, (uint8_t)0); curBitValue = bitCurPos = 0; } } void writeBit(fstream& file,int len, int realData,pair<uint16_t,uint8_t>& huffmanCode){ int codeLen=huffmanCode.second,code=huffmanCode.first; writeBitToFile(file, codeLen, code); writeBitToFile(file, len, realData); } double* ZigZag(double** originArray){ double* res=new double[ROW*COL]; // for(int i=0;i<64;i++){ // res[Zig[i]]=originArray[i/ROW][i%COL]; // } int cur=0,x=0,y=0; bool flag = true;//true是右上 false是左下 while (cur < 64) { res[cur++] = round(originArray[y][x]); if (flag) { x++; y--; } else { x--; y++; } if (x < 0 || y < 0 || x>7 || y>7) flag = !flag; if (x < 0 && y>7) { x = 1; y = 7; } if (x < 0) x = 0; else if (x > 7) { x = 7; y += 2; } if (y < 0) y = 0; else if (y > 7) { y = 7; x += 2; } } return res; } void writeByte(fstream& file,uint8_t val){ file.write((char*)&val, 1); // cout<<hex<<(int)val<<" "; } void writeTwoByte(fstream& file,uint16_t val){ writeByte(file, val>>8); writeByte(file, val&0xFF); } int getBitLength(int num){ int res=0; while(num){ res+=1; num>>=1; } return res; } double YCbCrValueLimit(double input){ if(input<-128) return -128; else if(input>128) return 128; return input; } //段类型 enum JPEGPType{ SOF0 = 0xC0, //帧开始 SOF1 = 0xC1, //帧开始 SOF2 = 0xC2, //帧开始 DHT = 0xC4, //哈夫曼表 SOI = 0xD8, //文件头 EOI = 0xD9, //文件尾 SOS = 0xDA, //扫描行开始 DQT = 0xDB, //定义量化表 DRI = 0xDD, //定义重新开始间隔 APP0 = 0xE0, //定义交换格式和图像识别信息 APP1 = 0xE1, //定义交换格式和图像识别信息 APP2 = 0xE2, //定义交换格式和图像识别信息 COM = 0xFE, //注释 FLAG = 0xFF //开始 };
