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干货第一时间送达

本文由知乎作者David LEE授权转载，不得擅自二次转载。原文链接：https://zhuanlan.zhihu.com/p/53060518

Opencv里的SGBM算法，之所以叫SGBM是因为opencv并没有使用MI作为匹配代价，而是仍然使用了块匹配的方法，相关cost的度量为Birchfield-Tomasi metric。而且opencv提供了多种cost aggregation的方式，包括只使用3个、5个或全部8个方向的方法。总体上的实现也比较直观，结合论文也比较好懂。

对于理论就不再赘述了，这里就直接探讨opencv中关于SGBM的源代码。

/* computes disparity for "roi" in img1 w.r.t. img2 and write it to disp1buf. that is, disp1buf(x, y)=d means that img1(x+roi.x, y+roi.y) ~ img2(x+roi.x-d, y+roi.y). minD <= d < maxD. disp2full is the reverse disparity map, that is: disp2full(x+roi.x,y+roi.y)=d means that img2(x+roi.x, y+roi.y) ~ img1(x+roi.x+d, y+roi.y) note that disp1buf will have the same size as the roi and disp2full will have the same size as img1 (or img2). On exit disp2buf is not the final disparity, it is an intermediate result that becomes final after all the tiles are processed. the disparity in disp1buf is written with sub-pixel accuracy (4 fractional bits, see StereoSGBM::DISP_SCALE), using quadratic interpolation, while the disparity in disp2buf is written as is, without interpolation. disp2cost also has the same size as img1 (or img2). It contains the minimum current cost, used to find the best disparity, corresponding to the minimal cost. */static void computeDisparitySGBM( const Mat& img1, const Mat& img2,Mat& disp1, const StereoSGBMParams& params,Mat& buffer ){const int ALIGN = 16;const int DISP_SHIFT = StereoMatcher::DISP_SHIFT;const int DISP_SCALE = (1 << DISP_SHIFT);const CostType MAX_COST = SHRT_MAX;int minD = params.minDisparity, maxD = minD + params.numDisparities;Size SADWindowSize;SADWindowSize.width = SADWindowSize.height = params.SADWindowSize > 0 ? params.SADWindowSize : 5;int ftzero = std::max(params.preFilterCap, 15) | 1;int uniquenessRatio = params.uniquenessRatio >= 0 ? params.uniquenessRatio : 10;int disp12MaxDiff = params.disp12MaxDiff > 0 ? params.disp12MaxDiff : 1; // consisit check 所允许的最大差异    int P1 = params.P1 > 0 ? params.P1 : 2, P2 = std::max(params.P2 > 0 ? params.P2 : 5, P1+1);int k, width = disp1.cols, height = disp1.rows;int minX1 = std::max(maxD, 0), maxX1 = width + std::min(minD, 0);int D = maxD - minD, width1 = maxX1 - minX1; // 视差值的有效搜索范围    int INVALID_DISP = minD - 1, INVALID_DISP_SCALED = INVALID_DISP*DISP_SCALE;int SW2 = SADWindowSize.width/2, SH2 = SADWindowSize.height/2;bool fullDP = params.mode == StereoSGBM::MODE_HH;int npasses = fullDP ? 2 : 1;const int TAB_OFS = 256*4, TAB_SIZE = 256 + TAB_OFS*2;PixType clipTab[TAB_SIZE];// 同stereoBM, xsobel索引表    for( k = 0; k < TAB_SIZE; k++ )clipTab[k] = (PixType)(std::min(std::max(k - TAB_OFS, -ftzero), ftzero) + ftzero);if( minX1 >= maxX1 ){disp1 = Scalar::all(INVALID_DISP_SCALED);return;}CV_Assert( D % 16 == 0 );// NR - the number of directions. the loop on x below that computes Lr assumes that NR == 8.    // if you change NR, please, modify the loop as well.    int D2 = D+16, NRD2 = NR2*D2;// the number of L_r(.,.) and min_k L_r(.,.) lines in the buffer:    // for 8-way dynamic programming we need the current row and    // the previous row, i.e. 2 rows in total    const int NLR = 2;const int LrBorder = NLR - 1;// for each possible stereo match (img1(x,y) <=> img2(x-d,y))    // we keep pixel difference cost (C) and the summary cost over NR directions (S).    // we also keep all the partial costs for the previous line L_r(x,d) and also min_k L_r(x, k)    size_t costBufSize = width1*D;size_t CSBufSize = costBufSize*(fullDP ? height : 1); // cost aggregation 采用8个方向的话则需要WHD大小的内存    size_t minLrSize = (width1 + LrBorder*2)*NR2, LrSize = minLrSize*D2; // minLr 存储最优视差对应的最小cost，大小为有效宽度（再加2）乘以8个方向                                  // Lr 在此基础上需要存储160个视差值所对应的全部cost。                                   // DP 算法每次只用到上一行或下一行的信息，因此只保留两行的数据，最后乘以NR2    int hsumBufNRows = SH2*2 + 2; // 一个匹配窗口所包含的行数再加1，方便滑动窗口法每次多算一行    size_t totalBufSize = (LrSize + minLrSize)*NLR*sizeof(CostType) + // minLr[] and Lr[]    costBufSize*(hsumBufNRows + 1)*sizeof(CostType) + // hsumBuf, pixdiff // costBufSize * 1 是pixeldiff的内存大小，一行各个像素的所有可能视差值对应的cost                           // costBufSize * hsumBufNRows 是hsumBuf的内存大小，滑动窗口内各行的像素对应的所有视差值的cost    CSBufSize*2*sizeof(CostType) + // C, S  // C 和S 都需要保存WHD个计算结果    width*16*img1.channels()*sizeof(PixType) + // temp buffer for computing per-pixel cost    width*(sizeof(CostType) + sizeof(DispType)) + 1024; // disp2cost + disp2if( buffer.empty() || !buffer.isContinuous() ||buffer.cols*buffer.rows*buffer.elemSize() < totalBufSize )buffer.reserveBuffer(totalBufSize);// summary cost over different (nDirs) directions    CostType* Cbuf = (CostType*)alignPtr(buffer.ptr(), ALIGN); // C    CostType* Sbuf = Cbuf + CSBufSize; // SCostType* hsumBuf = Sbuf + CSBufSize;CostType* pixDiff = hsumBuf + costBufSize*hsumBufNRows;CostType* disp2cost = pixDiff + costBufSize + (LrSize + minLrSize)*NLR; // 预留给hsumBuf, Lr[]和minLr[]    DispType* disp2ptr = (DispType*)(disp2cost + width);PixType* tempBuf = (PixType*)(disp2ptr + width);// add P2 to every C(x,y). it saves a few operations in the inner loops    for(k = 0; k < (int)CSBufSize; k++ )Cbuf[k] = (CostType)P2;for( int pass = 1; pass <= npasses; pass++ ){int x1, y1, x2, y2, dx, dy;if( pass == 1 ) // 正向遍历，先计算正向遍历可以计算的4个方向的Lr和minLr，并保存结果在C和S中        {y1 = 0; y2 = height; dy = 1;x1 = 0; x2 = width1; dx = 1;}else // 逆序遍历        {y1 = height-1; y2 = -1; dy = -1;x1 = width1-1; x2 = -1; dx = -1;}// 处理方向变化时重新分配指针        CostType *Lr[NLR]={0}, *minLr[NLR]={0};for( k = 0; k < NLR; k++ ){// shift Lr[k] and minLr[k] pointers, because we allocated them with the borders,            // and will occasionally use negative indices with the arrays            // we need to shift Lr[k] pointers by 1, to give the space for d=-1.            // however, then the alignment will be imperfect, i.e. bad for SSE,            // thus we shift the pointers by 8 (8*sizeof(short) == 16 - ideal alignment)            Lr[k] = pixDiff + costBufSize + LrSize*k + NRD2*LrBorder + 8;// 8是为了sse优化，NRD2 * LrBorder 是边界一个像素8个方向的所有视差值对应的大小            memset( Lr[k] - LrBorder*NRD2 - 8, 0, LrSize*sizeof(CostType) );minLr[k] = pixDiff + costBufSize + LrSize*NLR + minLrSize*k + NR2*LrBorder;memset( minLr[k] - LrBorder*NR2, 0, minLrSize*sizeof(CostType) );}for( int y = y1; y != y2; y += dy ){int x, d;DispType* disp1ptr = disp1.ptr<DispType>(y); // 视差图第y行            CostType* C = Cbuf + (!fullDP ? 0 : y*costBufSize); // 跳过前y行            CostType* S = Sbuf + (!fullDP ? 0 : y*costBufSize);if( pass == 1 ) // compute C on the first pass, and reuse it on the second pass, if any.            {int dy1 = y == 0 ? 0 : y + SH2, dy2 = y == 0 ? SH2 : dy1;for( k = dy1; k <= dy2; k++ ) // y = 0，先把滑动窗口第上半部分计算好存储在hsumBuf中                                              // y != 0，计算y + SH2行                {// 类似于stereoBM，保存并复用计算结果                    CostType* hsumAdd = hsumBuf + (std::min(k, height-1) % hsumBufNRows)*costBufSize;if( k < height ){// 计算第k行，每个像素的所有视差值的cost                        calcPixelCostBT( img1, img2, k, minD, maxD, pixDiff, tempBuf, clipTab, TAB_OFS, ftzero );memset(hsumAdd, 0, D*sizeof(CostType));for( x = 0; x <= SW2*D; x += D ) // 累加左半边窗口的cost                        {int scale = x == 0 ? SW2 + 1 : 1; // 第一行要加SW2 + 1次，因为第一个窗口从第一列开始，取不到前面的列就需要累加第一列                                                              // 后面相减 (pixSub) 也是一样的                            for( d = 0; d < D; d++ )hsumAdd[d] = (CostType)(hsumAdd[d] + pixDiff[x + d]*scale); // 累加当前行前SW2 + 1个像素每个视差值的cost                        }if( y > 0 ){// 滑动窗口法                            const CostType* hsumSub = hsumBuf + (std::max(y - SH2 - 1, 0) % hsumBufNRows)*costBufSize; // 所要减去的对应行                            const CostType* Cprev = !fullDP || y == 0 ? C : C - costBufSize; // 上一行的Cfor( x = D; x < width1*D; x += D ){const CostType* pixAdd = pixDiff + std::min(x + SW2*D, (width1-1)*D); // 所要加上和减去的列                                const CostType* pixSub = pixDiff + std::max(x - (SW2+1)*D, 0);{for( d = 0; d < D; d++ ){// 滑动窗口法                                        int hv = hsumAdd[x + d] = (CostType)(hsumAdd[x - D + d] + pixAdd[d] - pixSub[d]);// 当前行某个像素视差为d的cost为上一行对应的cost加上该像素匹配的cost                                        C[x + d] = (CostType)(Cprev[x + d] + hv - hsumSub[x + d]);}}}}else{for( x = D; x < width1*D; x += D ) // 开始对第0行进行计算，直到最后一个像素                            {const CostType* pixAdd = pixDiff + std::min(x + SW2*D, (width1-1)*D); // 前面累加了当前行前SW2个像素，现在从第SW2 + 1个像素开始累加                                const CostType* pixSub = pixDiff + std::max(x - (SW2+1)*D, 0); // 从-SW2列开始减去for( d = 0; d < D; d++ ) // 当前像素y = 0, x = x / D 的所有视差值                                    hsumAdd[x + d] = (CostType)(hsumAdd[x - D + d] + pixAdd[d] - pixSub[d]); // 滑动窗口，列方向上减去上一列，加上下一列                            }}}if( y == 0 ) // 针对第一行，初始化C                                 // 后面行的C 都需要前一行的信息                    {int scale = k == 0 ? SH2 + 1 : 1; // 第一行需要多加8次，因为后面的窗口从第一行开始，取不到前面的行就需要累加第一行的值                                                          // 后面相减 (pixSub) 也是一样的                        for( x = 0; x < width1*D; x++ )C[x] = (CostType)(C[x] + hsumAdd[x]*scale);}}// also, clear the S buffer                for( k = 0; k < width1*D; k++ )S[k] = 0;}// clear the left and the right borders            // 置0处理，一方面防止后面的数组越界，一方面方便后续累加            memset( Lr[0] - NRD2*LrBorder - 8, 0, NRD2*LrBorder*sizeof(CostType) );memset( Lr[0] + width1*NRD2 - 8, 0, NRD2*LrBorder*sizeof(CostType) );memset( minLr[0] - NR2*LrBorder, 0, NR2*LrBorder*sizeof(CostType) );memset( minLr[0] + width1*NR2, 0, NR2*LrBorder*sizeof(CostType) );/*             [formula 13 in the paper]             compute L_r(p, d) = C(p, d) +             min(L_r(p-r, d),             L_r(p-r, d-1) + P1,             L_r(p-r, d+1) + P1,             min_k L_r(p-r, k) + P2) - min_k L_r(p-r, k)             where p = (x,y), r is one of the directions.             we process all the directions at once:             0: r=(-dx, 0)             1: r=(-1, -dy)             2: r=(0, -dy)             3: r=(1, -dy)             4: r=(-2, -dy)             5: r=(-1, -dy*2)             6: r=(1, -dy*2)             7: r=(2, -dy)             */// y 处理完，开始处理x            for( x = x1; x != x2; x += dx ) // 注意pass = npass (2) 时为逆序            {int xm = x*NR2, xd = xm*D2;// 待处理的4个方向的前一个像素与当前像素视差值相差大于2时的cost                // 待处理的4个方向对英语官方注释中的0～3。注意dx, dy的符号                int delta0 = minLr[0][xm - dx*NR2] + P2, delta1 = minLr[1][xm - NR2 + 1] + P2;int delta2 = minLr[1][xm + 2] + P2, delta3 = minLr[1][xm + NR2 + 3] + P2;// 待处理的4个方向的Lr的指针                // NRD2为视差范围*方向数，减去后对应前一个像素所有8个方向的所有视差值所对应的Lr值。Lr从第0个方向开始存储                // D2的值为视差范围，每加上一个D2就意味着跳过一个方向                // 与前面的delta对应，但数组下标差D2倍，因为minLr存储的是8个方向的Lr的8个最小值，而Lr存储 8*视差范围 的所有值                /* 1 2 3                   0 x 0                   1 2 3 */CostType* Lr_p0 = Lr[0] + xd - dx*NRD2; // pass = 1, dx = 1，为当前行上一列像素Lr的第0个方向                                                        // pass = 2, dx = -1，为当前行下一列像素Lr的第0个方向                CostType* Lr_p1 = Lr[1] + xd - NRD2 + D2; // pass = 1，上一行上一列像素的Lr的第1个方向                                                          // pass = 2，下一行上一列像素的Lr的第1个方向                CostType* Lr_p2 = Lr[1] + xd + D2*2; // pass = 1，上一行当前列像素Lr的第2个方向                                                     // pass = 2，下一行当前列像素Lr的地2个方向                CostType* Lr_p3 = Lr[1] + xd + NRD2 + D2*3; // pass = 1，上一行下一列像素Lr的第3个方向                                                            // pass = 2，下一行下一列像素Lr的第3个方向// 解释：pass = 1时好理解。当pass = 2时，从最后一行的最后一列开始逆序处理。由于最后一行只能在正向遍历时计算出前4个方向的Lr值，                // 因此再处理倒数第二行时，只能访问下一行当前4个方向的Lr。                // 当pass = 2时，第一个方向Lr_p0，正序处理时它应该是上一列的像素，而逆序处理时应该是下一列的像素，因此由dx控制方向。                // 而行方向上上下行的差异在处理完分别交换Lr, minLr内的指针时就处理好了。                // 之后，倒数第二行开始逆序处理时，其计算结果也更新在了Lr的前4个方向中，相当于把正序处理时的结果覆盖了。                // 但因为用不到了，只要S能够正确累加被覆盖也没有关系                Lr_p0[-1] = Lr_p0[D] = Lr_p1[-1] = Lr_p1[D] =Lr_p2[-1] = Lr_p2[D] = Lr_p3[-1] = Lr_p3[D] = MAX_COST; // 将多申请的前后两个视差值置为最大cost，为后面循环中的数组越界做准备CostType* Lr_p = Lr[0] + xd; // 将指针调节至当前像素                const CostType* Cp = C + x*D;CostType* Sp = S + x*D;{int minL0 = MAX_COST, minL1 = MAX_COST, minL2 = MAX_COST, minL3 = MAX_COST;for( d = 0; d < D; d++ ){// 4个方向的 相同disp的cost 和 不同disp加上惩罚值后的cost 的计算                        int Cpd = Cp[d], L0, L1, L2, L3;L0 = Cpd + std::min((int)Lr_p0[d], std::min(Lr_p0[d-1] + P1, std::min(Lr_p0[d+1] + P1, delta0))) - delta0;L1 = Cpd + std::min((int)Lr_p1[d], std::min(Lr_p1[d-1] + P1, std::min(Lr_p1[d+1] + P1, delta1))) - delta1;L2 = Cpd + std::min((int)Lr_p2[d], std::min(Lr_p2[d-1] + P1, std::min(Lr_p2[d+1] + P1, delta2))) - delta2;L3 = Cpd + std::min((int)Lr_p3[d], std::min(Lr_p3[d-1] + P1, std::min(Lr_p3[d+1] + P1, delta3))) - delta3;// 存储对应的Lr值并获取各个方向的minLr                        Lr_p[d] = (CostType)L0;minL0 = std::min(minL0, L0);Lr_p[d + D2] = (CostType)L1;minL1 = std::min(minL1, L1);Lr_p[d + D2*2] = (CostType)L2;minL2 = std::min(minL2, L2);Lr_p[d + D2*3] = (CostType)L3;minL3 = std::min(minL3, L3);// 累加到S                        Sp[d] = saturate_cast<CostType>(Sp[d] + L0 + L1 + L2 + L3);}// 存储minLr                    minLr[0][xm] = (CostType)minL0;minLr[0][xm+1] = (CostType)minL1;minLr[0][xm+2] = (CostType)minL2;minLr[0][xm+3] = (CostType)minL3;}}if( pass == npasses ){for( x = 0; x < width; x++ ){disp1ptr[x] = disp2ptr[x] = (DispType)INVALID_DISP_SCALED;disp2cost[x] = MAX_COST;}for( x = width1 - 1; x >= 0; x-- ) // 逆序处理                {CostType* Sp = S + x*D;int minS = MAX_COST, bestDisp = -1;if( npasses == 1 ){int xm = x*NR2, xd = xm*D2;int minL0 = MAX_COST;int delta0 = minLr[0][xm + NR2] + P2;CostType* Lr_p0 = Lr[0] + xd + NRD2;Lr_p0[-1] = Lr_p0[D] = MAX_COST;CostType* Lr_p = Lr[0] + xd;const CostType* Cp = C + x*D;{for( d = 0; d < D; d++ ){int L0 = Cp[d] + std::min((int)Lr_p0[d], std::min(Lr_p0[d-1] + P1, std::min(Lr_p0[d+1] + P1, delta0))) - delta0;Lr_p[d] = (CostType)L0;minL0 = std::min(minL0, L0);int Sval = Sp[d] = saturate_cast<CostType>(Sp[d] + L0);if( Sval < minS ){minS = Sval;bestDisp = d;}}minLr[0][xm] = (CostType)minL0;}}else // 当pass = 2时，从最后一行开始，最后一行上各个像素的最优视差的确定只能参考之前pass = 1时计算的前4个方向                    {    // 后4个方向的结果需要最后一行计算完后才有                        {// 遍历寻找最优视差                            for( d = 0; d < D; d++ ){int Sval = Sp[d];if( Sval < minS ){minS = Sval;bestDisp = d;}}}}// 唯一匹配检测。要求除了bestDisp前后各一个视差之外，其余视差值对应的S必须大于minS * 1.x                    for( d = 0; d < D; d++ ){if( Sp[d]*(100 - uniquenessRatio) < minS*100 && std::abs(bestDisp - d) > 1 )break;}if( d < D ) // 不满足唯一匹配的要求的像素直接跳过                        continue;d = bestDisp;int _x2 = x + minX1 - d - minD; // _x2为当前像素x在右图上所对应的匹配像素                    if( disp2cost[_x2] > minS ){// 存储对应的右图像素的视差值和S                        disp2cost[_x2] = (CostType)minS;disp2ptr[_x2] = (DispType)(d + minD);}// 当最优视差不为视差搜索范围的首尾时则进行亚像素级别的视差值内查                    if( 0 < d && d < D-1 ){// do subpixel quadratic interpolation:                        //   fit parabola into (x1=d-1, y1=Sp[d-1]), (x2=d, y2=Sp[d]), (x3=d+1, y3=Sp[d+1])                        //   then find minimum of the parabola.                        int denom2 = std::max(Sp[d-1] + Sp[d+1] - 2*Sp[d], 1);d = d*DISP_SCALE + ((Sp[d-1] - Sp[d+1])*DISP_SCALE + denom2)/(denom2*2);}elsed *= DISP_SCALE;disp1ptr[x + minX1] = (DispType)(d + minD*DISP_SCALE); // 存储结果                }for( x = minX1; x < maxX1; x++ ){// we round the computed disparity both towards -inf and +inf and check                    // if either of the corresponding disparities in disp2 is consistent.                    // This is to give the computed disparity a chance to look valid if it is.                    // 如官方注释，左右图视差校验。                    // 经过前面的处理后，对于左图像素x，考虑之前得到的亚像素精度级别的视差d1                    // 可以获得两个可能的、位于d1前后的最优视差_d = d1 / scale 和 d_=_d+(scale - 1)/scale                    // 依此获取之前存储的对应的右图像素x - _d和x - d_                    // 查看二者存储的视差disp2ptr[_x] 和disp2tpr[x_]与当前视差_d和d_的差异                    // 若大于阈值，则说明consist check失败，当前视差为无效视差                    int d1 = disp1ptr[x];if( d1 == INVALID_DISP_SCALED )continue;int _d = d1 >> DISP_SHIFT;int d_ = (d1 + DISP_SCALE-1) >> DISP_SHIFT;int _x = x - _d, x_ = x - d_;if( 0 <= _x && _x < width && disp2ptr[_x] >= minD && std::abs(disp2ptr[_x] - _d) > disp12MaxDiff &&0 <= x_ && x_ < width && disp2ptr[x_] >= minD && std::abs(disp2ptr[x_] - d_) > disp12MaxDiff )disp1ptr[x] = (DispType)INVALID_DISP_SCALED;}}// now shift the cyclic buffers            std::swap( Lr[0], Lr[1] ); // 如此，当pass = 1时，index = 1为上一行，index = 0为当前行            std::swap( minLr[0], minLr[1] ); // 当pass = 2时，index = 1为下一行，index = 0为当前行        }}}

前面，算法用到了单行cost的计算函数 calcPixelCostBT，是采用Birchfeld-Tomasi metric 来计算cost的，因此函数有个后缀BT。对应的函数如下：

/*For each pixel row1[x], max(maxD, 0) <= minX <= x < maxX <= width - max(0, -minD),and for each disparity minD<=d<maxD the functioncomputes the cost (cost[(x-minX)*(maxD - minD) + (d - minD)]), depending on the difference betweenrow1[x] and row2[x-d]. The subpixel algorithm from"Depth Discontinuities by Pixel-to-Pixel Stereo" by Stan Birchfield and C. Tomasiis used, hence the suffix BT.the temporary buffer should contain width2*2 elements*/
static void calcPixelCostBT( const Mat& img1, const Mat& img2, int y,int minD, int maxD, CostType* cost,PixType* buffer, const PixType* tab,int tabOfs, int , int xrange_min = 0, int xrange_max = DEFAULT_RIGHT_BORDER )
{int x, c, width = img1.cols, cn = img1.channels();int minX1 = std::max(maxD, 0), maxX1 = width + std::min(minD, 0); // 视差计算范围int D = maxD - minD, width1 = maxX1 - minX1;//This minX1 & maxX2 correction is defining which part of calculatable line must be calculated//That is needs of parallel algorithmxrange_min = (xrange_min < 0) ? 0: xrange_min;xrange_max = (xrange_max == DEFAULT_RIGHT_BORDER) || (xrange_max > width1) ? width1 : xrange_max;maxX1 = minX1 + xrange_max;minX1 += xrange_min;width1 = maxX1 - minX1;int minX2 = std::max(minX1 - maxD, 0), maxX2 = std::min(maxX1 - minD, width);int width2 = maxX2 - minX2;const PixType *row1 = img1.ptr<PixType>(y), *row2 = img2.ptr<PixType>(y);PixType *prow1 = buffer + width2*2, *prow2 = prow1 + width*cn*2; // buffer后留下两行后面用tab += tabOfs;for( c = 0; c < cn*2; c++ ){prow1[width*c] = prow1[width*c + width-1] =prow2[width*c] = prow2[width*c + width-1] = tab[0];}int n1 = y > 0 ? -(int)img1.step : 0, s1 = y < img1.rows-1 ? (int)img1.step : 0; // n1 是左图的上一行，s1 是左图的下一行int n2 = y > 0 ? -(int)img2.step : 0, s2 = y < img2.rows-1 ? (int)img2.step : 0;int minX_cmn = std::min(minX1,minX2)-1;int maxX_cmn = std::max(maxX1,maxX2)+1;minX_cmn = std::max(minX_cmn, 1);maxX_cmn = std::min(maxX_cmn, width - 1);if( cn == 1 ){for( x = minX_cmn; x < maxX_cmn; x++ ){prow1[x] = tab[(row1[x+1] - row1[x-1])*2 + row1[x+n1+1] - row1[x+n1-1] + row1[x+s1+1] - row1[x+s1-1]]; // x 方向sobel滤波prow2[width-1-x] = tab[(row2[x+1] - row2[x-1])*2 + row2[x+n2+1] - row2[x+n2-1] + row2[x+s2+1] - row2[x+s2-1]]; // 右图逆序存储prow1[x+width] = row1[x]; // 第二行对应位置存储灰度值prow2[width-1-x+width] = row2[x];}}else{for( x = minX_cmn; x < maxX_cmn; x++ ){prow1[x] = tab[(row1[x*3+3] - row1[x*3-3])*2 + row1[x*3+n1+3] - row1[x*3+n1-3] + row1[x*3+s1+3] - row1[x*3+s1-3]];prow1[x+width] = tab[(row1[x*3+4] - row1[x*3-2])*2 + row1[x*3+n1+4] - row1[x*3+n1-2] + row1[x*3+s1+4] - row1[x*3+s1-2]];prow1[x+width*2] = tab[(row1[x*3+5] - row1[x*3-1])*2 + row1[x*3+n1+5] - row1[x*3+n1-1] + row1[x*3+s1+5] - row1[x*3+s1-1]];prow2[width-1-x] = tab[(row2[x*3+3] - row2[x*3-3])*2 + row2[x*3+n2+3] - row2[x*3+n2-3] + row2[x*3+s2+3] - row2[x*3+s2-3]];prow2[width-1-x+width] = tab[(row2[x*3+4] - row2[x*3-2])*2 + row2[x*3+n2+4] - row2[x*3+n2-2] + row2[x*3+s2+4] - row2[x*3+s2-2]];prow2[width-1-x+width*2] = tab[(row2[x*3+5] - row2[x*3-1])*2 + row2[x*3+n2+5] - row2[x*3+n2-1] + row2[x*3+s2+5] - row2[x*3+s2-1]];prow1[x+width*3] = row1[x*3];prow1[x+width*4] = row1[x*3+1];prow1[x+width*5] = row1[x*3+2];prow2[width-1-x+width*3] = row2[x*3];prow2[width-1-x+width*4] = row2[x*3+1];prow2[width-1-x+width*5] = row2[x*3+2];}}memset( cost + xrange_min*D, 0, width1*D*sizeof(cost[0]) );buffer -= width-1-maxX2; // 回退minD - 1步，不过要乘上视差数cost -= (minX1-xrange_min)*D + minD; // simplify the cost indices inside the loopfor( c = 0; c < cn*2; c++, prow1 += width, prow2 += width ){int diff_scale = c < cn ? 0 : 2;// precompute//   v0 = min(row2[x-1/2], row2[x], row2[x+1/2]) and//   v1 = max(row2[x-1/2], row2[x], row2[x+1/2]) and// 其实应该是：v0 = min((row2[x-1] + row2[x])/2, row2[x], (row2[x] + row2[x + 1])/2)// 和        v1 = max((row2[x-1] + row2[x])/2, row2[x], (row2[x] + row2[x + 1])/2)// 如官方注释，开始计算B.T. metrics，理论可以参考函数前注释给出的论文Depth Discontinuities by Pixel-to-Pixel Stereo// 简单来说，就是对于左图像素x和在某个视差值对应的右图像素x-d，不再如SAD一样单纯计算I_l(x) - I_r(x-d),// 而是先拟合下右图像素x-d左右 亚像素精度的视差值，即(row2[x-d-1] + row2[x-d])/2和(row2[x-d] + row2[x-d+1])/2，// 再计算左图像素与这三者的差并取最小值，即下面的c0；对于左图像素做同样的处理，得到下面的c1for( x = width-1-maxX2; x < width-1- minX2; x++ ) // 预先计算出右图的结果并保存{int v = prow2[x];int vl = x > 0 ? (v + prow2[x-1])/2 : v;int vr = x < width-1 ? (v + prow2[x+1])/2 : v;int v0 = std::min(vl, vr); v0 = std::min(v0, v);int v1 = std::max(vl, vr); v1 = std::max(v1, v);buffer[x] = (PixType)v0;          // 第一行存最小值buffer[x + width2] = (PixType)v1; // 第二行存最大值}for( x = minX1; x < maxX1; x++ ) // 针对左图像素依次计算cost{int u = prow1[x];int ul = x > 0 ? (u + prow1[x-1])/2 : u;int ur = x < width-1 ? (u + prow1[x+1])/2 : u;int u0 = std::min(ul, ur); u0 = std::min(u0, u);int u1 = std::max(ul, ur); u1 = std::max(u1, u);{for( int d = minD; d < maxD; d++ ){int v = prow2[width-x-1 + d]; // 之前右图是逆序存储，现在需要逆序取出，并加上视差值int v0 = buffer[width-x-1 + d]; // 最小值int v1 = buffer[width-x-1 + d + width2]; // 最大值int c0 = std::max(0, u - v1); c0 = std::max(c0, v0 - u);int c1 = std::max(0, v - u1); c1 = std::max(c1, u0 - v);// cost计算。与原论文不同的是，opencv的B.T. metrics包含了两个部分，// 一部分为prow1和prow2第一行所存储的左右图的sobel滤波结果的B.T. metrics，// 一部分为prow1和prow2第二行所存储的左右图的灰度值的B.T. metricscost[x*D + d] = (CostType)(cost[x*D+d] + (std::min(c0, c1) >> diff_scale));}}}}
}

最后，stereosgbm.cpp文件中还包含了视差图的后处理滤波函数filterSpeckles。该函数对视差图进行连通域滤波，去除像素数量小于设定阈值（参数speckleWindowSize）的无效区域，这对于获得一个干净、无飞点的深度图而言十分重要。

简单来说，该函数遍历所得的视差图，对于每一个像素，如果其4临域内的其他有效像素，与该像素的差异小于设定阈值（参数speckleRange），则将他们置为同一个区域。最后，对于具有相同标签的同一个区域，如果该区域所包含的像素数量小于阈值，就把该区域的像素置为无效视差。由于代码比较简单，官方也有注释，我就不再加上自己的注释了。

/*For each pixel row1[x], max(maxD, 0) <= minX <= x < maxX <= width - max(0, -minD),and for each disparity minD<=d<maxD the functioncomputes the cost (cost[(x-minX)*(maxD - minD) + (d - minD)]), depending on the difference betweenrow1[x] and row2[x-d]. The subpixel algorithm from"Depth Discontinuities by Pixel-to-Pixel Stereo" by Stan Birchfield and C. Tomasiis used, hence the suffix BT.the temporary buffer should contain width2*2 elements*/
template <typename T>
void filterSpecklesImpl(cv::Mat& img, int newVal, int maxSpeckleSize, int maxDiff, cv::Mat& _buf)
{using namespace cv;int width = img.cols, height = img.rows, npixels = width*height;size_t bufSize = npixels*(int)(sizeof(Point2s) + sizeof(int) + sizeof(uchar));if( !_buf.isContinuous() || _buf.empty() || _buf.cols*_buf.rows*_buf.elemSize() < bufSize )_buf.reserveBuffer(bufSize);uchar* buf = _buf.ptr();int i, j, dstep = (int)(img.step/sizeof(T));int* labels = (int*)buf;buf += npixels*sizeof(labels[0]);Point2s* wbuf = (Point2s*)buf;buf += npixels*sizeof(wbuf[0]);uchar* rtype = (uchar*)buf;int curlabel = 0;// clear out label assignmentsmemset(labels, 0, npixels*sizeof(labels[0]));for( i = 0; i < height; i++ ){T* ds = img.ptr<T>(i);int* ls = labels + width*i;for( j = 0; j < width; j++ ){if( ds[j] != newVal )   // not a bad disparity{if( ls[j] )     // has a label, check for bad label{if( rtype[ls[j]] ) // small region, zero out disparityds[j] = (T)newVal;}// no label, assign and propagateelse{Point2s* ws = wbuf; // initialize wavefrontPoint2s p((short)j, (short)i);  // current pixelcurlabel++; // next labelint count = 0;  // current region sizels[j] = curlabel;// wavefront propagationwhile( ws >= wbuf ) // wavefront not empty{count++;// put neighbors onto wavefrontT* dpp = &img.at<T>(p.y, p.x);T dp = *dpp;int* lpp = labels + width*p.y + p.x;if( p.y < height-1 && !lpp[+width] && dpp[+dstep] != newVal && std::abs(dp - dpp[+dstep]) <= maxDiff ){lpp[+width] = curlabel;*ws++ = Point2s(p.x, p.y+1);}if( p.y > 0 && !lpp[-width] && dpp[-dstep] != newVal && std::abs(dp - dpp[-dstep]) <= maxDiff ){lpp[-width] = curlabel;*ws++ = Point2s(p.x, p.y-1);}if( p.x < width-1 && !lpp[+1] && dpp[+1] != newVal && std::abs(dp - dpp[+1]) <= maxDiff ){lpp[+1] = curlabel;*ws++ = Point2s(p.x+1, p.y);}if( p.x > 0 && !lpp[-1] && dpp[-1] != newVal && std::abs(dp - dpp[-1]) <= maxDiff ){lpp[-1] = curlabel;*ws++ = Point2s(p.x-1, p.y);}// pop most recent and propagate// NB: could try least recent, maybe better convergencep = *--ws;}// assign label typeif( count <= maxSpeckleSize )   // speckle region{rtype[ls[j]] = 1;   // small region labelds[j] = (T)newVal;}elsertype[ls[j]] = 0;   // large region label}}}}
}

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