OpenCV 中的 warpAffine

warpAffine 是图像处理中比较常见的一种变换，可以将图像校正或对齐。

对于线性插值方式，OpenCV 首先将坐标映射保存成两张图，然后调用 remap 函数。第二步是比较耗时的部分，并且 warpPerspective 亦采用此处理。

remap 通过构建查找表来存储系数乘积，这样减少了乘法运算次数。

由于篇幅过长，将文章分成 warpAffine 和 remap 两部分。

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warpAffine

remap

WarpPerspective

cv::warpAffine

cv::warpAffine

hal::warpAffine

检查输入通道数量以及插值类型。
如果目的矩阵为空则创建内存，如果是原地操作则复制一份源数据。

    CV_INSTRUMENT_REGION();int interpolation = flags & INTER_MAX;CV_Assert( _src.channels() <= 4 || (interpolation != INTER_LANCZOS4 &&interpolation != INTER_CUBIC) );CV_OCL_RUN(_src.dims() <= 2 && _dst.isUMat() &&_src.cols() <= SHRT_MAX && _src.rows() <= SHRT_MAX,ocl_warpTransform_cols4(_src, _dst, _M0, dsize, flags, borderType,borderValue, OCL_OP_AFFINE))CV_OCL_RUN(_src.dims() <= 2 && _dst.isUMat(),ocl_warpTransform(_src, _dst, _M0, dsize, flags, borderType,borderValue, OCL_OP_AFFINE))Mat src = _src.getMat(), M0 = _M0.getMat();_dst.create( dsize.empty() ? src.size() : dsize, src.type() );Mat dst = _dst.getMat();CV_Assert( src.cols > 0 && src.rows > 0 );if( dst.data == src.data )src = src.clone();

如果未设置WARP_INVERSE_MAP，则对参数矩阵M求逆。

    double M[6] = {0};Mat matM(2, 3, CV_64F, M);if( interpolation == INTER_AREA )interpolation = INTER_LINEAR;CV_Assert( (M0.type() == CV_32F || M0.type() == CV_64F) && M0.rows == 2 && M0.cols == 3 );M0.convertTo(matM, matM.type());if( !(flags & WARP_INVERSE_MAP) ){double D = M[0]*M[4] - M[1]*M[3];D = D != 0 ? 1./D : 0;double A11 = M[4]*D, A22=M[0]*D;M[0] = A11; M[1] *= -D;M[3] *= -D; M[4] = A22;double b1 = -M[0]*M[2] - M[1]*M[5];double b2 = -M[3]*M[2] - M[4]*M[5];M[2] = b1; M[5] = b2;}

#if defined (HAVE_IPP) && IPP_VERSION_X100 >= 810 && !IPP_DISABLE_WARPAFFINECV_IPP_CHECK(){int type = src.type(), depth = CV_MAT_DEPTH(type), cn = CV_MAT_CN(type);if( ( depth == CV_8U || depth == CV_16U || depth == CV_32F ) &&( cn == 1 || cn == 3 || cn == 4 ) &&( interpolation == INTER_NEAREST || interpolation == INTER_LINEAR || interpolation == INTER_CUBIC) &&( borderType == cv::BORDER_TRANSPARENT || borderType == cv::BORDER_CONSTANT) ){ippiWarpAffineBackFunc ippFunc = 0;if ((flags & WARP_INVERSE_MAP) != 0){ippFunc =type == CV_8UC1 ? (ippiWarpAffineBackFunc)ippiWarpAffineBack_8u_C1R :type == CV_8UC3 ? (ippiWarpAffineBackFunc)ippiWarpAffineBack_8u_C3R :type == CV_8UC4 ? (ippiWarpAffineBackFunc)ippiWarpAffineBack_8u_C4R :type == CV_16UC1 ? (ippiWarpAffineBackFunc)ippiWarpAffineBack_16u_C1R :type == CV_16UC3 ? (ippiWarpAffineBackFunc)ippiWarpAffineBack_16u_C3R :type == CV_16UC4 ? (ippiWarpAffineBackFunc)ippiWarpAffineBack_16u_C4R :type == CV_32FC1 ? (ippiWarpAffineBackFunc)ippiWarpAffineBack_32f_C1R :type == CV_32FC3 ? (ippiWarpAffineBackFunc)ippiWarpAffineBack_32f_C3R :type == CV_32FC4 ? (ippiWarpAffineBackFunc)ippiWarpAffineBack_32f_C4R :0;}else{ippFunc =type == CV_8UC1 ? (ippiWarpAffineBackFunc)ippiWarpAffine_8u_C1R :type == CV_8UC3 ? (ippiWarpAffineBackFunc)ippiWarpAffine_8u_C3R :type == CV_8UC4 ? (ippiWarpAffineBackFunc)ippiWarpAffine_8u_C4R :type == CV_16UC1 ? (ippiWarpAffineBackFunc)ippiWarpAffine_16u_C1R :type == CV_16UC3 ? (ippiWarpAffineBackFunc)ippiWarpAffine_16u_C3R :type == CV_16UC4 ? (ippiWarpAffineBackFunc)ippiWarpAffine_16u_C4R :type == CV_32FC1 ? (ippiWarpAffineBackFunc)ippiWarpAffine_32f_C1R :type == CV_32FC3 ? (ippiWarpAffineBackFunc)ippiWarpAffine_32f_C3R :type == CV_32FC4 ? (ippiWarpAffineBackFunc)ippiWarpAffine_32f_C4R :0;}int mode =interpolation == INTER_LINEAR ? IPPI_INTER_LINEAR :interpolation == INTER_NEAREST ? IPPI_INTER_NN :interpolation == INTER_CUBIC ? IPPI_INTER_CUBIC :0;CV_Assert(mode && ippFunc);double coeffs[2][3];for( int i = 0; i < 2; i++ )for( int j = 0; j < 3; j++ )coeffs[i][j] = matM.at<double>(i, j);bool ok;Range range(0, dst.rows);IPPWarpAffineInvoker invoker(src, dst, coeffs, mode, borderType, borderValue, ippFunc, &ok);parallel_for_(range, invoker, dst.total()/(double)(1<<16));if( ok ){CV_IMPL_ADD(CV_IMPL_IPP|CV_IMPL_MT);return;}setIppErrorStatus();}}
#endif

调用命名空间中的 hal::warpAffine 函数，各参数独立传入。

    hal::warpAffine(src.type(), src.data, src.step, src.cols, src.rows, dst.data, dst.step, dst.cols, dst.rows,M, interpolation, borderType, borderValue.val);

hal::warpAffine

hal::warpAffine

parallel_for_

WarpAffineInvoker

dst(x,y)=src(M11x+M12y+M13,M21x+M22y+M23)\mathrm{dst}(x,y)=\mathrm{src}(M_{11}x+M_{12}y+M_{13}, M_{21}x+M_{22}y+M_{23})dst(x,y)=src(M11x+M12y+M13,M21x+M22y+M23)

OpenCV 屏蔽了 Carotene 中的实现。
根据描述构建出源和目的矩阵。
INTER_BITS 为5，即插值所用比特数。
预先计算行元素变换系数，adelta为 M11xM_{11}xM11x，bdelta为 M21xM_{21}xM21x。

    CALL_HAL(warpAffine, cv_hal_warpAffine, src_type, src_data, src_step, src_width, src_height, dst_data, dst_step, dst_width, dst_height, M, interpolation, borderType, borderValue);Mat src(Size(src_width, src_height), src_type, const_cast<uchar*>(src_data), src_step);Mat dst(Size(dst_width, dst_height), src_type, dst_data, dst_step);int x;AutoBuffer<int> _abdelta(dst.cols*2);int* adelta = &_abdelta[0], *bdelta = adelta + dst.cols;const int AB_BITS = MAX(10, (int)INTER_BITS);const int AB_SCALE = 1 << AB_BITS;for( x = 0; x < dst.cols; x++ ){adelta[x] = saturate_cast<int>(M[0]*x*AB_SCALE);bdelta[x] = saturate_cast<int>(M[3]*x*AB_SCALE);}

创建调用者 WarpAffineInvoker，parallel_for_ 函数并行调用。

    Range range(0, dst.rows);WarpAffineInvoker invoker(src, dst, interpolation, borderType,Scalar(borderValue[0], borderValue[1], borderValue[2], borderValue[3]),adelta, bdelta, M);parallel_for_(range, invoker, dst.total()/(double)(1<<16));

WarpAffineInvoker

WarpAffineInvoker

ParallelLoopBody

public:WarpAffineInvoker(const Mat &_src, Mat &_dst, int _interpolation, int _borderType,const Scalar &_borderValue, int *_adelta, int *_bdelta, const double *_M) :ParallelLoopBody(), src(_src), dst(_dst), interpolation(_interpolation),borderType(_borderType), borderValue(_borderValue), adelta(_adelta), bdelta(_bdelta),M(_M){}

operator()

处理操作符函数。

BLOCK_SZ指定分块大小。
XY存储源图上对应的坐标，A为辅助系数。
INTER_BITS 为5。
INTER_TAB_SIZE 为 2INTER_BITS=322^{\mathrm{INTER\_BITS}}=322INTER_BITS=32，这样双线性插值表大小为32x32x4。
AB_SCALE为 2102^{10}210。这样计算结果的 10.6 的格式存储。
处理区域为BLOCK_SZ/2行、BLOCK_SZ*2列的矩形。为什么？

    virtual void operator() (const Range& range) const CV_OVERRIDE{const int BLOCK_SZ = 64;AutoBuffer<short, 0> __XY(BLOCK_SZ * BLOCK_SZ * 2), __A(BLOCK_SZ * BLOCK_SZ);short *XY = __XY.data(), *A = __A.data();const int AB_BITS = MAX(10, (int)INTER_BITS);const int AB_SCALE = 1 << AB_BITS;int round_delta = interpolation == INTER_NEAREST ? AB_SCALE/2 : AB_SCALE/INTER_TAB_SIZE/2, x, y, x1, y1;#if CV_TRY_AVX2bool useAVX2 = CV_CPU_HAS_SUPPORT_AVX2;#endif#if CV_TRY_SSE4_1bool useSSE4_1 = CV_CPU_HAS_SUPPORT_SSE4_1;#endifint bh0 = std::min(BLOCK_SZ/2, dst.rows);int bw0 = std::min(BLOCK_SZ*BLOCK_SZ/bh0, dst.cols);bh0 = std::min(BLOCK_SZ*BLOCK_SZ/bw0, dst.rows);

xy指向结果矩阵的当前行行首。
X0为 M12y+M13M_{12}y+M_{13}M12y+M13
Y0为 M22x+M23M_{22}x+M_{23}M22x+M23
round_delta为16。
_XY将缓冲区__XY封装成了矩阵。
dpart为结果的 RoI 区域。

        for( y = range.start; y < range.end; y += bh0 ){for( x = 0; x < dst.cols; x += bw0 ){int bw = std::min( bw0, dst.cols - x);int bh = std::min( bh0, range.end - y);Mat _XY(bh, bw, CV_16SC2, XY), matA;Mat dpart(dst, Rect(x, y, bw, bh));for( y1 = 0; y1 < bh; y1++ ){short* xy = XY + y1*bw*2;int X0 = saturate_cast<int>((M[1]*(y + y1) + M[2])*AB_SCALE) + round_delta;int Y0 = saturate_cast<int>((M[4]*(y + y1) + M[5])*AB_SCALE) + round_delta;

如果是最近邻方法。
WarpAffineInvoker_Blockline_SSE41

                    if( interpolation == INTER_NEAREST ){x1 = 0;#if CV_TRY_SSE4_1if( useSSE4_1 )opt_SSE4_1::WarpAffineInvoker_Blockline_SSE41(adelta + x, bdelta + x, xy, X0, Y0, bw);else#endif{#if CV_SIMD128{v_int32x4 v_X0 = v_setall_s32(X0), v_Y0 = v_setall_s32(Y0);int span = v_uint16x8::nlanes;for( ; x1 <= bw - span; x1 += span ){v_int16x8 v_dst[2];#define CV_CONVERT_MAP(ptr,offset,shift) v_pack(v_shr<AB_BITS>(shift+v_load(ptr + offset)),\v_shr<AB_BITS>(shift+v_load(ptr + offset + 4)))v_dst[0] = CV_CONVERT_MAP(adelta, x+x1, v_X0);v_dst[1] = CV_CONVERT_MAP(bdelta, x+x1, v_Y0);#undef CV_CONVERT_MAPv_store_interleave(xy + (x1 << 1), v_dst[0], v_dst[1]);}}#endiffor( ; x1 < bw; x1++ ){int X = (X0 + adelta[x+x1]) >> AB_BITS;int Y = (Y0 + bdelta[x+x1]) >> AB_BITS;xy[x1*2] = saturate_cast<short>(X);xy[x1*2+1] = saturate_cast<short>(Y);}}}

对于双线性插值。
alpha指向当前行。
avx2可以调用 warpAffineBlockline
v_mask为向量掩码。
每次处理span*2个数。
v_setall_s32 通过 OPENCV_HAL_IMPL_NEON_INIT 宏来定义。
v_load 从存储器中加载寄存器内容。
计算 M11x+M12y+M13M_{11}x+M_{12}y+M_{13}M11x+M12y+M13 和 M21x+M22y+M23M_{21}x+M_{22}y+M_{23}M21x+M22y+M23 时，是两个v_int32x4相加（vaddq_s32），得到v_int32x4的结果。然后右移（10-5）位。
v_shr 右移。
v_pack 将两个数据宽度减半后拼到一起。
两次右移后
v_store_interleave 将2个寄存器中的数据交错存储到内存中。
v_shl 左移。
v_store 将寄存器内容存储到内存中。
v_Y0和v_X0合并。

                    else{short* alpha = A + y1*bw;x1 = 0;#if CV_TRY_AVX2if ( useAVX2 )x1 = opt_AVX2::warpAffineBlockline(adelta + x, bdelta + x, xy, alpha, X0, Y0, bw);#endif#if CV_SIMD128{v_int32x4 v__X0 = v_setall_s32(X0), v__Y0 = v_setall_s32(Y0);v_int32x4 v_mask = v_setall_s32(INTER_TAB_SIZE - 1);int span = v_float32x4::nlanes;for( ; x1 <= bw - span * 2; x1 += span * 2 ){v_int32x4 v_X0 = v_shr<AB_BITS - INTER_BITS>(v__X0 + v_load(adelta + x + x1));v_int32x4 v_Y0 = v_shr<AB_BITS - INTER_BITS>(v__Y0 + v_load(bdelta + x + x1));v_int32x4 v_X1 = v_shr<AB_BITS - INTER_BITS>(v__X0 + v_load(adelta + x + x1 + span));v_int32x4 v_Y1 = v_shr<AB_BITS - INTER_BITS>(v__Y0 + v_load(bdelta + x + x1 + span));v_int16x8 v_xy[2];v_xy[0] = v_pack(v_shr<INTER_BITS>(v_X0), v_shr<INTER_BITS>(v_X1));v_xy[1] = v_pack(v_shr<INTER_BITS>(v_Y0), v_shr<INTER_BITS>(v_Y1));v_store_interleave(xy + (x1 << 1), v_xy[0], v_xy[1]);v_int32x4 v_alpha0 = v_shl<INTER_BITS>(v_Y0 & v_mask) | (v_X0 & v_mask);v_int32x4 v_alpha1 = v_shl<INTER_BITS>(v_Y1 & v_mask) | (v_X1 & v_mask);v_store(alpha + x1, v_pack(v_alpha0, v_alpha1));}}#endif

X和Y为映射到源图上的像素坐标。alpha将Y和X的小数部分合并存储。

                        for( ; x1 < bw; x1++ ){int X = (X0 + adelta[x+x1]) >> (AB_BITS - INTER_BITS);int Y = (Y0 + bdelta[x+x1]) >> (AB_BITS - INTER_BITS);xy[x1*2] = saturate_cast<short>(X >> INTER_BITS);xy[x1*2+1] = saturate_cast<short>(Y >> INTER_BITS);alpha[x1] = (short)((Y & (INTER_TAB_SIZE-1))*INTER_TAB_SIZE +(X & (INTER_TAB_SIZE-1)));}}}

cv::remap 从src中找到dpart的源值。最近邻方式不需要第二张图。

                if( interpolation == INTER_NEAREST )remap( src, dpart, _XY, Mat(), interpolation, borderType, borderValue );else{Mat _matA(bh, bw, CV_16U, A);remap( src, dpart, _XY, _matA, interpolation, borderType, borderValue );}}}}

成员变量。

private:Mat src;Mat dst;int interpolation, borderType;Scalar borderValue;int *adelta, *bdelta;const double *M;

参考资料：

Warp Affine
How to work with OpenCV application based on OpenVX API
OpenVX sample #7163
opencv/cmake/FindOpenVX.cmake
Hybrid CV/DL pipelines with OpenCV 4.4 G-API
opencv和openvx
Showing our vision with OpenVX™ 1.1 support for PowerVR GPUs
Amdovx Core
OpenVX 1.3 is Here!
Color Copy OpenVX* Sample
opencv ncnn warpaffine 性能测试
OpenCV warpAffine的天坑
Geometric Transformations of Images
Decompose a 2D arbitrary transform into only scaling and rotation
Decompose affine transformation (including shear in x and y)
Decomposing an Affine transformation
Decomposing an Affine transformation
Given this transformation matrix, how do I decompose it into translation, rotation and scale matrices?
Opencv 仿射变换原理代码解析
如何通俗地讲解「仿射变换」这个概念？
OpenCV代码提取：warpAffine函数的实现
NEON优化——OpenCV WarpAffine最近邻
Subtracting 0x8000 from an int
OpenCV2:Mat属性type，depth，step
OpenCV中如何获取Mat类型中的步长stride及分析 C++实现
NEON is the new black: fast JPEG optimization on ARM server
大端序与小端序
Remapping
C++ 命令模式讲解和代码示例
Specify an origin to warpPerspective() function in OpenCV 2.x
计算机视觉2D几何基元及其变换介绍和OpenCV WarpPerspective源码分析