OpenCV中resize函数五种插值算法的实现过程

最新版OpenCV2.4.7中，cv::resize函数有五种插值算法：最近邻、双线性、双三次、基于像素区域关系、兰索斯插值。下面用for循环代替cv::resize函数来说明其详细的插值实现过程，其中部分代码摘自于cv::resize函数中的源代码。

每种插值算法的前部分代码是相同的，如下：

cv::Mat matSrc, matDst1, matDst2;matSrc = cv::imread("lena.jpg", 2 | 4);matDst1 = cv::Mat(cv::Size(800, 1000), matSrc.type(), cv::Scalar::all(0));matDst2 = cv::Mat(matDst1.size(), matSrc.type(), cv::Scalar::all(0));double scale_x = (double)matSrc.cols / matDst1.cols;double scale_y = (double)matSrc.rows / matDst1.rows;

1、最近邻：公式，

                  

for (int i = 0; i < matDst1.cols; ++i){int sx = cvFloor(i * scale_x);sx = std::min(sx, matSrc.cols - 1);for (int j = 0; j < matDst1.rows; ++j){int sy = cvFloor(j * scale_y);sy = std::min(sy, matSrc.rows - 1);matDst1.at<cv::Vec3b>(j, i) = matSrc.at<cv::Vec3b>(sy, sx);}}cv::imwrite("nearest_1.jpg", matDst1);cv::resize(matSrc, matDst2, matDst1.size(), 0, 0, 0);cv::imwrite("nearest_2.jpg", matDst2);

2、双线性：由相邻的四像素(2*2)计算得出，公式，

uchar* dataDst = matDst1.data;int stepDst = matDst1.step;uchar* dataSrc = matSrc.data;int stepSrc = matSrc.step;int iWidthSrc = matSrc.cols;int iHiehgtSrc = matSrc.rows;for (int j = 0; j < matDst1.rows; ++j){float fy = (float)((j + 0.5) * scale_y - 0.5);int sy = cvFloor(fy);fy -= sy;sy = std::min(sy, iHiehgtSrc - 2);sy = std::max(0, sy);short cbufy[2];cbufy[0] = cv::saturate_cast<short>((1.f - fy) * 2048);cbufy[1] = 2048 - cbufy[0];for (int i = 0; i < matDst1.cols; ++i){float fx = (float)((i + 0.5) * scale_x - 0.5);int sx = cvFloor(fx);fx -= sx;if (sx < 0) {fx = 0, sx = 0;}if (sx >= iWidthSrc - 1) {fx = 0, sx = iWidthSrc - 2;}short cbufx[2];cbufx[0] = cv::saturate_cast<short>((1.f - fx) * 2048);cbufx[1] = 2048 - cbufx[0];for (int k = 0; k < matSrc.channels(); ++k){*(dataDst+ j*stepDst + 3*i + k) = (*(dataSrc + sy*stepSrc + 3*sx + k) * cbufx[0] * cbufy[0] + *(dataSrc + (sy+1)*stepSrc + 3*sx + k) * cbufx[0] * cbufy[1] + *(dataSrc + sy*stepSrc + 3*(sx+1) + k) * cbufx[1] * cbufy[0] + *(dataSrc + (sy+1)*stepSrc + 3*(sx+1) + k) * cbufx[1] * cbufy[1]) >> 22;}}}cv::imwrite("linear_1.jpg", matDst1);cv::resize(matSrc, matDst2, matDst1.size(), 0, 0, 1);cv::imwrite("linear_2.jpg", matDst2);

3、双三次：由相邻的4*4像素计算得出，公式类似于双线性

int iscale_x = cv::saturate_cast<int>(scale_x);int iscale_y = cv::saturate_cast<int>(scale_y);for (int j = 0; j < matDst1.rows; ++j){float fy = (float)((j + 0.5) * scale_y - 0.5);int sy = cvFloor(fy);fy -= sy;sy = std::min(sy, matSrc.rows - 3);sy = std::max(1, sy);const float A = -0.75f;float coeffsY[4];coeffsY[0] = ((A*(fy + 1) - 5*A)*(fy + 1) + 8*A)*(fy + 1) - 4*A;coeffsY[1] = ((A + 2)*fy - (A + 3))*fy*fy + 1;coeffsY[2] = ((A + 2)*(1 - fy) - (A + 3))*(1 - fy)*(1 - fy) + 1;coeffsY[3] = 1.f - coeffsY[0] - coeffsY[1] - coeffsY[2];short cbufY[4];cbufY[0] = cv::saturate_cast<short>(coeffsY[0] * 2048);cbufY[1] = cv::saturate_cast<short>(coeffsY[1] * 2048);cbufY[2] = cv::saturate_cast<short>(coeffsY[2] * 2048);cbufY[3] = cv::saturate_cast<short>(coeffsY[3] * 2048);for (int i = 0; i < matDst1.cols; ++i){float fx = (float)((i + 0.5) * scale_x - 0.5);int sx = cvFloor(fx);fx -= sx;if (sx < 1) {fx = 0, sx = 1;}if (sx >= matSrc.cols - 3) {fx = 0, sx = matSrc.cols - 3;}float coeffsX[4];coeffsX[0] = ((A*(fx + 1) - 5*A)*(fx + 1) + 8*A)*(fx + 1) - 4*A;coeffsX[1] = ((A + 2)*fx - (A + 3))*fx*fx + 1;coeffsX[2] = ((A + 2)*(1 - fx) - (A + 3))*(1 - fx)*(1 - fx) + 1;coeffsX[3] = 1.f - coeffsX[0] - coeffsX[1] - coeffsX[2];short cbufX[4];cbufX[0] = cv::saturate_cast<short>(coeffsX[0] * 2048);cbufX[1] = cv::saturate_cast<short>(coeffsX[1] * 2048);cbufX[2] = cv::saturate_cast<short>(coeffsX[2] * 2048);cbufX[3] = cv::saturate_cast<short>(coeffsX[3] * 2048);for (int k = 0; k < matSrc.channels(); ++k){matDst1.at<cv::Vec3b>(j, i)[k] = abs((matSrc.at<cv::Vec3b>(sy-1, sx-1)[k] * cbufX[0] * cbufY[0] + matSrc.at<cv::Vec3b>(sy, sx-1)[k] * cbufX[0] * cbufY[1] +matSrc.at<cv::Vec3b>(sy+1, sx-1)[k] * cbufX[0] * cbufY[2] + matSrc.at<cv::Vec3b>(sy+2, sx-1)[k] * cbufX[0] * cbufY[3] +matSrc.at<cv::Vec3b>(sy-1, sx)[k] * cbufX[1] * cbufY[0] + matSrc.at<cv::Vec3b>(sy, sx)[k] * cbufX[1] * cbufY[1] +matSrc.at<cv::Vec3b>(sy+1, sx)[k] * cbufX[1] * cbufY[2] + matSrc.at<cv::Vec3b>(sy+2, sx)[k] * cbufX[1] * cbufY[3] +matSrc.at<cv::Vec3b>(sy-1, sx+1)[k] * cbufX[2] * cbufY[0] + matSrc.at<cv::Vec3b>(sy, sx+1)[k] * cbufX[2] * cbufY[1] +matSrc.at<cv::Vec3b>(sy+1, sx+1)[k] * cbufX[2] * cbufY[2] + matSrc.at<cv::Vec3b>(sy+2, sx+1)[k] * cbufX[2] * cbufY[3] +matSrc.at<cv::Vec3b>(sy-1, sx+2)[k] * cbufX[3] * cbufY[0] + matSrc.at<cv::Vec3b>(sy, sx+2)[k] * cbufX[3] * cbufY[1] +matSrc.at<cv::Vec3b>(sy+1, sx+2)[k] * cbufX[3] * cbufY[2] + matSrc.at<cv::Vec3b>(sy+2, sx+2)[k] * cbufX[3] * cbufY[3] ) >> 22);}}}cv::imwrite("cubic_1.jpg", matDst1);cv::resize(matSrc, matDst2, matDst1.size(), 0, 0, 2);cv::imwrite("cubic_2.jpg", matDst2);

4、基于像素区域关系：共分三种情况，图像放大时类似于双线性插值，图像缩小(x轴、y轴同时缩小)又分两种情况，此情况下可以避免波纹出现。

cv::resize(matSrc, matDst2, matDst1.size(), 0, 0, 3);cv::imwrite("area_2.jpg", matDst2);double inv_scale_x = 1. / scale_x;double inv_scale_y = 1. / scale_y;int iscale_x = cv::saturate_cast<int>(scale_x);int iscale_y = cv::saturate_cast<int>(scale_y);bool is_area_fast = std::abs(scale_x - iscale_x) < DBL_EPSILON && std::abs(scale_y - iscale_y) < DBL_EPSILON;if (scale_x >= 1 && scale_y >= 1) //zoom out{if (is_area_fast) //integer multiples{for (int j = 0; j < matDst1.rows; ++j){int sy = j * scale_y;for (int i = 0; i < matDst1.cols; ++i){int sx = i * scale_x;matDst1.at<cv::Vec3b>(j, i) = matSrc.at<cv::Vec3b>(sy, sx);}}cv::imwrite("area_1.jpg", matDst1);return 0;}for (int j = 0; j < matDst1.rows; ++j){double fsy1 = j * scale_y;double fsy2 = fsy1 + scale_y;double cellHeight = cv::min(scale_y, matSrc.rows - fsy1);int sy1 = cvCeil(fsy1), sy2 = cvFloor(fsy2);sy2 = std::min(sy2, matSrc.rows - 1);sy1 = std::min(sy1, sy2);float cbufy[2];cbufy[0] = (float)((sy1 - fsy1) / cellHeight);cbufy[1] = (float)(std::min(std::min(fsy2 - sy2, 1.), cellHeight) / cellHeight);for (int i = 0; i < matDst1.cols; ++i){double fsx1 = i * scale_x;double fsx2 = fsx1 + scale_x;double cellWidth = std::min(scale_x, matSrc.cols - fsx1);int sx1 = cvCeil(fsx1), sx2 = cvFloor(fsx2);sx2 = std::min(sx2, matSrc.cols - 1);sx1 = std::min(sx1, sx2);float cbufx[2];cbufx[0] = (float)((sx1 - fsx1) / cellWidth);cbufx[1] = (float)(std::min(std::min(fsx2 - sx2, 1.), cellWidth) / cellWidth);for (int k = 0; k < matSrc.channels(); ++k){matDst1.at<cv::Vec3b>(j, i)[k] = (uchar)(matSrc.at<cv::Vec3b>(sy1, sx1)[k] * cbufx[0] * cbufy[0] + matSrc.at<cv::Vec3b>(sy1 + 1, sx1)[k] * cbufx[0] * cbufy[1] + matSrc.at<cv::Vec3b>(sy1, sx1 + 1)[k] * cbufx[1] * cbufy[0] + matSrc.at<cv::Vec3b>(sy1 + 1, sx1 + 1)[k] * cbufx[1] * cbufy[1]);}}}cv::imwrite("area_1.jpg", matDst1);return 0;}//zoom in,it is emulated using some variant of bilinear interpolationfor (int j = 0; j < matDst1.rows; ++j){int  sy = cvFloor(j * scale_y);float fy = (float)((j + 1) - (sy + 1) * inv_scale_y);fy = fy <= 0 ? 0.f : fy - cvFloor(fy);short cbufy[2];cbufy[0] = cv::saturate_cast<short>((1.f - fy) * 2048);cbufy[1] = 2048 - cbufy[0];for (int i = 0; i < matDst1.cols; ++i){int sx = cvFloor(i * scale_x);float fx = (float)((i + 1) - (sx + 1) * inv_scale_x);fx = fx < 0 ? 0.f : fx - cvFloor(fx);if (sx < 0) {fx = 0, sx = 0;}if (sx >= matSrc.cols - 1) {fx = 0, sx = matSrc.cols - 2;}short cbufx[2];cbufx[0] = cv::saturate_cast<short>((1.f - fx) * 2048);cbufx[1] = 2048 - cbufx[0];for (int k = 0; k < matSrc.channels(); ++k){matDst1.at<cv::Vec3b>(j, i)[k] = (matSrc.at<cv::Vec3b>(sy, sx)[k] * cbufx[0] * cbufy[0] + matSrc.at<cv::Vec3b>(sy + 1, sx)[k] * cbufx[0] * cbufy[1] + matSrc.at<cv::Vec3b>(sy, sx + 1)[k] * cbufx[1] * cbufy[0] + matSrc.at<cv::Vec3b>(sy + 1, sx + 1)[k] * cbufx[1] * cbufy[1]) >> 22;}}}cv::imwrite("area_1.jpg", matDst1);

5、兰索斯插值：由相邻的8*8像素计算得出，公式类似于双线性

int iscale_x = cv::saturate_cast<int>(scale_x);int iscale_y = cv::saturate_cast<int>(scale_y);for (int j = 0; j < matDst1.rows; ++j){float fy = (float)((j + 0.5) * scale_y - 0.5);int sy = cvFloor(fy);fy -= sy;sy = std::min(sy, matSrc.rows - 5);sy = std::max(3, sy);const double s45 = 0.70710678118654752440084436210485;const double cs[][2] = {{1, 0}, {-s45, -s45}, {0, 1}, {s45, -s45}, {-1, 0}, {s45, s45}, {0, -1}, {-s45, s45}};float coeffsY[8];if (fy < FLT_EPSILON) {for (int t = 0; t < 8; t++)coeffsY[t] = 0;coeffsY[3] = 1;} else {float sum = 0;double y0 = -(fy + 3) * CV_PI * 0.25, s0 = sin(y0), c0 = cos(y0);for (int t = 0; t < 8; ++t){double dy = -(fy + 3 -t) * CV_PI * 0.25;coeffsY[t] = (float)((cs[t][0] * s0 + cs[t][1] * c0) / (dy * dy));sum += coeffsY[t];}sum = 1.f / sum;for (int t = 0; t < 8; ++t)coeffsY[t] *= sum;}short cbufY[8];cbufY[0] = cv::saturate_cast<short>(coeffsY[0] * 2048);cbufY[1] = cv::saturate_cast<short>(coeffsY[1] * 2048);cbufY[2] = cv::saturate_cast<short>(coeffsY[2] * 2048);cbufY[3] = cv::saturate_cast<short>(coeffsY[3] * 2048);cbufY[4] = cv::saturate_cast<short>(coeffsY[4] * 2048);cbufY[5] = cv::saturate_cast<short>(coeffsY[5] * 2048);cbufY[6] = cv::saturate_cast<short>(coeffsY[6] * 2048);cbufY[7] = cv::saturate_cast<short>(coeffsY[7] * 2048);for (int i = 0; i < matDst1.cols; ++i){float fx = (float)((i + 0.5) * scale_x - 0.5);int sx = cvFloor(fx);fx -= sx;if (sx < 3) {fx = 0, sx = 3;}if (sx >= matSrc.cols - 5) {fx = 0, sx = matSrc.cols - 5;}float coeffsX[8];if (fx < FLT_EPSILON) {for ( int t = 0; t < 8; t++ )coeffsX[t] = 0;coeffsX[3] = 1;} else {float sum = 0;double x0 = -(fx + 3) * CV_PI * 0.25, s0 = sin(x0), c0 = cos(x0);for (int t = 0; t < 8; ++t){double dx = -(fx + 3 -t) * CV_PI * 0.25;coeffsX[t] = (float)((cs[t][0] * s0 + cs[t][1] * c0) / (dx * dx));sum += coeffsX[t];}sum = 1.f / sum;for (int t = 0; t < 8; ++t)coeffsX[t] *= sum;}short cbufX[8];cbufX[0] = cv::saturate_cast<short>(coeffsX[0] * 2048);cbufX[1] = cv::saturate_cast<short>(coeffsX[1] * 2048);cbufX[2] = cv::saturate_cast<short>(coeffsX[2] * 2048);cbufX[3] = cv::saturate_cast<short>(coeffsX[3] * 2048);cbufX[4] = cv::saturate_cast<short>(coeffsX[4] * 2048);cbufX[5] = cv::saturate_cast<short>(coeffsX[5] * 2048);cbufX[6] = cv::saturate_cast<short>(coeffsX[6] * 2048);cbufX[7] = cv::saturate_cast<short>(coeffsX[7] * 2048);for (int k = 0; k < matSrc.channels(); ++k){matDst1.at<cv::Vec3b>(j, i)[k] = abs((matSrc.at<cv::Vec3b>(sy-3, sx-3)[k] * cbufX[0] * cbufY[0] + matSrc.at<cv::Vec3b>(sy-2, sx-3)[k] * cbufX[0] * cbufY[1] +matSrc.at<cv::Vec3b>(sy-1, sx-3)[k] * cbufX[0] * cbufY[2] + matSrc.at<cv::Vec3b>(sy, sx-3)[k] * cbufX[0] * cbufY[3] +matSrc.at<cv::Vec3b>(sy+1, sx-3)[k] * cbufX[0] * cbufY[4] + matSrc.at<cv::Vec3b>(sy+2, sx-3)[k] * cbufX[0] * cbufY[5] +matSrc.at<cv::Vec3b>(sy+3, sx-3)[k] * cbufX[0] * cbufY[6] + matSrc.at<cv::Vec3b>(sy+4, sx-3)[k] * cbufX[0] * cbufY[7] +matSrc.at<cv::Vec3b>(sy-3, sx-2)[k] * cbufX[1] * cbufY[0] + matSrc.at<cv::Vec3b>(sy-2, sx-2)[k] * cbufX[1] * cbufY[1] +matSrc.at<cv::Vec3b>(sy-1, sx-2)[k] * cbufX[1] * cbufY[2] + matSrc.at<cv::Vec3b>(sy, sx-2)[k] * cbufX[1] * cbufY[3] +matSrc.at<cv::Vec3b>(sy+1, sx-2)[k] * cbufX[1] * cbufY[4] + matSrc.at<cv::Vec3b>(sy+2, sx-2)[k] * cbufX[1] * cbufY[5] +matSrc.at<cv::Vec3b>(sy+3, sx-2)[k] * cbufX[1] * cbufY[6] + matSrc.at<cv::Vec3b>(sy+4, sx-2)[k] * cbufX[1] * cbufY[7] +matSrc.at<cv::Vec3b>(sy-3, sx-1)[k] * cbufX[2] * cbufY[0] + matSrc.at<cv::Vec3b>(sy-2, sx-1)[k] * cbufX[2] * cbufY[1] +matSrc.at<cv::Vec3b>(sy-1, sx-1)[k] * cbufX[2] * cbufY[2] + matSrc.at<cv::Vec3b>(sy, sx-1)[k] * cbufX[2] * cbufY[3] +matSrc.at<cv::Vec3b>(sy+1, sx-1)[k] * cbufX[2] * cbufY[4] + matSrc.at<cv::Vec3b>(sy+2, sx-1)[k] * cbufX[2] * cbufY[5] +matSrc.at<cv::Vec3b>(sy+3, sx-1)[k] * cbufX[2] * cbufY[6] + matSrc.at<cv::Vec3b>(sy+4, sx-1)[k] * cbufX[2] * cbufY[7] +matSrc.at<cv::Vec3b>(sy-3, sx)[k] * cbufX[3] * cbufY[0] + matSrc.at<cv::Vec3b>(sy-2, sx)[k] * cbufX[3] * cbufY[1] +matSrc.at<cv::Vec3b>(sy-1, sx)[k] * cbufX[3] * cbufY[2] + matSrc.at<cv::Vec3b>(sy, sx)[k] * cbufX[3] * cbufY[3] +matSrc.at<cv::Vec3b>(sy+1, sx)[k] * cbufX[3] * cbufY[4] + matSrc.at<cv::Vec3b>(sy+2, sx)[k] * cbufX[3] * cbufY[5] +matSrc.at<cv::Vec3b>(sy+3, sx)[k] * cbufX[3] * cbufY[6] + matSrc.at<cv::Vec3b>(sy+4, sx)[k] * cbufX[3] * cbufY[7] +matSrc.at<cv::Vec3b>(sy-3, sx+1)[k] * cbufX[4] * cbufY[0] + matSrc.at<cv::Vec3b>(sy-2, sx+1)[k] * cbufX[4] * cbufY[1] +matSrc.at<cv::Vec3b>(sy-1, sx+1)[k] * cbufX[4] * cbufY[2] + matSrc.at<cv::Vec3b>(sy, sx+1)[k] * cbufX[4] * cbufY[3] +matSrc.at<cv::Vec3b>(sy+1, sx+1)[k] * cbufX[4] * cbufY[4] + matSrc.at<cv::Vec3b>(sy+2, sx+1)[k] * cbufX[4] * cbufY[5] +matSrc.at<cv::Vec3b>(sy+3, sx+1)[k] * cbufX[4] * cbufY[6] + matSrc.at<cv::Vec3b>(sy+4, sx+1)[k] * cbufX[4] * cbufY[7] +matSrc.at<cv::Vec3b>(sy-3, sx+2)[k] * cbufX[5] * cbufY[0] + matSrc.at<cv::Vec3b>(sy-2, sx+2)[k] * cbufX[5] * cbufY[1] +matSrc.at<cv::Vec3b>(sy-1, sx+2)[k] * cbufX[5] * cbufY[2] + matSrc.at<cv::Vec3b>(sy, sx+2)[k] * cbufX[5] * cbufY[3] +matSrc.at<cv::Vec3b>(sy+1, sx+2)[k] * cbufX[5] * cbufY[4] + matSrc.at<cv::Vec3b>(sy+2, sx+2)[k] * cbufX[5] * cbufY[5] +matSrc.at<cv::Vec3b>(sy+3, sx+2)[k] * cbufX[5] * cbufY[6] + matSrc.at<cv::Vec3b>(sy+4, sx+2)[k] * cbufX[5] * cbufY[7] +matSrc.at<cv::Vec3b>(sy-3, sx+3)[k] * cbufX[6] * cbufY[0] + matSrc.at<cv::Vec3b>(sy-2, sx+3)[k] * cbufX[6] * cbufY[1] +matSrc.at<cv::Vec3b>(sy-1, sx+3)[k] * cbufX[6] * cbufY[2] + matSrc.at<cv::Vec3b>(sy, sx+3)[k] * cbufX[6] * cbufY[3] +matSrc.at<cv::Vec3b>(sy+1, sx+3)[k] * cbufX[6] * cbufY[4] + matSrc.at<cv::Vec3b>(sy+2, sx+3)[k] * cbufX[6] * cbufY[5] +matSrc.at<cv::Vec3b>(sy+3, sx+3)[k] * cbufX[6] * cbufY[6] + matSrc.at<cv::Vec3b>(sy+4, sx+3)[k] * cbufX[6] * cbufY[7] +matSrc.at<cv::Vec3b>(sy-3, sx+4)[k] * cbufX[7] * cbufY[0] + matSrc.at<cv::Vec3b>(sy-2, sx+4)[k] * cbufX[7] * cbufY[1] +matSrc.at<cv::Vec3b>(sy-1, sx+4)[k] * cbufX[7] * cbufY[2] + matSrc.at<cv::Vec3b>(sy, sx+4)[k] * cbufX[7] * cbufY[3] +matSrc.at<cv::Vec3b>(sy+1, sx+4)[k] * cbufX[7] * cbufY[4] + matSrc.at<cv::Vec3b>(sy+2, sx+4)[k] * cbufX[7] * cbufY[5] +matSrc.at<cv::Vec3b>(sy+3, sx+4)[k] * cbufX[7] * cbufY[6] + matSrc.at<cv::Vec3b>(sy+4, sx+4)[k] * cbufX[7] * cbufY[7] ) >> 22);// 4194304}}}cv::imwrite("Lanczos_1.jpg", matDst1);cv::resize(matSrc, matDst2, matDst1.size(), 0, 0, 4);cv::imwrite("Lanczos_2.jpg", matDst2);

    以上代码的实现结果与cv::resize函数相同，但是执行效率非常低，只是为了详细说明插值过程。OpenCV中默认采用C++ Concurrency进行优化加速，你也可以采用TBB、OpenMP等进行优化加速。