人脸对齐过程实现 c++和python

c++ 实现版本：

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1 人脸检测
     1.1 使用mtcnn-ncnn进行人脸检测,会输出face box和landmark5
         face box: [x1,y1,x2,y2]
         landmark5: [left_eye,right_eye, nose, month_left, month_right]
 2 图像变换(使用Egien矩阵库)
     2.1 下载Egien
     2.2 创建一个项目, 引用Egien,
     2.3 使用SVD分解, 计算变换矩阵, 
     2.4 进行图像的仿射变换
     =================================================
     代码如下：
     #pragma once
     #include<Dense>
     #include"opencv_base.h"
 
     using namespace std;
     using namespace Eigen;
 
     /*
     使用五点人脸对齐
     left_eye, right_eye, nose, left_month, right_month
     */
     static  Mat face_align_bypoint5(Mat src_frame, vector<Point2d> landmark5, vector<Point2d> box) {
         MatrixXf src_landmark_mtx(5, 2);
         int i = 0;
         for (size_t r = 0; r < landmark5.size(); r++)
         {
             src_landmark_mtx(r, 0) = landmark5.at(r).x;
             src_landmark_mtx(r, 1) = landmark5.at(r).y;
             i++;
         }
 
         Matrix<float, 5, 2> dst_landmark_mtx;
         dst_landmark_mtx << 30.2946, 51.6963,
             65.5318, 51.6963,
             48.0252, 71.7366,
             33.5493, 92.3655,
             62.7299, 92.3655;
 
         int rows = src_landmark_mtx.rows();
         int cols = src_landmark_mtx.cols();
         MatrixXf mean1 = src_landmark_mtx.colwise().mean(); // [1,2]
         MatrixXf mean2 = dst_landmark_mtx.colwise().mean(); // [1,2]
         float col_mean_1 = mean1(0, 0);  // 列的均值
         float col_mean_2 = mean2(0, 0);
 
         //cout << src_landmark_mtx << endl;
         //cout << dst_landmark_mtx << endl;
 
         // std = sqrt(mean(abs(x - x.mean())**2))
         Matrix<float, 5, 2> m1, m2;
         for (size_t r = 0; r < rows; r++)
         {
             for (size_t c = 0; c < cols; c++)
             {
                 src_landmark_mtx(r, c) -= mean1(0, c);
                 dst_landmark_mtx(r, c) -= mean2(0, c);
 
                 auto abs_v1 = std::abs(src_landmark_mtx(r, c));
                 auto abs_v2 = std::abs(dst_landmark_mtx(r, c));
                 m1(r, c) = pow(abs_v1, 2);
                 m2(r, c) = pow(abs_v2, 2);
             }
         }
 
         float std1 = sqrt(m1.mean());
         float std2 = sqrt(m2.mean());
         src_landmark_mtx /= std1;
         dst_landmark_mtx /= std2;
 
         //printf_s(" ============= std norm =============\n");
         //cout << src_landmark_mtx << endl;
         //cout << dst_landmark_mtx << endl;
 
         MatrixXf m = src_landmark_mtx.transpose() * dst_landmark_mtx;  // [2,2]
         JacobiSVD<MatrixXf> svd(m, ComputeThinU | ComputeThinV);
         MatrixXf VT = svd.matrixV().transpose();
         MatrixXf U = svd.matrixU();
         MatrixXf  A = svd.singularValues();
         MatrixXf R = (U*VT).transpose();  // [2,2]
 
         //printf_s(" ============= svd =============\n");
         //cout << VT << endl;
         //cout << U << endl;
         //cout << A << endl;
         //cout << R << endl;
 
         MatrixXf M(3, 3);
         M.row(2) << 0., 0., 1.;
         MatrixXf t1 = (std1 / std2)*R;  // [2,2]
         MatrixXf t2 = mean2.transpose() - (std1 / std2)*R*mean1.transpose();  // [2,1]
         M.row(0) << t1(0, 0), t1(0, 1), t2(0, 0);
         M.row(1) << t1(1, 0), t1(1, 1), t2(1, 0);
 
         //printf_s(" ============= transformer =============\n");
         //cout << M << endl;
 
         //printf_s(" ============= face transformer =============\n");
         Mat cv_transformMat = (Mat_<double>(2, 3) << \
             M(0, 0), M(0, 1), M(0, 2), \
             M(1, 0), M(1, 1), M(1, 2));
         Mat align_img = Mat::zeros(src_frame.rows * 3, src_frame.cols * 3, src_frame.type());
         src_frame.copyTo(align_img(Rect(100, 100, src_frame.cols, src_frame.rows)));
         for (size_t k = 0; k < box.size(); k++)
         {
             box.at(k).x += 100;
             box.at(k).y += 100;
         }
         //rectangle(align_img, 
         //  Rect(box[0].x, box[0].y, 
         //  box[3].x - box[0].x, 
         //  box[3].y - box[0].y),
         //  Scalar(0, 255, 0), 1, 1);
         for (size_t k = 0; k < landmark5.size(); k++)
         {
             landmark5.at(k).x += 100;
             landmark5.at(k).y += 100;
             //circle(align_img, landmark5.at(k), 2, Scalar(0, 255, 0), 1);
         }
 
         //imshow("align", align_img);
         warpAffine(align_img, align_img, cv_transformMat, align_img.size());
 
         //printf_s(" ============= point transformer =============\n");
         Rect roi(0, 0, 0, 0);
         for (size_t r = 0; r < box.size(); r++)
         {
             auto x = box.at(r).x, y = box.at(r).y;
             box[r].x = x * M(0, 0) + y * M(0, 1) + M(0, 2);
             box[r].y = x * M(1, 0) + y * M(1, 1) + M(1, 2);
         }
         for (size_t r = 0; r < landmark5.size(); r++)
         {
             auto x = landmark5.at(r).x, y = landmark5.at(r).y;
             landmark5[r].x = x * M(0, 0) + y * M(0, 1) + M(0, 2);
             landmark5[r].y = x * M(1, 0) + y * M(1, 1) + M(1, 2);
         }
 
         // 由于box的点对齐后会出现 脸不全的情况，需要使用对齐后的关键点来矫正box
         auto dis_left_eye_right_eye = landmark5[1].x - landmark5[0].x;
         auto dis_left_month_left_eye = landmark5[landmark5.size() - 2].y - landmark5[0].y;
         box[0].x = min(box[0].x, landmark5[0].x - dis_left_eye_right_eye / 2);      // left top X;
         box[0].y = min(box[0].y, landmark5[0].y - dis_left_month_left_eye / 1.1);       // left top Y;
         box[box.size() - 1].x = max(box[box.size() - 1].x, landmark5[1].x + dis_left_eye_right_eye / 2);        // right bottom X;
         box[box.size() - 1].y = max(box[box.size() - 1].y, landmark5[landmark5.size() - 1].y + dis_left_month_left_eye / 1.1);      // right bottom y;
 
 
         roi.x = max(0, int(box[0].x));
         roi.y = max(0, int(box[0].y));
         roi.width = min(int(box.at(box.size() - 1).x - roi.x) + 10, align_img.cols - roi.x);
         roi.height = min(int(box.at(box.size() - 1).y - roi.y) + 10, align_img.rows - roi.y);
         Mat align_face = align_img(roi);
 
         //// draw
         //rectangle(align_img, roi, Scalar(0, 0, 255), 1, 1);
         //for (size_t k = 0; k < landmark5.size(); k++)
         //{
         //  circle(align_img, landmark5.at(k), 2, Scalar(0, 0, 255), 1);
         //}
 
         //resize(align_face, align_face, Size(300, 350));
 
         //imshow("src", src_frame);
         //imshow("align2", align_img);
         //imshow("align3", align_face);
         //waitKey(0);
 
         return align_face;
     }
 
     static Mat face_align_bypoint72(Mat src_frame, vector<Point2d> landmark72, vector<Point2d> box) {
         int rows = landmark72.size();
         int cols = 2;
         MatrixXf src_landmark_mtx(rows, 2);
         int i = 0;
         for (size_t r = 0; r < landmark72.size(); r++)
         {
             src_landmark_mtx(r, 0) = landmark72.at(r).x;
             src_landmark_mtx(r, 1) = landmark72.at(r).y;
             i++;
         }
         MatrixXf dst_landmark_mtx(rows, 2);
         dst_landmark_mtx << 32.00, 210.00,
             42.00, 281.00,
             54.00, 353.00,
             73.00, 424.00,
             118.00, 497.00,
             189.00, 558.00,
             265.00, 579.00,
             335.00, 553.00,
             400.00, 494.00,
             444.00, 425.00,
             465.00, 353.00,
             477.00, 282.00,
             484.00, 211.00,
             107.00, 256.00,
             132.00, 241.00,
             158.00, 238.00,
             185.00, 245.00,
             205.00, 267.00,
             181.00, 274.00,
             154.00, 275.00,
             128.00, 268.00,
             160.00, 254.00,
             73.000, 212.00,
             107.00, 190.00,
             148.00, 194.00,
             182.00, 207.00,
             214.00, 231.00,
             179.00, 226.00,
             143.00, 219.00,
             107.00, 213.00,
             312.00, 266.00,
             334.00, 243.00,
             361.00, 235.00,
             387.00, 239.00,
             412.00, 254.00,
             392.00, 268.00,
             364.00, 275.00,
             336.00, 273.00,
             361.00, 253.00,
             298.00, 230.00,
             334.00, 207.00,
             369.00, 196.00,
             411.00, 192.00,
             447.00, 213.00,
             412.00, 215.00,
             374.00, 221.00,
             337.00, 228.00,
             229.00, 270.00,
             224.00, 314.00,
             220.00, 357.00,
             204.00, 402.00,
             225.00, 409.00,
             295.00, 410.00,
             320.00, 404.00,
             303.00, 359.00,
             296.00, 315.00,
             287.00, 270.00,
             260.00, 392.00,
             188.00, 465.00,
             227.00, 464.00,
             264.00, 467.00,
             302.00, 461.00,
             340.00, 466.00,
             305.00, 487.00,
             264.00, 492.00,
             223.00, 485.00,
             226.00, 475.00,
             263.00, 481.00,
             302.00, 476.00,
             300.00, 467.00,
             263.00, 467.00,
             229.00, 465.00;
 
         MatrixXf mean1 = src_landmark_mtx.colwise().mean(); // [1,2]
         MatrixXf mean2 = dst_landmark_mtx.colwise().mean(); // [1,2]
         float col_mean_1 = mean1(0, 0);  // 列的均值
         float col_mean_2 = mean2(0, 0);
 
         cout << src_landmark_mtx << endl;
         cout << dst_landmark_mtx << endl;
 
         // std = sqrt(mean(abs(x - x.mean())**2))
         MatrixXf m1(rows, 2), m2(rows, 2);
         for (size_t r = 0; r < rows; r++)
         {
             for (size_t c = 0; c < cols; c++)
             {
                 src_landmark_mtx(r, c) -= mean1(0, c);
                 dst_landmark_mtx(r, c) -= mean2(0, c);
 
                 auto abs_v1 = std::abs(src_landmark_mtx(r, c));
                 auto abs_v2 = std::abs(dst_landmark_mtx(r, c));
                 m1(r, c) = pow(abs_v1, 2);
                 m2(r, c) = pow(abs_v2, 2);
             }
         }
 
         float std1 = sqrt(m1.mean());
         float std2 = sqrt(m2.mean());
         src_landmark_mtx /= std1;
         dst_landmark_mtx /= std2;
 
         printf_s(" ============= std norm =============\n");
 
         cout << src_landmark_mtx << endl;
         cout << dst_landmark_mtx << endl;
 
         MatrixXf m = src_landmark_mtx.transpose() * dst_landmark_mtx;  // [2,2]
         JacobiSVD<MatrixXf> svd(m, ComputeThinU | ComputeThinV);
         MatrixXf VT = svd.matrixV().transpose();
         MatrixXf U = svd.matrixU();
         MatrixXf  A = svd.singularValues();
         MatrixXf R = (U*VT).transpose();  // [2,2]
 
         printf_s(" ============= svd =============\n");
         cout << VT << endl;
         cout << U << endl;
         cout << A << endl;
         cout << R << endl;
 
         MatrixXf M(3, 3);
         M.row(2) << 0., 0., 1.;
         MatrixXf t1 = (std1 / std2)*R;  // [2,2]
         MatrixXf t2 = mean2.transpose() - (std1 / std2)*R*mean1.transpose();  // [2,1]
         M.row(0) << t1(0, 0), t1(0, 1), t2(0, 0);
         M.row(1) << t1(1, 0), t1(1, 1), t2(1, 0);
 
         printf_s(" ============= transformer =============\n");
         cout << M << endl;
 
 
         printf_s(" ============= face transformer =============\n");
         Mat cv_transformMat = (Mat_<double>(2, 3) << \
             M(0, 0), M(0, 1), M(0, 2), \
             M(1, 0), M(1, 1), M(1, 2));
         Mat align_img = Mat::zeros(src_frame.rows * 3, src_frame.cols * 3, CV_8UC3);
         src_frame.copyTo(align_img(Rect(100, 100, src_frame.cols, src_frame.rows)));
         for (size_t k = 0; k < box.size(); k++)
         {
             box.at(k).x += 100;
             box.at(k).y += 100;
         }
         //rectangle(align_img, Rect(box[0].x, box[0].y, box[3].x - box[0].x, box[3].y - box[0].y),
         //  Scalar(0, 255, 0), 1, 1);
         for (size_t k = 0; k < landmark72.size(); k++)
         {
             landmark72.at(k).x += 100;
             landmark72.at(k).y += 100;
             //circle(align_img, landmark72.at(k), 2, Scalar(0, 255, 0), 1);
         }
 
         //imshow("align", align_img);
         warpAffine(align_img, align_img, cv_transformMat, align_img.size());
 
         printf_s(" ============= point transformer =============\n");
         Rect roi(0, 0, 0, 0);
         for (size_t r = 0; r < box.size(); r++)
         {
             auto x = box.at(r).x, y = box.at(r).y;
             box[r].x = x * M(0, 0) + y * M(0, 1) + M(0, 2);
             box[r].y = x * M(1, 0) + y * M(1, 1) + M(1, 2);
         }
         for (size_t r = 0; r < landmark72.size(); r++)
         {
             auto x = landmark72.at(r).x, y = landmark72.at(r).y;
             landmark72[r].x = x * M(0, 0) + y * M(0, 1) + M(0, 2);
             landmark72[r].y = x * M(1, 0) + y * M(1, 1) + M(1, 2);
         }
 
         // 由于box的点对齐后会出现 脸不全的情况，需要使用对齐后的关键点来矫正box
 
         //auto dis_left_eye_right_eye = landmark72[38].x - landmark72[21].x;
         //auto dis_left_month_left_eye = landmark72[58].y - landmark72[21].y;
         //box[0].x = min(box[0].x, landmark72[21].x - dis_left_eye_right_eye / 2);      // left top X;
         //box[0].y = min(box[0].y, landmark72[21].y - dis_left_month_left_eye / 1.1);       // left top Y;
         //box[box.size() - 1].x = max(box[box.size() - 1].x, landmark72[38].x + dis_left_eye_right_eye / 2);        // right bottom X;
         //box[box.size() - 1].y = max(box[box.size() - 1].y, landmark72[58].y + dis_left_month_left_eye / 1.1);     // right bottom y;
         //roi.x = max(0, int(box[0].x));
         //roi.y = max(0, int(box[0].y));
         //roi.width = min(int(box.at(box.size() - 1).x - roi.x) + 10, align_img.cols - roi.x);
         //roi.height = min(int(box.at(box.size() - 1).y - roi.y) + 10, align_img.rows - roi.y);
 
         // 使用脸部外围的极值点来矫正
         double min_x = landmark72[0].x, min_y = landmark72[41].y;
         double max_x = landmark72[12].x, max_y = landmark72[6].y;
         box[0].x = min(box[0].x, min_x);
         box[0].y = min(box[0].y, min_y);
         roi.x = max(0, int(box[0].x));
         roi.y = max(0, int(box[0].y));
         roi.width = min(int(max_x - roi.x) + 5, align_img.cols - roi.x);
         roi.height = min(int(max_y - roi.y) + 5, align_img.rows - roi.y);
         if (roi.width <= 0 || roi.height <= 0)
         {
             return align_img;
         }
 
         Mat align_face = align_img(roi);
 
         //// draw box & keypoints
         //rectangle(align_img, roi, Scalar(0, 0, 255), 1, 1);
         //for (size_t k = 0; k < landmark72.size(); k++)
         //{
         //  circle(align_img, landmark72.at(k), 2, Scalar(0, 0, 255), 1);
         //}
 
         //resize(align_face, align_face, Size(300, 350));
 
         //imshow("src", src_frame);
         //imshow("align2", align_img);
         //imshow("align3", align_face);
         //waitKey(0);
 
         return align_face;
     }
     =================================================
 3 输出
     3.1 输出的图像就是垂直的人脸图像

　　Python 实现过程：

1 人脸检测
     1.1 使用mtcnn-tensorflow进行人脸检测,会输出face box和landmark5
         face box: [x1,y1,x2,y2]
         landmark5: [left_eye,right_eye, nose, month_left, month_right]
 2 图像变换(使用numpy矩阵库)
     2.1 使用SVD分解, 计算变换矩阵, 
     2.2 进行图像的仿射变换
     ==========================================
              
     # 计算旋转矩阵
     def transformation_from_points(points1, points2):
         points1 = points1.astype(np.float64)
         points2 = points2.astype(np.float64)
         c1 = np.mean(points1, axis=0)
         c2 = np.mean(points2, axis=0)
         points1 -= c1
         points2 -= c2
         s1 = np.std(points1)
         s2 = np.std(points2)
         points1 /= s1
         points2 /= s2
         U, S, Vt = np.linalg.svd(points1.T * points2)
         R = (U * Vt).T
         M = np.vstack([
             np.hstack(((s2 / s1) * R, c2.T - (s2 / s1) * R * c1.T)),
             np.asmatrix([0., 0., 1.])])
         return M
 
 
     # 关键点对齐
     def landmark_alignment(src_landmark, M):
         M_matrix = np.asmatrix(M)
         assert M_matrix.shape == (3, 3)
         rows, cols = src_landmark.shape
         src_landmark2 = src_landmark.copy()
         for i in range(rows):
             x, y = src_landmark[i, 0], src_landmark[i, 1]
             x1 = x * M_matrix[0, 0] + y * M_matrix[0, 1] + M_matrix[0, 2]
             y1 = x * M_matrix[1, 0] + y * M_matrix[1, 1] + M_matrix[1, 2]
             src_landmark2[i] = [x1, y1]
 
         src_landmark2 = src_landmark2.astype(np.int)
         return src_landmark2
 
 
     # 人脸对齐
     def face_alignment(src_landmark5, image_numpy):
         h, w, c = image_numpy.shape
         # 5点对齐后的基准点
         dst_landmark5 = np.asmatrix([[30.2946, 51.6963],  # left eye
                                      [65.5318, 51.6963],  # right eye
                                      [48.0252, 71.7366],  # nose
                                      [33.5493, 92.3655],  # left month
                                      [62.7299, 92.3655]])  # right month
         # 68点对齐后的基准点
         dst_landmark68 = np.asmatrix([[282, 156], [278, 176], [277, 198], [276, 219],
                                       [279, 241], [287, 262], [299, 280], [315, 293],
                                       [333, 300], [352, 300], [372, 293], [391, 282],
                                       [406, 270], [418, 253], [426, 236], [434, 217],
                                       [439, 197], [301, 138], [313, 128], [328, 127],
                                       [343, 130], [356, 138], [384, 144], [400, 142],
                                       [417, 145], [431, 156], [437, 171], [365, 160],
                                       [362, 174], [359, 188], [357, 202], [337, 211],
                                       [344, 215], [352, 219], [360, 219], [368, 218],
                                       [312, 152], [322, 147], [332, 149], [340, 159],
                                       [330, 159], [320, 157], [385, 169], [396, 164],
                                       [407, 167], [414, 176], [405, 177], [394, 174],
                                       [317, 242], [329, 237], [341, 235], [347, 238],
                                       [356, 237], [364, 243], [371, 253], [361, 258],
                                       [351, 259], [343, 259], [335, 257], [326, 251],
                                       [322, 242], [339, 243], [346, 245], [354, 245],
                                       [366, 251], [353, 247], [345, 247], [338, 245]])
 
         # 计算旋转矩阵
         M = transformation_from_points(src_landmark5, dst_landmark5)
         # 旋转图像
         align_image = cv2.warpAffine(image_numpy, M[:2], (w, h))
 
         # M = cv2.getPerspectiveTransform(np.asarray(src_landmark5, np.float32),
         #                                 np.asarray(dst_landmark5, np.float32))
         # align_image = cv2.warpPerspective(image_numpy, M, (w, h))
         return align_image, M
     ==========================================
 3 输出
     3.1 输出的图像就是垂直的人脸图像