vector<Rect> faces;

Mat smallImg = Mat(cvRound(grayImg.rows / scale), cvRound(grayImg.cols / scale), CV_8UC1);

resize(grayImg, smallImg, smallImg.size(), 0, 0, INTER_LINEAR);

cascade.detectMultiScale(smallImg, faces, 1.1, 2, 0 | CASCADE_DO_CANNY_PRUNING | CASCADE_FIND_BIGGEST_OBJECT | CASCADE_DO_ROUGH_SEARCH | CASCADE_SCALE_IMAGE, Size(30, 30));

if (faces.empty()) {

return false;

} else {

boundingBox.startX = cvRound(faces[0].x * scale);

boundingBox.startY = cvRound(faces[0].y * scale);

boundingBox.width = cvRound((faces[0].width) * scale);

boundingBox.height = cvRound((faces[0].height) * scale);

boundingBox.centerX = boundingBox.startX + boundingBox.width / 2.0;

boundingBox.centerY = boundingBox.startY+ boundingBox.height / 2.0;

return true;

}

cout << "Starting GetMeanShape..." <<endl;

Mat_<double> result = Mat::zeros(shapes[0].rows, 2, CV_64FC1);

for (int i = 0; i < shapes.size(); i++) {

result = result + projectShape(shapes[i], bounding_box[i]);

}

result = 1.0 / shapes.size() * result;

return result;

Mat_<double> temp(shape.rows, 2);

for (int j = 0; j < shape.rows; j++) {

temp(j, 0) = (shape(j, 0) - bounding_box.centerX) / (bounding_box.width / 2.0);

temp(j, 1) = (shape(j, 1) - bounding_box.centerY) / (bounding_box.height / 2.0);

}

return temp;

Mat_<double> temp(shape.rows, 2);

for (int j = 0; j < shape.rows; j++) {

temp(j, 0) = (shape(j, 0) * bounding_box.width / 2.0 + bounding_box.centerX);

temp(j, 1) = (shape(j, 1) * bounding_box.height / 2.0 + bounding_box.centerY);

}

return temp;

rotation = Mat::zeros(2, 2, CV_64FC1);

scale = 0;

// center the data

double center_x_1 = 0;

double center_y_1 = 0;

double center_x_2 = 0;

double center_y_2 = 0;

for (int i = 0; i < shape1.rows; i++) {

center_x_1 += shape1(i, 0);

center_y_1 += shape1(i, 1);

center_x_2 += shape2(i, 0);

center_y_2 += shape2(i, 1);

}

center_x_1 /= shape1.rows;

center_y_1 /= shape1.rows;

center_x_2 /= shape2.rows;

center_y_2 /= shape2.rows;

Mat_<double> temp1 = shape1.clone();

Mat_<double> temp2 = shape2.clone();

for (int i = 0; i < shape1.rows; i++) {

temp1(i, 0) -= center_x_1;

temp1(i, 1) -= center_y_1;

temp2(i, 0) -= center_x_2;

temp2(i, 1) -= center_y_2;

}

//至此，temp1(与shape1形状相同)和temp2(与shape2形状相同)已经移到了以(0,0)为原点的坐标系

Mat_<double> covariance1, covariance2; //covariance = 协方差

Mat_<double> mean1, mean2;

// calculate covariance matrix

calcCovarMatrix(temp1, covariance1, mean1, CV_COVAR_COLS); //输出covariance1为temp1的协方差，mean1为temp1的均值

calcCovarMatrix(temp2, covariance2, mean2, CV_COVAR_COLS);

double s1 = sqrt(norm(covariance1)); //norm用来计算covariance1的L2范数

double s2 = sqrt(norm(covariance2));

scale = s1 / s2;

temp1 = 1.0 / s1 * temp1;

temp2 = 1.0 / s2 * temp2;

// 至此，通过缩放，temp1和temp2的差距最小（周叔说，这是最小二乘法）

double num = 0;

double den = 0;

for (int i = 0; i < shape1.rows; i++) {

num = num + temp1(i, 1) * temp2(i, 0) - temp1(i, 0) * temp2(i, 1);

den = den + temp1(i, 0) * temp2(i, 0) + temp1(i, 1) * temp2(i, 1);

}

double norm = sqrt(num * num + den * den);

double sin_theta = num / norm;

double cos_theta = den / norm;

rotation(0, 0) = cos_theta;

rotation(0, 1) = -sin_theta;

rotation(1, 0) = sin_theta;

rotation(1, 1) = cos_theta;

assert(v_1.size() == v_2.size());

assert(v_1.size() != 0);

double sum_1 = 0;

double sum_2 = 0;

double exp_1 = 0;

double exp_2 = 0;

double exp_3 = 0;

for (int i = 0; i < v_1.size(); i++) {

sum_1 += v_1[i];

sum_2 += v_2[i];

}

exp_1 = sum_1 / v_1.size(); // 计算第1个向量各元素的期望

exp_2 = sum_2 / v_2.size(); // 计算第2个向量各元素的期望

for (int i = 0; i < v_1.size(); i++) {

exp_3 = exp_3 + (v_1[i] - exp_1) * (v_2[i] - exp_2);

}

return exp_3 / v_1.size();