⼈脸姿态估计（计算欧拉⾓）
1.什么是⼈脸姿态估计问题
⼈脸姿态估计主要是获得脸部朝向的⾓度信息。⼀般可以⽤旋转矩阵、旋转向量、四元数或欧拉⾓表⽰（这四个量也可以互相转换）。⼀般⽽⾔，欧拉⾓可读性更好⼀些，使⽤更为⼴泛。本⽂获得的⼈脸姿态信息⽤三个欧拉⾓（pitch，yaw，roll）表⽰。
欧拉⾓动图注解
pitch：俯仰⾓，表⽰物体绕x轴旋转
yaw：偏航⾓，表⽰物体绕y轴旋转
roll：翻滚⾓，表⽰物体绕z轴旋转
2.计算步骤
1）⾸先定义⼀个具有n个关键点的3D脸部模型，n可以根据⾃⼰对准确度的容忍程度进⾏定义，以下⽰例定义6个关键点的3D脸部模型（左眼⾓，右眼⾓，⿐尖，左嘴⾓，右嘴⾓，下颌）；
2）采⽤⼈脸检测以及⾯部关键点检测得到上述3D脸部对应的2D⼈脸关键点；
3）采⽤Opencv的solvePnP函数解出旋转向量；
4）将旋转向量转换为欧拉⾓；
3.定义6关键点的3D Model困境儿童
C++
// 3D model points.
std::vector<cv::Point3d> model_points;
model_points.push_back(cv::Point3d(0.0f, 0.0f, 0.0f)); // No tip
model_points.push_back(cv::Point3d(0.0f, -330.0f, -65.0f)); // Chin
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model_points.push_back(cv::Point3d(-225.0f, 170.0f, -135.0f)); // Left eye left corner
model_points.push_back(cv::Point3d(225.0f, 170.0f, -135.0f)); // Right eye right corner
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model_points.push_back(cv::Point3d(-150.0f, -150.0f, -125.0f)); // Left Mouth corner
model_points.push_back(cv::Point3d(150.0f, -150.0f, -125.0f)); // Right mouth corner
python
# 3D model points.
model_points = np.array([
(0.0, 0.0, 0.0), # No tip
(0.0, -330.0, -65.0), # Chin
(-225.0, 170.0, -135.0), # Left eye left corner
(225.0, 170.0, -135.0), # Right eye right corne
(-150.0, -150.0, -125.0), # Left Mouth corner
(150.0, -150.0, -125.0) # Right mouth corner
])
4.关键点检测
利⽤相关算法进⾏⼈脸关键点检测，⼀般常见68个关键点检测模型，其具体顺序如下所⽰，⽽6个关键点对应的索引id分别为：
下巴：8
⿐尖：30
左眼⾓：36
右眼⾓：45
左嘴⾓：48
右嘴⾓：54
C++
// 2D image points. If you change the image, you need to change vector
std::vector<cv::Point2d> image_points;
image_points.push_back( cv::Point2d(359, 391) ); // No tip
image_points.push_back( cv::Point2d(399, 561) ); // Chin
image_points.push_back( cv::Point2d(337, 297) ); // Left eye left corner image_points.push_back( cv::Point2d(513, 301) ); // Right eye right corner image_points.push_back( cv::Point2d(345, 465) ); // Left Mouth corner
image_points.push_back( cv::Point2d(453, 469) ); // Right mouth corner python
#2D image points. If you change the image, you need to change vector image_points = np.array([
(359, 391), # No tip
(399, 561), # Chin
(337, 297), # Left eye left corner
(513, 301), # Right eye right corne
(345, 465), # Left Mouth corner
(453, 469) # Right mouth corner
], dtype="double")
5.⽤Opencv的solvePnP函数解出旋转向量
OpenCV中solvePnP 和 solvePnPRansac都可以⽤来估计Po。第⼆个solvePnPRansac利⽤随机抽样⼀致算法（Random sample connsus，RANSAC）的思想，虽然计算出的姿态更加精确，但速度慢、没法实现实时系统，所以我们这⾥只关注第⼀个solvePnP函数，具体的参数可以参见Opencv⽂档。
solvePnP implements veral algorithms for po estimation which can be lected using the parameter
flag. By default it us the flag SOLVEPNP_ITERATIVE which is esntially the DLT solution followed by
Levenberg-Marquardt optimization. SOLVEPNP_P3P us only 3 points for calculating the po and it
should be ud only when using solvePnPRansac.
C++: bool solvePnP(InputArray objectPoints, InputArray imagePoints, InputArray cameraMatrix, InputArray
distCoeffs, OutputArray rvec, OutputArray tvec, bool uExtrinsicGuess=fal, int
flags=SOLVEPNP_ITERATIVE )
确定po也就是确定从3D model到图⽚中⼈脸的仿射变换矩阵，它包含旋转和平移的信息。solvePnP函数输出结果包括旋转向量(roatation vector)和平移向量(translation vector)。这⾥我们只关⼼旋转信息，所以主要将对 roatation vector进⾏操作。
在调⽤solvePnP函数前需要初始化cameraMatrix，也就是相机内参，并调⽤solvePnP函数：
c++
// Camera internals
double focal_length = im.cols; // Approximate focal length.
cv::Point2d center = cv::ls / 2, im.rows / 2);
cv::Mat camera_matrix = (cv::Mat_<double>(3, 3) << focal_length, 0, center.x, 0, focal_length, center.y, 0, 0, 1);
cv::Mat dist_coeffs = cv::Mat::zeros(4, 1, cv::DataType<double>::type); // Assuming no lens distortion多功能打印机
cv::Mat rotation_vector; // Rotation in axis-angle form
cv::Mat translation_vector;
朝多音字组词// Solve for po
cv::solvePnP(model_points, landmarks, camera_matrix, dist_coeffs, rotation_vector, translation_vector);
python
# Camera internals
focal_length = size[1]
center = (size[1]/2, size[0]/2)
camera_matrix = np.array(
[[focal_length, 0, center[0]],
酒精图片
[0, focal_length, center[1]],韩式烫发
[0, 0, 1]], dtype = "double"
)
print "Camera Matrix :\n {0}".format(camera_matrix)
dist_coeffs = np.zeros((4,1)) # Assuming no lens distortion
(success, rotation_vector, translation_vector) = cv2.solvePnP(model_points, image_points, camera_matrix, dist_coeffs, flags=cv2.CV_ITERATIVE)
print "Rotation Vector:\n {0}".format(rotation_vector)
print "Translation Vector:\n {0}".format(translation_vector)
6.将旋转向量转换为欧拉⾓
1）旋转向量—>旋转矩阵—>欧拉⾓
旋转向量转旋转矩阵
theta = (rvec)
r = rvec / theta
R_ = np.array([[0, -r[2][0], r[1][0]],
[r[2][0], 0, -r[0][0]],
[-r[1][0], r[0][0], 0]])
R = np.cos(theta) * np.eye(3) + (1 - np.cos(theta)) * r * r.T + np.sin(theta) * R_
print('旋转矩阵')
print(R)
旋转矩阵转欧拉⾓
def isRotationMatrix(R):
Rt = np.transpo(R) #旋转矩阵R的转置
shouldBeIdentity = np.dot(Rt, R) #R的转置矩阵乘以R
I = np.identity(3, dtype=R.dtype) # 3阶单位矩阵
擦玻璃的拼音n = (I - shouldBeIdentity) #默认求⼆范数
return n < 1e-6 # ⽬的是判断矩阵R是否正交矩阵（旋转矩阵按道理须为正交矩阵，如此其返回值理论为0）
def rotationMatrixToAngles(R):
asrt (isRotationMatrix(R)) #判断是否是旋转矩阵（⽤到正交矩阵特性）
sy = math.sqrt(R[0, 0] * R[0, 0] + R[1, 0] * R[1, 0]) #矩阵元素下标都从0开始（对应公式中是sqrt(r11*r11+r21*r21)），sy=sqrt(cosβ*cosβ) singular = sy < 1e-6 # 判断β是否为正负90°
if not singular: #β不是正负90°
x = math.atan2(R[2, 1], R[2, 2])
y = math.atan2(-R[2, 0], sy)
z = math.atan2(R[1, 0], R[0, 0])
el: #β是正负90°
x = math.atan2(-R[1, 2], R[1, 1])
y = math.atan2(-R[2, 0], sy) #当z=0时，此公式也OK，上⾯图⽚中的公式也是OK的
z = 0
x = x*180.0/3.141592653589793
y = y*180.0/3.141592653589793
z = z*180.0/3.141592653589793
return np.array([x, y, z])
2）旋转向量—>四元数—>欧拉⾓
