This is an example using Adrian Bulat's face_alignment library and Python to draw the head's basis vectors

3DHeadOrientation.py

import numpy as np
import cv2
import face_alignment

# Initialize the face alignment tracker
fa = face_alignment.FaceAlignment(face_alignment.LandmarksType._3D, flip_input=True, device="cuda")

# Start the webcam capture, exit with 'q'
cap = cv2.VideoCapture(0)
while(not (cv2.waitKey(1) & 0xFF == ord('q'))):
    ret, frame = cap.read()
    if(ret):
        # Clear the indices frame
        canonical = np.zeros(frame.shape)

        # Run the face alignment tracker on the webcam image
        imagePoints = fa.get_landmarks_from_image(frame)
        if(imagePoints is not None):
            imagePoints = imagePoints[0]

            # Compute the Mean-Centered-Scaled Points
            mean = np.mean(imagePoints, axis=0) # <- This is the unscaled mean
            scaled = (imagePoints / np.linalg.norm(imagePoints[42] - imagePoints[39])) * 0.06 # Set the inner eye distance to 60cm (just because)
            centered = scaled - np.mean(scaled, axis=0) # <- This is the scaled mean

            # Construct a "rotation" matrix (strong simplification, might have shearing)
            rotationMatrix = np.empty((3,3))
            rotationMatrix[0,:] = (centered[16] - centered[0])/np.linalg.norm(centered[16] - centered[0])
            rotationMatrix[1,:] = (centered[8] - centered[27])/np.linalg.norm(centered[8] - centered[27])
            rotationMatrix[2,:] = np.cross(rotationMatrix[0, :], rotationMatrix[1, :])
            invRot = np.linalg.inv(rotationMatrix)

            # Object-space points, these are what you'd run OpenCV's solvePnP() with
            objectPoints = centered.dot(invRot)

            # Draw the computed data
            for i, (imagePoint, objectPoint) in enumerate(zip(imagePoints, objectPoints)):
                # Draw the Point Predictions
                cv2.circle(frame, (imagePoint[0], imagePoint[1]), 3, (0,255,0))

                # Draw the X Axis
                cv2.line(frame, tuple(mean[:2].astype(int)), 
                                tuple((mean+(rotationMatrix[0,:] * 100.0))[:2].astype(int)), (0, 0, 255), 3)
                # Draw the Y Axis
                cv2.line(frame, tuple(mean[:2].astype(int)), 
                                tuple((mean-(rotationMatrix[1,:] * 100.0))[:2].astype(int)), (0, 255, 0), 3)
                # Draw the Z Axis
                cv2.line(frame, tuple(mean[:2].astype(int)), 
                                tuple((mean+(rotationMatrix[2,:] * 100.0))[:2].astype(int)), (255, 0, 0), 3)
                
                # Draw the indices in Object Space
                cv2.putText(canonical, str(i), 
                            ((int)((objectPoint[0] * 1000.0) + 320.0), 
                             (int)((objectPoint[1] * 1000.0) + 240.0)), 
                            cv2.FONT_HERSHEY_SIMPLEX, 0.3, (255, 255, 255), 1, cv2.LINE_AA)

        cv2.imshow('Webcam View', frame)
        cv2.imshow('Canonical View', canonical)

# When everything is done, release the capture
cap.release()
cv2.destroyAllWindows()

Hi. This process is giving good results for video.
I want to calculate pitch, yaw, roll of a face.
So,
I added these lines

   def rotationMatrixToEulerAngles(R) :
       sy = math.sqrt(R[0,0] * R[0,0] +  R[1,0] * R[1,0])
       singular = sy < 1e-6
      if  not singular :
          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])
     else :
           x = math.atan2(-R[1,2], R[1,1])
           y = math.atan2(-R[2,0], sy)
           z = 0
    return np.array([x, y, z])


 eulerAngles=rotationMatrixToEulerAngles(rotationMatrix)        
 pitch, yaw, roll = [math.radians(_) for _ in eulerAngles]
 pitch = math.degrees(math.asin(math.sin(pitch)))
 roll = -math.degrees(math.asin(math.sin(roll)))
 yaw = math.degrees(math.asin(math.sin(yaw)))
  rotate_degree=[ str(int(pitch)), str(int(yaw)),str(int(roll))]

Your process is giving good results for pitch, roll, yaw.
But, Instead of video, i have taken directory containing different persons in different orientation images and applied above concept. Giving bad results for pitch, roll, yaw values.
Can you tell the process of calculating pitch, roll, yaw angles

Thanks
Sandhya

Hi. This process is giving good results for video.
I want to calculate pitch, yaw, roll of a face.
So,
I added these lines

   def rotationMatrixToEulerAngles(R) :
       sy = math.sqrt(R[0,0] * R[0,0] +  R[1,0] * R[1,0])
       singular = sy < 1e-6
      if  not singular :
          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])
     else :
           x = math.atan2(-R[1,2], R[1,1])
           y = math.atan2(-R[2,0], sy)
           z = 0
    return np.array([x, y, z])


 eulerAngles=rotationMatrixToEulerAngles(rotationMatrix)        
 pitch, yaw, roll = [math.radians(_) for _ in eulerAngles]
 pitch = math.degrees(math.asin(math.sin(pitch)))
 roll = -math.degrees(math.asin(math.sin(roll)))
 yaw = math.degrees(math.asin(math.sin(yaw)))
  rotate_degree=[ str(int(pitch)), str(int(yaw)),str(int(roll))]

Your process is giving good results for pitch, roll, yaw.
But, Instead of video, i have taken directory containing different persons in different orientation images and applied above concept. Giving bad results for pitch, roll, yaw values.
Can you tell the process of calculating pitch, roll, yaw angles

Thanks
Sandhya

Hi Sandhya,
Have you fixed your results? It seems right results to me.

Hi,
Thanks for your reply.
Sorry for late response.

import numpy as np
import cv2
import face_alignment
import math
def rotationMatrixToEulerAngles(R) :
sy = math.sqrt(R[0,0] * R[0,0] + R[1,0] * R[1,0])
singular = sy < 1e-6
if not singular :
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])
else :
x = math.atan2(-R[1,2], R[1,1])
y = math.atan2(-R[2,0], sy)
z = 0
return np.array([x, y, z])
#Initialize the face alignment tracker
fa = face_alignment.FaceAlignment(face_alignment.LandmarksType.3D, flip_input=True, device="cpu")
frame=cv2.imread("model9.jpg") #("model9.jpg")
canonical = np.zeros(frame.shape)
#Run the face alignment tracker on the image
#imagePoints = fa.get_landmarks_from_image(frame)
imagePoints = fa.get_landmarks(frame)
if(imagePoints is not None):
imagePoints = imagePoints[0]
# Compute the Mean-Centered-Scaled Points
mean = np.mean(imagePoints, axis=0) # <- This is the unscaled mean
scaled = (imagePoints / np.linalg.norm(imagePoints[42] - imagePoints[39])) * 0.06 # Set the inner eye distance to 60cm (just because)
centered = scaled - np.mean(scaled, axis=0) # <- This is the scaled mean
# Construct a "rotation" matrix (strong simplification, might have shearing)
rotationMatrix = np.empty((3,3))
rotationMatrix[0,:] = (centered[16] - centered[0])/np.linalg.norm(centered[16] - centered[0])
rotationMatrix[1,:] = (centered[8] - centered[27])/np.linalg.norm(centered[8] - centered[27])
rotationMatrix[2,:] = np.cross(rotationMatrix[0, :], rotationMatrix[1, :])
eulerAngles=rotationMatrixToEulerAngles(rotationMatrix)
pitch, yaw, roll = [math.radians()*100.0 for _ in eulerAngles]
pitch = math.degrees(math.asin(math.sin(pitch)))
roll = -math.degrees(math.asin(math.sin(roll)))
yaw = math.degrees(math.asin(math.sin(yaw)))
# rotate_degree=[ str(int(pitch)), str(int(roll)),str(int(yaw))]
rotate_degree=[math.floor(pitch),math.floor(roll),math.floor(yaw)]
print ("Rotate_Degree:",rotate_degree)
cv2.imshow('Webcam View', frame)
cv2.imshow('Canonical View', canonical)
cv2.waitKey(0)

With the above code, if i print rotate_degree giving result as Rotate_Degree: ['16', '44', '-20'], where as from https://azure.microsoft.com/en-us/services/cognitive-services/face/#demo link getting values for pitch, roll, yaw as like this
"headPose": {
"pitch": 6.0,
"roll": 24.7,
"yaw": 11.1
}
What should i modify to get the results??

My model9.jpg image is

Thanks in Advance.
Regards,
Sandhyalaxmi Kanna

Hi,
Thanks for your reply.
Sorry for late response.

import numpy as np
import cv2
import face_alignment
import math
def rotationMatrixToEulerAngles(R) :
sy = math.sqrt(R[0,0] * R[0,0] + R[1,0] * R[1,0])
singular = sy < 1e-6
if not singular :
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])
else :
x = math.atan2(-R[1,2], R[1,1])
y = math.atan2(-R[2,0], sy)
z = 0
return np.array([x, y, z])
#Initialize the face alignment tracker
fa = face_alignment.FaceAlignment(face_alignment.LandmarksType.3D, flip_input=True, device="cpu") frame=cv2.imread("model9.jpg") #("model9.jpg") canonical = np.zeros(frame.shape) #Run the face alignment tracker on the image #imagePoints = fa.get_landmarks_from_image(frame) imagePoints = fa.get_landmarks(frame) if(imagePoints is not None): imagePoints = imagePoints[0] # Compute the Mean-Centered-Scaled Points mean = np.mean(imagePoints, axis=0) # <- This is the unscaled mean scaled = (imagePoints / np.linalg.norm(imagePoints[42] - imagePoints[39])) * 0.06 # Set the inner eye distance to 60cm (just because) centered = scaled - np.mean(scaled, axis=0) # <- This is the scaled mean # Construct a "rotation" matrix (strong simplification, might have shearing) rotationMatrix = np.empty((3,3)) rotationMatrix[0,:] = (centered[16] - centered[0])/np.linalg.norm(centered[16] - centered[0]) rotationMatrix[1,:] = (centered[8] - centered[27])/np.linalg.norm(centered[8] - centered[27]) rotationMatrix[2,:] = np.cross(rotationMatrix[0, :], rotationMatrix[1, :]) eulerAngles=rotationMatrixToEulerAngles(rotationMatrix) pitch, yaw, roll = [math.radians()*100.0 for _ in eulerAngles]
pitch = math.degrees(math.asin(math.sin(pitch)))
roll = -math.degrees(math.asin(math.sin(roll)))
yaw = math.degrees(math.asin(math.sin(yaw)))

rotate_degree=[ str(int(pitch)), str(int(roll)),str(int(yaw))]

rotate_degree=[math.floor(pitch),math.floor(roll),math.floor(yaw)]
print ("Rotate_Degree:",rotate_degree)
cv2.imshow('Webcam View', frame)
cv2.imshow('Canonical View', canonical)
cv2.waitKey(0)

With the above code, if i print rotate_degree giving result as Rotate_Degree: ['16', '44', '-20'], where as from https://azure.microsoft.com/en-us/services/cognitive-services/face/#demo link getting values for pitch, roll, yaw as like this "headPose": { "pitch": 6.0, "roll": 24.7, "yaw": 11.1 }
What should i modify to get the results??

My model9.jpg image is

Thanks in Advance.
Regards,
Sandhyalaxmi Kanna

        rotationMatrix = np.empty((3, 3))
        rotationMatrix[0, :] = (centered[16] - centered[0]) / np.linalg.norm(centered[16] - centered[0])
        rotationMatrix[1, :] = (centered[8] - centered[27]) / np.linalg.norm(centered[8] - centered[27])
        rotationMatrix[2, :] = np.cross(rotationMatrix[0, :], rotationMatrix[1, :])

        eulerAngles = rotationMatrixToEulerAngles(rotationMatrix)
        pitch, yaw, roll = eulerAngles
        pitch = np.degrees(np.arcsin(np.sin(pitch)))
        roll = -np.degrees(np.arcsin(np.sin(roll)))
        yaw = -np.degrees(np.arcsin(np.sin(yaw)))

Thanks @patrickwangqy. It is working very well.

np.arcsin(np.sin(pitch))

why?

np.arcsin(np.sin(pitch))

why?

angle range

you clip it with -90+90 deg? but what if actual YAW > 90 deg ?

it is impossible

possible.