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,
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.