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I have an application which extract the basic keypoints of the face. This includes the the corners of the eyes, the corners of the mouth, the nose, and the face border.
Is there any build application or algorithm which I can apply so that I can detect the face angle(how much is it oriented to the left or how much is it oriented to the right)?
You will have to detect the face plane in 3D system. This would involve finding extrinsic parameters (orientation and pose) of the face plane with respect to camera. Base on how the face plane is related to image sensor plane, you can determine its orientation towards right and left.
There are numerous posts about extrinsic parameters in stackoverflow. A quick search would help you in finding the extrinsic parameters.
P.S : You will have to calibrate your camera, before you find extrinsic parameters