Calculate center pose given face mesh vertex positions in augmented faces

[jakehockman]

I would like to manually calculate the center pose given the 3D positions of all the vertices.

From the iOS GARAugmentedFace documentation is says the center pose is "The transform from camera to the center of the face, defined to have the origin located behind the nose and between the two cheek bones."

I was hoping the center pose would correspond to the relative positions of a few vertices but it seems this is not the case. The vertical component appears about half-way between vertices [4, 5] and the depth is approximately between [227, 137] and [447, 366] but I imagine the actual calculation is more complex than that.

Thanks for all your hard work!

https://developers.google.com/ar/reference/ios/interface_g_a_r_augmented_face#a0c13e14623a118cf46dfb1c67b6bc31b
https://developers.google.com/ar/develop/unity-arf/augmented-faces/developer-guide