Algorithm 1. Contour fitting algorithm

Input: 2D face landmarks $K^{\left(i\right)}(i=1,\cdots ,68)$ and 3D mesh V.

Output: Final 3D facial landmarks ($v_i$).

1: Set V based on an initial guess.

2: Repeat:

3: Project all vertices of V onto an image plane and construct a convex hull of the projected V.

4: Calculate normal directions of the contour landmarks in the image.

5: Consider a point contacting the convex hull as a contact point.

6: Find the closest vertex of V from the contact point only if the vertex is visible at the current view.

7: Update it as the new vertex of V.

8: Update V with Equation (4).

9: Continue Until: the matching errors are minimized in Equation (4).