• Input
  • 2D points (e.g. facial landmarks) on an image
  • Camera parameters (extrinsic and intrinsic) of the image
  • Aligned 3D mesh to the image
• Output
  • 3D positions (or face id and uv) of the 2D points projected on the 3D mesh

Input: image and 2D points	Output: 3D positions

• Step 0: Check original data in ./data/

  • max-planck.obj: A head model of famous guy in physics and sometimes in CG. Gottten from here.
  • max-planck_10k.obj: A decimated version of the above original mesh. Used for testing with smaller mesh.
  • rendered.png: Rendered max-planck.obj by Blender.
  • camera_param.json: Camera parameters of rendered.png.

• Step 1: 2D points preparation

  • You may skip this step. Data is includes in ./data/
  • Run python detection.py. The following files will be generated.
    • detected.txt: Detected 2D facial landmark positions.
    • detected.png: Visualization of 2D facial landmarks. Not used for the following steps.
  • Dependency: face_alignment, skimage, cv2 and numpy

• Step 2: Projection

  • Run python projection.py. Then you will get the following files after a couple of minutes.
    • projected.ply: Projected 2D facial landmarks
    • intersections.json: Ray intersection information
  • Dependency: trimesh and numpy
    • trimesh is used to load .obj while the main process only depends on numpy

A ray corresponding to 2D landmark and camera parameters is cast. Then Möller-Trumbore algorithm is used to detect the intersection between ray and triangles. No acceleration technique (e.g., BVH) is used, assuming input 2D points are sparse and not many.