Face landmarks detection webcam screen coordinates to NDC

Questions
1

Using face-landmarks-detection, with a 640x480 webcam I get keypoints like:

// sample face
const FACE = {
  "keypoints": [
    {"x":356.2804412841797,"y":295.1960563659668,"z":-23.786449432373047,"name":"lips"},
    {"x":354.8859405517578,"y":264.69520568847656,"z":-36.718435287475586},
    {"x":355.2180862426758,"y":275.3360366821289,"z":-21.183712482452393},
    ...
}
// from https://github.com/tensorflow/tfjs-models/blob/a8f500809f5afe38feea27870c77e7ba03a6ece4/face-landmarks-detection/demos/shared/triangulation.js
const TRIANGULATION = [127, 34, 139, 11, 0, 37, 232, 231, 120, 72, 37, 39, 128, 121, 47, 232, ... ]

These keypoints are the result of my face projected onto my webcam: I’d like to “unproject” those points to the threejs world basis.

My approach would be:

  1. create a perspective camera for the webcam (I assume I know fov/near/far webcam’s values):
    const webcam = new THREE.PerspectiveCamera(85, 640/480, 0.2, 3);
webcam.updateProjectionMatrix();
webcam.updateMatrixWorld(true);
  2. create a geometry:
    const geom = new THREE.BufferGeometry();
// Vertices
const arr = [];
FACE.keypoints.forEach(({ x, y, z }) => arr.push(x, y, z));
const vertices = new Float32Array(arr);
geom.setAttribute("position", new THREE.BufferAttribute(vertices, 3));
// Indices
geom.setIndex(TRIANGULATION);
  3. compute screen2ndcMatrix matrix
    const screen2ndcMatrix = new THREE.Matrix4()
screen2ndcMatrix.set(
  // NEED HELP
)
  4. apply screen2ndcMatrix > webcam.projectionMatrixInverse > webcam.matrixWorld to my geometry
    geom
  .applyMatrix4(screen2ndcMatrix) // screen to ndc
  .applyMatrix4(webcam.projectionMatrixInverse) // ndc to camera
  .applyMatrix4(webcam.matrixWorld); // camera to world

I need help for 3… I have tried:

// ndc -> screen
screen2ndcMatrix.set(
  640/2, 0, 0, 640/2,
  0, -320/2, 0, 320/2,
  0, 0, 0.5, 0.5,
  0, 0, 0, 1
);
// screen -> ndc
screen2ndcMatrix.invert();

but without success:

image
image1386Ă—840 16.4 KB

2

ok, what I missed was my landmark z component has to be in the range [0, 1] before applying screen2ndcMatrix, like here:

image
image1580Ă—795 430 KB

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