## Camera and Projector Calibration

Our first attempt at calibration was to use the method described
in "One-Shot Active 3D Shape Acquisition" [Proesmans1996]. Unfortunately,
the explanation in the paper was not very complete and so we opted
for a more straight-forward approach for camera and projector
calibration.
We measured the base of the Einstein bust and found that it was
3" x 2.5" x 2.5". We defined our coordinate space as having one
corner of the base as the origin, and alis-aligning the faces of the
base. We now have a correspondence between six 2D pixel coordinates and
six 3D points in reality.

Since we are looking for an orthographic
camera matrix "C", we can simply solve for the 2x4 matrix that maps
the real points using the pseudoinverse:

Now we choose some grid points on the two visible faces of the base.
We call one point the origin of "projector space" and determine
the location of the other points in "projector space" by counting
the number of grid squares right and up from the origin. To
find the 3D location of each of our selected grid points, we
essentially warp the grid of each face into real-world coordinates,
which is especially easy to do because we are assuming the camera
is orthographic. We can now solve for the orthographic projector
matrix in exactly the same way as we solved for the camera matrix.
Only four points are necessary, but we used six for more accuracy:

Once you have the camera and projection matrices, you can do the
reconstruction, as discussed in the next section...