Why is inverse intrinsic matrix denoted with dimensions [3, 4]?

Question

I am working with the multinerf Framework from Google Research.
It’s great to work with and things are actually pretty clear down to the paragraph existing data loaders under Intrinsic camera poses:

Intrinsic camera poses

pixtocams= [N, 3, 4] numpy array of inverse intrinsic matrices, OR [3,
4] numpy array of a single shared inverse intrinsic matrix. These
should be in OpenCV format, e.g.
camtopix = np.array([
  [focal,     0,  width/2],
  [    0, focal, height/2],
  [    0,     0,        1],
])
pixtocam = np.linalg.inv(camtopix)

I don’t quite understand why they are talking about an inverse intrinsic matrix (or matrices) of the dimensions [3, 4]. The inverse intrinsic matrix should have the dimensions [3, 3], shouldn’t it?

Asked By: GutzeK456

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Answer 1

I think that it’s a typo, since you can’t really invert a 3×4 matrix (it must be singular). You’re right that the dimensions should be 3×3. You can see that immediately below the passage you quoted, they give this example of an inverse intrinsic matrix:

camtopix = np.array([
  [focal,     0,  width/2],
  [    0, focal, height/2],
  [    0,     0,        1],
])
pixtocam = np.linalg.inv(camtopix)

which is 3×3.

Answered By: BrokenBenchmark

Why is inverse intrinsic matrix denoted with dimensions [3, 4]?

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