CODEWITHSUNDEEP
opencvgraphics3dcomputer-visioncamera-calibration
Carpetfizz
Carpetfizz

Reputation: 9169

Camera projection matrix principal point

I'm a little confused about the purpose of adding the offsets of the principal point, in the camera matrix. These equations are from OpenCV Docs.

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I understand all of this except for adding c_x and c_y. I've read that we do this in order to shift the origin of the projected point so that it's relative to (0, 0), the top left of the image. However, I don't know how adding the coordinates of the center of the image (the principal point) accomplishes this. I think it's simple geometry, but I'm having a hard time understanding.

Upvotes: 3

Views: 6209

Answers (1)

Nico Schertler
Nico Schertler

Reputation: 32627

Just take a look at the diagram in your question. The x/y coordinate system has its origin somewhere around the center of the image. I.e., there can be negative coordinates. The u/v coordinate system has its origin at the top left corner, i.e., there can be no negative coordinates. For the purpose of this question, I will consider the x/y coordinate system to already be scaled with fx, fy, i.e., (x, y) = (fx * x', fy * y').

What you want to do is transform the coordinates from the x/y coordinate system to the u/v coordinate system. Let's look at a few examples:

  • The origin in x/y (0, 0) will map to (cx, cy) in u/v.
  • The top left corner (i.e., (0, 0) in u/v) has the coordinates (-cx, -cy) in x/y.

You could establish many more examples. They all have in common that (u, v) = (x, y) + (fx, fy). And this is the transform stated in the equations.

Upvotes: 4

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