About the camera calibration parameters

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1) The K matrix is "normal" camera matrix that you know.

2) The P matrix however, is not the Projection matrix. It is the new camera matrix if you have rectified an image using rectifyImage(). See this source code, for the member function fx() of image_geometry::PinholeCamera class. Notice how it is accessing the P matrix to return the focal length (and centre of projection)

3) I had run into this trouble recently when rectifying images because I was accessing the K matrix using fullIntrinsicMatrix() function after rectifying the image (which is wrong since camera matrix changes after rectification).

Great! But my calibration result of a monocular camera gives different camera matrix K and projection matrix P:

image_width: 1280
image_height: 720
camera_name: head_camera
camera_matrix:
rows: 3
cols: 3
data: [1191.684030513793, 0, 612.2327036330117, 0, 1190.477585826093, 386.1943923951908, 0, 0, 1]
distortion_model: plumb_bob
distortion_coefficients:
rows: 1
cols: 5
data: [-0.4279928528758908, 0.2098535466268812, 0.001734967304558237, -0.0001708439997913541, 0]
rectification_matrix:
rows: 3
cols: 3
data: [1, 0, 0, 0, 1, 0, 0, 0, 1]
projection_matrix:
rows: 3
cols: 4
data: [1030.564331054688, 0, 602.9148174812726, 0, 0, 1139.198486328125, 388.5892694416107, 0, 0, 0, 1, 0]

which makes me confused...