Defining decentering distortion

Decentering distortion is the non-symmetric distortion due to the misalignment of the lens elements when the camera is assembled. The decentering distortion values may be provided to you as P1 to P4 coefficients or in tabular format.

The equation for decentering distortion is:

delta x = (1 + P3r2 + P4r4 ...) (P1 (r2+2x2) + 2P2xy)
delta y = (1 + P3r2 + P4r4 ...) (2P1xy + P2(r2+2y2)

where:

x: the x-image coordinate of a given image point
y: the y-image coordinate of a given image point
Pn: the decentering distortion coefficients
delta x: the distortion of an image point at x and y in the x-axis
delta y: the distortion of an image point at x and y in the y-axis

The decentering distortion parameter is optional and the coefficients may or may not appear in the camera calibration report.

Note: It is recommended that you obtain the decentering distortion values for digital cameras. Because the manufacturing of digital cameras and their lenses is often not as precise as that for high-end photogrammetric cameras, the decentering distortion tends to be higher.