Distortion (optics) - Software Correction

Software Correction

Radial distortion, whilst primarily dominated by low order radial components, can be corrected using Brown's distortion model. Brown's model caters for both radial distortion and for tangential distortion caused by physical elements in a lens not being perfectly aligned. The latter is thus also known as decentering distortion.

$x_\mathrm{u} = (x_\mathrm{d} - x_\mathrm{c})(1 + K_1r^2 + K_2r^4 + \cdots) + (P_1(r^2 + 2(x_\mathrm{d} - x_\mathrm{c})^2) + 2P_2(x_\mathrm{d} - x_\mathrm{c})(y_\mathrm{d} - y_\mathrm{c}))(1 + P_3r^2 + \cdots)$

$y_\mathrm{u} = (y_\mathrm{d} - y_\mathrm{c})(1 + K_1r^2 + K_2r^4 + \cdots) + (P_2(r^2 + 2(y_\mathrm{d} - y_\mathrm{c})^2) + 2P_1(x_\mathrm{d} - x_\mathrm{c})(y_\mathrm{d} - y_\mathrm{c}))(1 + P_3r^2 + \cdots)$

where:

= distorted image point as projected on image plane using specified lens,

= undistorted image point as projected by an ideal pin-hole camera,

= distortion center (assumed to be the principal point),

= radial distortion coefficient,

= tangential distortion coefficient,

=, and

= an infinite series.

Barrel distortion typically will have a positive term for whereas pincushion distortion will have a negative value. Moustache distortion will have a non-monotonic radial geometric series where for some the sequence will change sign.

Software can correct those distortions by warping the image with a reverse distortion. This involves determining which distorted pixel corresponds to each undistorted pixel, which is non-trivial due to the non-linearity of the distortion equation. Lateral chromatic aberration (purple/green fringing) can be significantly reduced by applying such warping for red, green and blue separately.

An alternative method iteratively computes the undistorted pixel position.

Read more about this topic: Distortion (optics)

Famous quotes containing the word correction:

“There are always those who are willing to surrender local self-government and turn over their affairs to some national authority in exchange for a payment of money out of the Federal Treasury. Whenever they find some abuse needs correction in their neighborhood, instead of applying the remedy themselves they seek to have a tribunal sent on from Washington to discharge their duties for them, regardless of the fact that in accepting such supervision they are bartering away their freedom.”
—Calvin Coolidge (1872–1933)