Question regarding distortion-radial

[DevTGHa]

Hello,

I was reading the OpenLensIO lens distortion specification (https://ris-pub.smpte.org/ris-osvp-metadata-camdkit/res/OpenLensIO_v1-0-1.pdf), and I have a question about the radial distortion model.

Regarding the radial term, the document notes:

Note that coefficient subscripts are alternating numerator and denominator in order that the distortion model is extensible to higher powers.

From this, I understand that the ordering of the k coefficients differs from OpenCV's convention:

OpenCV

$$R = \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6}$$

OpenTrackIO

$$R = \frac{1 + k_1 r^2 + k_3 r^4 + k_5 r^6}{1 + k_2 r^2 + k_4 r^4 + k_6 r^6}$$

I understand the motivation behind the interleaved numbering: it keeps the model extensible beyond six radial coefficients without renumbering existing terms.

My question is, what would happen for the simpler, non-rational case. The conventional polynomial radial model uses only k1, k2, k3 with no denominator (i.e. no undistortion/division term):

$$R = 1 + k_1 r^2 + k_2 r^4 + k_3 r^6$$

How should this conventional k1, k2, k3 model be expressed within the OpenTrackIO standard? Specifically, which coefficient indices should k1, k2, k3 map to, and what values should the remaining coefficients take so that the rational form reduces to the simple polynomial?

Thank you.

[yudin-s]

For a plain OpenCV-style polynomial with three radial coefficients, I would put those three values in the numerator positions and leave the rational denominator coefficients unset/zero.

Using the interleaved OpenTrackIO/OpenLensIO numbering you wrote, that means:

conventional polynomial k1 -> standard k1
conventional polynomial k2 -> standard k3
conventional polynomial k3 -> standard k5

standard k2 = 0
standard k4 = 0
standard k6 = 0

Then the rational form becomes:

$$R = \frac{1 + k_1 r^2 + k_3 r^4 + k_5 r^6}{1 + 0 r^2 + 0 r^4 + 0 r^6}$$

which is just:

$$R = 1 + k_1 r^2 + k_3 r^4 + k_5 r^6$$

The main trap is the index interleaving: OpenCV’s second radial coefficient maps to standard k3, not standard k2.

[DevTGHa]

Thanks! That makes sense. I got confused by a few examples with 3 radial distortion values, as having 2 numerator and 1 denominator terms is not very common.