Distortion Models

To take the bending effects of lenses, especially those with a high field of view (FOV), most accurately into account, different distortion models have been introduced over the years. uvc ros driver supports two of those models:

• the radtan model
• the equidistant model

Both models are based on the following intrinsic parameters derived from the calibration:

• focal length
• principal point
• distortion coefficients

The following models put the positions of pixels in the incoming distorted image in relation to the postions in the rectified image and thus imply methods of calculating where an image point in the distorted picture is to be found. Since the relative position to the principal point is pivotal for the bending effects, the formulas depend on the distances to it along the axes and .

Furthermore the normalized distance to the pricipal point is used for the correction calculations.

Radtan Model

The radtan model is primarily targeted towards lenses with a low FOV up to 100° as the model itself treats the incident rays as unbent and corrects minor distortions with the obtained distortion coefficients both radially (parameters k_c1, k_c2) and tangentially (parameters k_c3, k_c4).

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The correction consists of the radial correction factor and the tangential components

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Equidistant Model

The equidistant model reflects the nature of physical lenses better and can thus be applied for fish-eye lenses with a FOV of up to 170°. Like other commonly used models the equidistant model's distortion depends on the incidence angle of incoming rays. For the following calculations, the average focal length of the focal lengths in x and y direction will be used. Due to the fact that most camera sensors use square pixels, they are usually very similar.

Additionally the a correction factor compensates for the model's insufficiencies and lens imperfections. In contrast to the radtan model there are no tangential corrections.

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Comparison between the models

As mentioned before, when using the radtan model accurate distortion correction is provided only for low FOVs. The following images demonstrate the limitations of the model. While the corrected image using the radtan model (left) cannot hold up with the distortion of a fisheye lens with a FOV of around 150° (center), the equidistant model shows a good rectification (right).