Intrinsic calibration models

Every camera is individually calibrated in production. We use two different models depending on the field of view of the camera.

Fisheye model

This applies to the wide opening angle (O3R225) cameras. For these cameras, we use the fisheye distortion model as described below.

For unprojection: intrinsic calibration model

This model is used for converting pixel positions to 3D vectors. It corresponds to modelID=2. The following formulas show how to apply the model:

Fish eye model for unprojection

Where

$\left(\begin{array}{c}i_x \ i_y\end{array}\right)$ are the input coordinates as integer numbers, in pixels,
$v = \left(\begin{array}{c}v_x\ v_y\ v_z\end{array}\right)$ is the resulting 3D direction vector in the optical coordinate system,
$f_x, f_y, m_x, m_y, \alpha, k_1, k_2, k_3, k_4, \theta^*_{max}$ are the model parameters obtained from the modelParameters array.

For projection: inverse intrinsic calibration model

This model is used for converting directions given as 3D vectors to pixel position. This corresponds to modelID=3. The following formulas show how to apply the model:

Fish eye model for projection

Where

$v = \left(\begin{array}{c}v_x\ v_y\ v_z\end{array}\right)$ is the input direction vector in the optical coordinate system,
$\left(\begin{array}{c}i_x \ i_y\end{array}\right)$ are the resulting image coordinates (the upper left pixel has coordinates $(0, 0)$ ),
$f_x, f_y, m_x, m_y, \alpha, k_1, k_2, k_3, k_4, \theta_{max}$ are the model parameters obtained from the modelParameters array.

Bouguet model

For unprojection: intrinsic calibration model

This model is used for converting pixel positions to 3D vectors. It corresponds to modelID=0. The following formulas show how to apply the model:

Bouguet model for unprojection

Where

$\left(\begin{array}{c}i_x \ i_y\end{array}\right)$ are the input coordinates are integer numbers, in pixels,
$v = \left(\begin{array}{c}v_x\ v_y\ v_z\end{array}\right)$ is the resulting 3D direction vector in the optical coordinate system,
$f_x, f_y, m_x, m_y, \alpha, k_1, k_2, k_3, k_4, k_5$ are the model parameters obtained from the modelParameters array.

For projection: inverse intrinsic calibration model

This model is used for converting directions given as 3D vectors to pixel position. This corresponds to modelID=1. The following formulas show how to apply the model:

Bouguet model for projection

Where

$v = \left(\begin{array}{c}v_x\ v_y\ v_z\end{array}\right)$ is the input direction vector in the optical coordinate system,
$\left(\begin{array}{c}i_x \ i_y\end{array}\right)$ are the resulting image coordinates (the upper left pixel has coordinates $(0, 0)$ ),
$f_x, f_y, m_x, m_y, \alpha, k_1, k_2, k_3, k_4, k_5$ are the model parameters obtained from the modelParameters array.