pycvcam.OrthographicExtrinsic._transform#

OrthographicExtrinsic._transform(world_points, *, dx=False, dp=False)[source]#

Compute the transformation from the world_points to the normalized_points.

Lets consider world_points in the global coordinate system \(\vec{X}_w = (X_w, Y_w, Z_w)\), the corresponding normalized_points in the camera normalized coordinate system are given \(\vec{x}_n\) can be optained by :

\[\vec{X}_c = R \cdot \vec{X}_w + T\]
\[\vec{x}_n = (X_c, Y_c)\]

where \(R\) is the rotation matrix, \(T\) is the translation vector, and \(Z_c\) the depth of the point in the camera coordinate system is ignored.

The jacobians with respect to the extrinsic parameters is an array with shape (n_points, 2, 6), where the last dimension contains the jacobian with respect to the rotation vector and translation vector. The jacobian with respect to the world points is an array with shape (n_points, 2, 3).

Warning

This method is not intended to be used directly, but rather through the pycvcam.core.Transform.transform() method. Please ensure, the shape of the input world_points is (n_points, 3) before calling this method.

Parameters:

  • world_points (numpy.ndarray) – Array of world 3dpoints to be transformed with shape (n_points, 3).

  • dx (bool, optional) – If True, the Jacobian of the normalized points with respect to the input 3D world points is computed. Default is False. The output will be a 2D array of shape (n_points, 2, 3).

  • dp (bool, optional) – If True, the Jacobian of the normalized points with respect to the pose parameters is computed. Default is False. The output will be a 2D array of shape (n_points, 2, 6).

Returns:

  • normalized_points (numpy.ndarray) – The normalized points in camera normalized coordinates. Shape (n_points, 2).

  • jacobian_dx (Optional[numpy.ndarray]) – The jacobian of the normalized points with respect to the world points. Shape (n_points, 2, 3) if dx is True, otherwise None.

  • jacobian_dp (Optional[numpy.ndarray]) – The jacobian of the normalized points with respect to the extrinsic parameters. Shape (n_points, 2, 6) if dp is True, otherwise None.

Return type:

Tuple[ndarray, ndarray | None, ndarray | None]