OwenModel.compute_pixel_jacobian

giant.camera_models.owen_model:

OwenModel.compute_pixel_jacobian(vectors_in_camera_frame, image=0, temperature=0)

This method computes the Jacobian matrix \(\partial\mathbf{x}_P/\partial\mathbf{x}_C\) where \(\mathbf{x}_C\) is a vector in the camera frame that projects to \(\mathbf{x}_P\) which is the pixel location.

This method is used in the LimbScanning process in order to predict the change in a projected pixel location with respect to a change in the projected vector. The vectors_in_camera_frame input should be a 3xn array of vectors which the Jacobian is to be computed for.

Mathematically the Jacobian matrix is defined as

\[\frac{\partial\mathbf{x}_P}{\partial\mathbf{x}_C} = \frac{\partial\mathbf{x}_P}{\partial\mathbf{x}_I} \frac{\partial\mathbf{x}_I}{\partial\mathbf{x}_C'} \frac{\partial\mathbf{x}_C'}{\partial\mathbf{x}_C}\]

where

\begin{gather} \frac{\partial\mathbf{x}_P}{\partial\mathbf{x}_I} = (1+a_1T+a_2T^2+a_3T^3) \mathbf{K}_{2x2} \\ \frac{\partial\mathbf{x}_I}{\partial\mathbf{x}_C'} = \frac{f}{z_C'}\left[ \begin{array}{ccc}1 & 0 & \frac{-x_C'}{z_C'} \\ 0 & 1 & \frac{-y_C'}{z_C'} \end{array}\right] \\ \frac{\partial\mathbf{x}_C'}{\partial\mathbf{x}_C} = \mathbf{T}_{\boldsymbol{\delta\theta}} \end{gather}

\(\mathbf{x}_C'\) is the camera frame point after applying the misalignment, \(\boldsymbol{\delta\theta}\) is the misalignment vector, \(\mathbf{x}_C\) is the camera frame point before misalignment is applied, \(\mathbf{x}_P\) is the pixel location, \(\mathbf{x}_I\) is the gnomic location, \(a_{1-3}\) are the temperature coefficients, \(T\) is the temperature, \(k_x\) is the inverse of the pixel pitch in the x direction, \(k_y\) is the inverse of the pixel pitch in the y direction, \(f\) is the focal length, \(\mathbf{K}_{2x2}\) is the first 2 rows and columns of the intrinsic_matrix, and \(\mathbf{T}_{\boldsymbol{\delta\theta}}\) is the rotation matrix corresponding to rotation vector \(\boldsymbol{\delta\theta}\).

Parameters:

• vectors_in_camera_frame (Sequence | ndarray) – The vectors to compute the Jacobian at

• image (int) – The index of the image being projected onto (only applicable with multiple misalignments)

• temperature (Real) – The temperature to project the points at

Returns:

The Jacobian matrix as a nx2x3 array

Return type:

ndarray