Tasks:

1. Talk to optics
   1. Ask optics team what the resolution of the camera sensor would be if we took a picture of an object on the ground (not in space)
2. Understand the limitation caused by scaling up the image scene but not the camera

Look into (Direct Linear Transform) DLT/Zhangs method and populate this page.

Direct Linear Transform (DLT)

The Direct Linear Transform (DLT) algorithm is commonly used for camera calibration and mapping 3D world coordinates to 2D image coordinates. It is based on the principle that a linear relationship exists between these two coordinate systems when projecting from a 3D space to a 2D plane.

Key Steps in DLT:

1. Internal Parameters (Intrinsic Matrix):

   The intrinsic matrix describes the camera's internal characteristics, such as focal length, sensor size, and lens distortion. It helps map 3D points from the camera’s frame into the 2D image plane.

2. External Parameters (Extrinsic Matrix):

   The extrinsic matrix consists of the rotation and translation of the camera with respect to the world coordinates. It transforms world coordinates into the camera's frame of reference.

3. Homogeneous Coordinates:

   The 3D world coordinates

   $\begin{bmatrix} X \\ Y \\ Z \\ 1 \end{bmatrix}$

   are projected onto the 2D image plane

   $\begin{bmatrix} u \\ v \\ 1 \end{bmatrix}$ using the combined intrinsic and extrinsic matrices.

The DLT equation is typically formulated as:

$s \cdot \begin{bmatrix} u \\ v \\ 1 \end{bmatrix} = K \cdot [R|t] \cdot \begin{bmatrix} X \\ Y \\ Z \\ 1 \end{bmatrix}$

Where:

• $s$ is a scaling factor,
• $K$ is the intrinsic matrix,
• $[R|t]$ is the extrinsic matrix (rotation and translation).

In the context of your sensor model, DLT helps establish the relationship between your satellite’s internal camera parameters (such as focal length) and external parameters (its position and orientation in space) when observing a scene on Earth.