Solution:

Perspective transformation:

A robot vision system can be used to identify the coordinates of certain points on a part. When a camera is used to do an automated manipulation task the coordinates of the camera or the coordinates of the image will come in the perspective vector $\eta^{\top}$ in the Homogenous coordinate transformation matrix.

Transformation means the transfer of an object from one state to another. Perspective transformation works in the same principle in which human vision and camera work which is the conversion of the 3D world into a 2D image.

Hence, the perspective vector will not be zero and the global scaling factor will be less than 1.

The camera converts a 3D object into a 2D object, the image becomes inverted, depth information is lost and the object is scaled or compressed $(\sigma\lt1)$

$ \mathrm{T}=\left[\begin{array}{cc} R k(\theta) & p \\ \eta \mathrm{T} & \sigma \end{array}\right] $

Inverse perspective transformation:

The key to using robot vision to plan the motion of a robotic arm is the inverse perspective transformation. It gives the 3D information of the object w.r.t. the camera coordinate frame.

Perspective transformation gives only (x, y) coordinates of the object. With inverse perspective transformation, the depth of information can be recovered.