I have a problem with understanding a specific operation related to the mapping of an ellipse, captured by a camera, to a plane:
According to this paper, given the calibration matrix $K$ of a camera, a symmetric conic matrix $C'$ can be mapped to a conic $C = K^T C' K$ on the normalized image plane.
I do not understand what the operation $K^T C' K$ is doing and what this normalized image plane might correspond to. Any comment to help me understand what is happening geometrically with this operation would be appreciated.
Note: I did notice that $K^T$ is a lower triangular matrix, $K$ is an upper triangular matrix, and $C'$ is symmetric (not diagonal) but I am unsure of what to do with this information.
This is simply the way that bilinear forms are transformed by a coordinate transformation. The original conic has the homogeneous coordinate matrix equation $\mathbf x'^TC'\mathbf x'=0$. The calibration matrix gives you a transformation $\mathbf x'=K\mathbf x$ from points on the normalized image plane to the original image plane. Substituting this into the first equation, you get $(K\mathbf x)^TC'(K\mathbf x) = \mathbf x^T(K^TC'K)\mathbf x=0$, therefore the conic on the normalized image plane is represented by the matrix $K^TC'K$.