Image warping

The image points are converted by a pair of functions $f_{u}(u,v),f_{v}(u,v)$ into a new image

$$ \begin{cases} u^{’} = f_{u}(u,v) \ v^{’} = f_{v}(u,v) \end{cases} $$

It’s also possible to invert warping

$$ \begin{cases} u = g_{u}(u^{’},v^{’}) \ v = g_{v}(u^{’},v^{’}) \end{cases} \space \forall \space (u^{’},v^{’}): I^{’}(u^{’},v^{’}) = I(g_{u}(u^{’},v^{’}),g_{v}(u^{’},v^{’})) $$

Warping to compensate lens distortion

once the lens distortion parameter are computed by camera calibration it’s possible to get back the un-distorted points by a backward warp