I am studying about the KLT tracker algorithm. In the KLT tracker, we can try to estimate the optical flow for corner points (because these are good features to track) between frames and the computed optical flow allows us to obtain the trajectory of the moving object.

This problem is formulated as an LK-alignment problem where we are given an image $I$ and a template $T$. There exist some warping function $W(x;p)$ that maps the image $I$ to the template $T$. The optimisation for LK-alignment is given as $$min_p \sum_x [I(W(x;p)) - T(x)]^2$$ However, this optimisation is expressed as $$min_{\Delta p}\sum_x[I(W(x;p+\Delta p)) -T(x)]^2$$ assuming that we have an initial estimate of $p$.

My question is why can the tracking problem be framed as an LK-alignment problem. I do not see how solving for $p$ or $\Delta p$ gives us the optical flow vectors for each frame.

Would appreciate much enlightenment over this topic.


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