I am reading the paper: Lucas, B. D., & Kanade, T. (1981). An iterative image registration technique with an application to stereo vision.

I am having some trouble understanding section 4.3 regarding performance. It takes into consideration two signals:

  1. $F(x) = \sin(x)$

  2. $G(x) = \sin(x + h)$

Then it says that $h$ will converge to $|h| < \pi$. And that it suggests that range of convergence can be improved by suppressing high spatial frequencies in the image.

How was the conclusion regarding suppression of high frequencies obtained?


Here is my interpretation. Consider a value/ point on $F(x)$ at $x = 60$ deg. This will match with the value of $F(x)$ at $x = 120$ deg as well. So, the difference in $x$ (or $h$) is less than $\pi$. Now, consider the first signal $F(x)$ as it is and the second signal, $G(x)$, as set of signals that contains high frequencies as well as low frequencies. Superimpose these high frequency signals on the $F(x)$. If $F(x)$ is taken as reference, due to high frequency signals, a smaller $x$ will provide a match for the value at $x = 60$ deg. Thus $h$ will be smaller. Is this the right way of thinking?



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