Understanding the performance of Lucas Kanade Iterative Image Registration Technique

Question

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?

Edit:

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?