# Understanding the performance of Lucas Kanade Iterative Image Registration Technique

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?