On the Filter Size

[hbb1]

If a filter is small enough, we are able to approximate a pixel using a point, so as to achieving high accuracy. However, if the filter is too small, gradient can not be well received. So Here is a trade-off.

[hbb1]

Experiment setup

We assume the initial scale per-point is small enough, so the low pass filter dominate the training at the beginning.

Filter radius	Visualization
$0.001$
$\sqrt{2}/3 * 1$
$\sqrt{2}/ 2$
$\sqrt{2}/3 * 2$
$\sqrt{2}/3 * 3$
$10$

I empirically set R = $\sqrt{2}/2$.

[hbb1]

clase as completed.