Here a good interpretation could be that in order to discard the hard, sharp edges (which are not likely the case for the realistic lighting situation), we'd rather not view the light source as a single emitting point. The idea of Monte Carlo lighting does just that by taking a random point from the light source and try from the pixel (receiving point) to perceive lighting from that randomly chosen source point; this is also why in the picture in the middle, there would be blurred regions, since we are taking (if using basic Monte Carlo) a relatively too small or too large amount of samples for each receiving point and the noise of randomization is quite obvious.
AronisGod
Wow, so if we augment Monte Carlo integration with some sort of spatial pixel blurring, convolution, we could achieve a fairly good smooth shadow transition.
Here a good interpretation could be that in order to discard the hard, sharp edges (which are not likely the case for the realistic lighting situation), we'd rather not view the light source as a single emitting point. The idea of Monte Carlo lighting does just that by taking a random point from the light source and try from the pixel (receiving point) to perceive lighting from that randomly chosen source point; this is also why in the picture in the middle, there would be blurred regions, since we are taking (if using basic Monte Carlo) a relatively too small or too large amount of samples for each receiving point and the noise of randomization is quite obvious.
Wow, so if we augment Monte Carlo integration with some sort of spatial pixel blurring, convolution, we could achieve a fairly good smooth shadow transition.