From this image, we can see that for a particular point on the ground, the probability that a random direction will hit the light source is very low. In this case, is the expected value still the integration of all light at that point? Or is the variance high in this case?
ellenluo
I believe the expected value is still the integration since Monte Carlo is always an unbiased estimator. However, in this case, variance is high because we're only using three sample rays from each point. This means the odds of missing the light/blocker is very high. On the limit, this would approximate the actual lighting but with a small number of samples this method performs poorly.
Gilbert-Han
The image looks noisy because noise is introduced by the random sampling; is it common to generate noisy images and then apply a denoising filter?
taoong
Would the image look less noisy if the number of samples increased drastically? From my understanding it would be less noisy because of the law of large numbers, but I'm not sure whether this would make the shading result more accurate/realistic.
hilary217
how much would increasing the number of samples help in here ? Does having an unbiased estimator always work or do we actually prefer biased estimator sometimes?
samparadis
It is my understanding that continuously increasing the number of samples would eventually allow the image to converge. Importance sampling allows the image to converge with fewer samples through samping in the parts of the image that contribute the most.
From this image, we can see that for a particular point on the ground, the probability that a random direction will hit the light source is very low. In this case, is the expected value still the integration of all light at that point? Or is the variance high in this case?
I believe the expected value is still the integration since Monte Carlo is always an unbiased estimator. However, in this case, variance is high because we're only using three sample rays from each point. This means the odds of missing the light/blocker is very high. On the limit, this would approximate the actual lighting but with a small number of samples this method performs poorly.
The image looks noisy because noise is introduced by the random sampling; is it common to generate noisy images and then apply a denoising filter?
Would the image look less noisy if the number of samples increased drastically? From my understanding it would be less noisy because of the law of large numbers, but I'm not sure whether this would make the shading result more accurate/realistic.
how much would increasing the number of samples help in here ? Does having an unbiased estimator always work or do we actually prefer biased estimator sometimes?
It is my understanding that continuously increasing the number of samples would eventually allow the image to converge. Importance sampling allows the image to converge with fewer samples through samping in the parts of the image that contribute the most.