Assignment 4

Part 2

Question 1

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Part 3

Question 2

There is less noise in regions of the floor where the specular highlight is very likely to reflect the yellow light source. Since the yellow light source is very large, in the area of floor where specular rays tend to reflect towards the yellow light, these rays are quite likely to intersect the yellow light. It's reflection is therefore consistently visible and noise is low.

The area of the floor whose specular highlight is very likely to reflect the blue light, however, has severe noise. Because the blue light is very small, few rays which reflect towards it actually intersect it and the blue light's reflection appears in few samples.

Question 3

When sampling only the light source in this scene, the worst case noise from the bsdf-only render becomes the best case and the best case from the bsdf-only render becomes the worst case.

The blue light's reflection, which formerly appeared as sparse noise, looks nearly perfect. Since the light is quite physically small, consecutive sample rays strike at similar locations and give extremely consistent results.

However, the yellow light's reflection is fairly noisy due to the large surface area being sampled over. The variance of angle and distance between consecutive sample rays is large enough to show significant noise.

Question 4

Jack Sprat could eat no fat. His wife could eat no lean. Likewise, the look of our platter when we sample solely according to the light source or the BSDF. However, bring the two sampling techniques together and they complement one another well; a proper blend of their results will produce more desirable, statistically unbiased, results.

The improved results are due not only to blending, but also because of the weight applied to each according to its "quality" in light of the heuristic used to obtain it. This quality can be roughly explained as:

Given:
- a sample
- the heuristic which produced this sample
- and all other heuristics we are using to produce samples

What is the probability that this particular heuristic would have produced this particular sample over all possible heuristics which could have produced it?

By weighting our results in such a fashion, we downplay the importance of samples whose existence is not statistically probable. This alleviates the far-spread noise seen in the bsdf-only render. Here, several statistically unlikely rays were produced which succeeded in striking the blue light, creating bright points far afield of where one would expect. In multi-importance sampling, these rays are seen as far less likely to have been produced by the bsdf than by simply sampling the light from this point, and we weight down the errant bsdf-produced rays accordingly.

Part 4

Question 5

It is in the regions of specular highlight that the bsdf-sampled image really shines. When the eye ray glances specular surfaces at low angles, the pdf for reflection rays tends to send them in a fairly uniform direction. This leads to little variance, from one sample to the next, in the location sampled on the environment map and, hence, very little noise.

Overall, however, the bsdf-sampled image is extremely noisy. The noise is most pronounced on less specular objects and the areas on specular objects where a specular highlight is not present. Here, there is less favor to the direction of reflection, leading to reflection rays with great variation in direction. Compounding the effect of widely scattered reflection rays, the environment map's high frequency changes in light levels guarantee wide ranging results from one widely spaced sample to the next and, thus, high frequency noise in areas of low specularity.

Question 6

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Question 7

Question 8

• This is largely due to the high contrast and high-frequency light distribution in this scene's environment map.