The "Fading" Image
Box Filter
The following images were all created using a "box" filter.
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1 Sample per pixel |
4 Samples per pixel |
16 Samples per pixel |
256 Samples per pixel |
| Regular Sampling |
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| Jittered Sampling |
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| Multi-Jittered Sampling |
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Adaptive Sampling
I tried several different methods of adaptive sampling. The first one I tried
uses a recursive subdivision of a square pixel (or filter support) and
continues division for at most 8 iterations, or when the differences of the
corners of the sub-square are all less than a particular threshold value. In
this case, the threshold was 0.02.
But I am not impressed by the result, particularly given the amount of time
required to produce this image. What I think is a better method is to compute
a regular sample, then another, very different sample, and if they are far
off, refine each and re-compute. To maximize the combinatorial disparity
between the samples, probably the best choice is to use the Fibonacci
sequence. I think it will work well, because it approximates an exponential,
and adjacent numbers in the sequence are "highly" relatively prime. The
following uses a maximum of 12 Fibonacci iterations.
Mark suggested doing something similar, but using jittered samples rather than
uniform samples, as in this image
"Tent" Filter
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16 Samples per pixel |
256 Samples per pixel |
| Regular Sampling |
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| Jittered Sampling |
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| Multi-Jittered Sampling |
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