Timeline for Properties of the image reconstruction filter in rendering
Current License: CC BY-SA 4.0
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| Nov 27, 2020 at 22:49 | answer | added | Nathan Reed | timeline score: 0 | |
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| Mar 2, 2020 at 12:00 | answer | added | lightxbulb | timeline score: 1 | |
| Mar 2, 2020 at 11:28 | comment | added | 0xbadf00d | @lightxbulb I don't think that we can show (b) in its previous form, but I've managed to replace the desired inequality by an inequality in terms of the average over the filter support. Do you think we can show this now? | |
| Mar 2, 2020 at 11:27 | history | edited | 0xbadf00d | CC BY-SA 4.0 |
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| Feb 21, 2020 at 11:38 | comment | added | lightxbulb | I haven't looked into PBRT in a while, let alone waddled through their implementation details, so I cannot answer your question. The questions you have, however, illustrates something notable about the PBRT book: it doesn't go into enough theoretical details - it's more of a book about how to implement the PBRT code, and not so much on the fundamentals of light transport. I would recommend reading the papers on MLT, rather than trying to reverse-engineer the theory from their code. | |
| Feb 21, 2020 at 9:50 | comment | added | 0xbadf00d | @lightxbulb So, it seems like $h_j$ is simply $1$ if the ray from the camera to the first vertex has an intersection with the image plane corresponding to pixel $j$ and $0$ otherwise. Am I missing something? | |
| Feb 21, 2020 at 9:50 | comment | added | 0xbadf00d | @lightxbulb Wait a second. When $I_j$ is estimated using Metropolis Light Transport, is the filter being applied at all? From the pbrt implementation (see pbr-book.org/3ed-2018/Light_Transport_III_Bidirectional_Methods/…) this doesn't seem to be the case, since the samples are directly splatted to the single pixel corresponding to the raster position. | |
| Feb 20, 2020 at 10:04 | comment | added | 0xbadf00d | @lightxbulb I'll think about that. Thanks. What's worrying me more at the moment is the scaling problem described here: computergraphics.stackexchange.com/q/9589/9254. I'm sure you know the answer to it. Would be great if you could take a look. | |
| Feb 20, 2020 at 6:17 | comment | added | lightxbulb | Functions in $L^2$ and $L^1$. It's just an idea, I haven't looked into the details of applying this to your problem. But it solves a similar problem where $e = f - \int f$. I believe it should be applicable to your problem with a few more details taken care of. | |
| Feb 20, 2020 at 6:10 | comment | added | 0xbadf00d | @lightxbulb What are $e$ and $h$ in your equation? | |
| Feb 20, 2020 at 6:05 | comment | added | lightxbulb | If you can rewrite the reconstruction as convolution with a low pass filter, I believe you can use Young's theorem to get a bound. Sketch: $\|e * h\|^2_2 \leq \|e\|^2_2\|h\|^2_1$, if the 1-norm of $h$ is less or equal to 1 (should probably hold for your low pass filter), then you can bound the lhs by the 2-norm of $e$. | |
| Feb 20, 2020 at 5:57 | comment | added | 0xbadf00d | @lightxbulb Yes, that' clear. But, again, I'm lacking information on $h$. Can we say more if we assume that $h$ is a "Box filter"? | |
| Feb 20, 2020 at 5:48 | comment | added | lightxbulb | With the $\alpha$ it's trivial if you can guarantee that $\exists \alpha, \forall x, \, |h_j(x)f(x) - I_j|^2 \leq \alpha |f(x) - \int f|^2$. Note that this may prove problematic only at points where the right hand-side is zero. So I guess you need some extra assumptions on $h$. | |
| Feb 20, 2020 at 5:34 | comment | added | 0xbadf00d | (b) is closely related to the asymptotic variance of estimates of $I_j$. I've missed a constant on the right-hand side. Does it change your comment? | |
| Feb 20, 2020 at 5:32 | history | edited | 0xbadf00d | CC BY-SA 4.0 |
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| Feb 20, 2020 at 5:21 | comment | added | lightxbulb | Technically you can pick it to be whatever you like. In practice it is a low-pass filter and the first requirement is obviously desirable. You cannot guarantee the second one for arbitrary $f$ and $h$. How did you come up with (b)? | |
| Feb 19, 2020 at 18:56 | history | asked | 0xbadf00d | CC BY-SA 4.0 |