Bidirectional related question

Practical and theoretical implementation discussion.
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khalidsalman
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Bidirectional related question

Post by khalidsalman » Sat Jan 07, 2012 6:25 am

Hi all,

In his book, Jensen has a short description of bidirectional path tracing in which he states that "it is important to pay attention to the fact light propagates flux, and not radiance". This sentence puzzled me long enough that I found no other way but to ask this beautiful forum.

Although I'm not questioning the validity of this sentence, I'm not able to comprehend it. Don't we measure radiance arriving from light sources during path tracing? why is this not the case with particle tracing? why on the later we propagate flux and cannot propagate radiance?

Thanks for your help!

joonghyun
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Re: Bidirectional related question

Post by joonghyun » Sat Jan 07, 2012 9:05 am

khalidsalman wrote:"it is important to pay attention to the fact light propagates flux, and not radiance".
Well. "Informally speaking", this is just related to algorithmic efficiency. It's simply better using flux than radiance in performance reason in practice.
You can understand this reason easily why...
If light path carries only flux then, you should take the exact contributable amount of path when connecting the vertice btw. the two different sub paths.
Light sub path carries flux and eye sub path carries importance (dual of radiance). their scale and pdf are fundamentally different.
Simply, this can be viewed as yet another "Jacobian factor" to scale the energy to compute actual contribution falling down to the image plane at the filter support some region.
khalidsalman wrote: Don't we measure radiance arriving from light sources during path tracing? why is this not the case with particle tracing? why on the later we propagate flux and cannot propagate radiance?
As I have already said, we don't have to.. :) I recommend you reading Global Illumination Compendium by Philip Dutre if you still don't understand this notion.

**Edited: I forgot to tell you that you can do basically the same thing with radiance instead of flux.
Last edited by joonghyun on Sat Jan 07, 2012 4:31 pm, edited 1 time in total.

apaffy
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Re: Bidirectional related question

Post by apaffy » Sat Jan 07, 2012 2:52 pm

This is just a question of units isn't it?

Flux (specifically radiant flux) is the total power of the light measured in Watts.
Radiance is power per unit area per unit projected solid angle.

Example: consider a uniform light source of area 3m^2 with flux 10W. Each point of the light source emits uniformly over a hemisphere which has total projected solid angle of pi. As such the radiance carried by any ray (in this hemisphere) from this light source is 10/3pi W/srm^2.

(Replace with "luminous flux" and "luminance" if lumens are more your thing than Watts.)

ingenious
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Re: Bidirectional related question

Post by ingenious » Sat Jan 07, 2012 3:05 pm

I find both the statement by Jensen and the reply by joonghyun above confusing. It's a matter of mathematical frameworks and playing with units, really. To me, the cleanest framework of all is Veach's path integral formulation of light transport, which only ever deals with radiance. And for this reason I do not recommend the Advanced Global Illumination book. The concepts there can be very confusing, especially Lafortune's the GRDF, the adjoint equations and classifications. On the other hand, Veach's framework is simple and rigorous, but only mentioned in the book, which in my opinion is extremely unfair. In addition, it is the only framework in which bidirectional path tracing with multiple importance sampling and Metropolis light transport have been well explained, as acknowledged by the book's authors.

And yes, we are in general recording and filtering radiance on the image plane. Because a raster image is a point sampling of a (possibly filtered) reconstruction of the incoming radiance function over the image plane. You could probably interpret this as some form of flux density estimation. It's a matter of playing with math. More important are the insights and possibilities the framework gives you and what you get in practice. I personally think Veach's path integral framework is very good, and for this reason have some reservations about the AGI book.
Image Click here. You'll thank me later.

joonghyun
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Re: Bidirectional related question

Post by joonghyun » Sat Jan 07, 2012 4:28 pm

ingenious wrote:It's a matter of mathematical frameworks and playing with units, really. To me, the cleanest framework of all is Veach's path integral formulation of light transport, which only ever deals with radiance. And for this reason I do not recommend the Advanced Global Illumination book. The concepts there can be very confusing, especially Lafortune's the GRDF, the adjoint equations and classifications. On the other hand, Veach's framework is simple and rigorous, but only mentioned in the book, which in my opinion is extremely unfair. In addition, it is the only framework in which bidirectional path tracing with multiple importance sampling and Metropolis light transport have been well explained, as acknowledged by the book's authors.
What I meant by was just how to connect the eye paths if light path is given as the flux form.
You're right. we all know this is trivially unit matter and anybody who once read the first one two chapters in that book. This is just another description and I agree on the fact that GRDF actually remains as somewhat theoretical stuff compared to Veach's mathematical rigor and MIS used as if it is 'de facto' in the bidirectional world. ;) However, I think personally AGI is still attractive enough with its reach and in-depth contents in terms of at least 'theoretic' tool.

ingenious
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Re: Bidirectional related question

Post by ingenious » Sat Jan 07, 2012 4:56 pm

I don't think the GDRF and the operators & stuff in AGI are "more theoretical" than Veach's framework. In fact, they are derived from light transport intuition, so they can be considered more "practical" in that sense. Veach's framework is actually more abstract, as it has the notion of path measure and integration over an abstract path space. But it's actually cleaner and conceptually simpler, which makes it more practical. You construct a path, compute its measurement contribution (which is very nicely defined and is easy to understand), divide by the sampling PDF and accumulate.
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joonghyun
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Re: Bidirectional related question

Post by joonghyun » Sun Jan 08, 2012 3:14 am

ingenious wrote:I don't think the GDRF and the operators & stuff in AGI are "more theoretical" than Veach's framework.
ingenious. Firstly, I 'never' mentioned that GRDF is more theoretical... I only mentioned that GRDF 'remains' to be theoretical because not many people currently seems to use it to build bdir. instead they use Veach's formulation with MIS. For the second, I didn't want to compare two formulations which one is better. Actually I think Veach's path formulation framework is way more robust and general than Larfortune's GRDF in the theoretical sense in terms of possible number of paths we can think of. In historical perspective, Veach's paper published later than Larfortune's. :) I have no objections on this fact. So everything is evident.

AGI is just viable knowledge box containing many theoretical references in one place (including somewhat obsolete). One can feels incomportable in the sense that standard (Veach's path formulation) is very missing on its way in that book. Therefore, ingenious warned that bias. I think it's still useful for GI rookey wanting to know in-depth theory step-by-step. In this viewpoint, AGI is regarded as one of the available sources of 'theoretical' framework that one can find to build bdir (what the 'fundamental' difference btw the two is how to define 'bidirectional', there are at least two approaches as far as I know. First one is vertex connection as I mentioned and second one is sampling method of sub paths from each direction,of course second one need some clever weighting (MIS).

khalidsalman
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Re: Bidirectional related question

Post by khalidsalman » Sun Jan 08, 2012 8:08 am

Thanks all for the useful input.

Ingenious made a good case for path integral formulation, so I'll make sure to read that in more details next.

in describing BRDF asymmetry due to refraction, Veach mentions that: "The main thing to notice is that the(eta_t/eta_i)^2 factor is not present in the adjoint BSDF. Thus, importance and light particles are not scaled when they cross the interface. (Notice that this corresponds to the intuitive idea that light particles carry “power”, since power (unlike radiance) is conserved when light enters a different medium." this is on page 147.

so Veach considers that: importance transport is equivalent to particle tracing (which transmits 'power'), whereas path tracing is equivalent to radiance transport. Doesn't this agree with Jensen's statement above?

my confusion is the following: radiance transport is a clear concept. But for me importance transport is so confusing, I don't buy into the idea of 'sensors transmitting importance', and I'm yet to find a clear interpretation with a physical sense that I can understand.

I also don't get why importance was introduced at all, shouldn't life be much easier with incoming and outgoing radiance alone? what is the purpose of adding importance to light transport framework?

If I understand the above, I believe other pieces should fall into place.

Clearly, I'm having a problem with the fundamentals, I should have declared that from the beginning :D

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