## Veach thesis - formula question

Practical and theoretical implementation discussion.
spectral
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### Re: Veach thesis - formula question

So, I have redo the same but taking care of X(o)...X(n) and here is what I got : mis.png (6 KiB) Viewed 6199 times
You see, in the last equation, there is a p_t(Xj) in the denominator and the nominator, they cancel ! Or they are not the same ?

Something else, in the equation (3.3) you use L_i(X_i), then even in your recursive MIS computation you need to keep track of each vertex position, normal etc... to compute each L_i(X_i)... so, you're still limited with the path length ?

Thx
Spectral
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spectral
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### Re: Veach thesis - formula question

I have just discover that Anthony Pajot also has this formulation in his thesis, page 47 http://www.irit.fr/~Anthony.Pajot/publi ... erIrit.pdf.
But so, why not directly computing thus formulation ?
Spectral
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Dietger
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### Re: Veach thesis - formula question

Yes, for the balance heuristic they do cancel. However in the power heuristic they do not cancel out. Also, sometimes it is acceptable (and convenient) to use approximations of the probabilities for computing MIS weights, in which case they no longer cancel. For example, for practical Russian roulette schemes it is often somewhat cumbersome to compute the correct reverse Russian roulette probabilities. Instead you could use a simpler approximation for the Russian roulette probability (or ignore it altogether) for the MIS weights. Although using approximations can compromise the theoretical optimality of your MIS weights, this may be acceptable for the sake of convenience.

spectral
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### Re: Veach thesis - formula question

Dietger wrote:Yes, for the balance heuristic they do cancel. However in the power heuristic they do not cancel out. Also, sometimes it is acceptable (and convenient) to use approximations of the probabilities for computing MIS weights, in which case they no longer cancel. For example, for practical Russian roulette schemes it is often somewhat cumbersome to compute the correct reverse Russian roulette probabilities. Instead you could use a simpler approximation for the Russian roulette probability (or ignore it altogether) for the MIS weights. Although using approximations can compromise the theoretical optimality of your MIS weights, this may be acceptable for the sake of convenience.
Thanks, I see... interesting And about the following question http://igad2.nhtv.nl/ompf2/viewtopic.ph ... =526#p1531, do you have an advice ?

Thx
Spectral
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spectral
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### Re: Veach thesis - formula question

Hi,

Just another question, what to do in a BDPT when a light-ray or camera-ray hit a light ?

Should I :
1) If the previous vertex is not specular, I stop the ray
2) If the previous vertex is specular, I accumulate the light radiance

Should I do this for both camera and light path ?
Spectral
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Dietger
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### Re: Veach thesis - formula question

These are just yet other sampling strategies, so you should just mix them with the all the others bidirectional strategies using MIS. If an eye path hits a light source, you should accumulate the MIS corrected radiance, weather the last vertex was specular or not (this is already accounted for by MIS). The same is true for light paths hitting the camera, although most people just ignore this strategy for simplicity, as its contribution is usually low. The probability of randomly hitting the image plane is infinitely small for pinhole camera's and close to zero for finite aperture lenses except for regions with massive DOF.

jameszhao00
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Joined: Mon May 07, 2012 3:28 am

### Re: Veach thesis - formula question

Quick question:

I was writing out and simplifying the path integral formula and noticed an extra cos term appearing near the sensor parts. Am I simplifying something incorrectly? I've always seen eye path throughputs start at 1.

For example, for a ED-L path with 1 light vertex, we have (all pdfs are in solid angle, geometry-like terms in [...])

We * W(a->b) * [cos(a_wi) * cos(b_wo) / |a-b|^2] * f(a->b->c) * [cos(b_wi) * cos(c_wo) / |b-c|^2] * Le

divided by

P(We) * P(Wa->b) * [cos(b_wo) / |a-b|^2] * P(C)

becomes

We/P(We) * W(a->b)/P(Wa->b) * cos(a_wi) * f(a->b->c) * [cos(b_wi) * cos(c_wo) / |b-c|^2] * Le/P(C)

And for a pinhole camera, We*W(a->b)/(P(We)*P(Wa->b)) = 1 (is this incorrect?) so we get

cos(a_wi) * f(a->b->c) * [cos(b_wi) * cos(c_wo) / |b-c|^2] * Le/P(C)

Why is there an extra cos(a_wi) in there?

We*W(a->b)/(P(We)*P(Wa->b)) = 1 comes from https://sites.google.com/site/qmcrender ... edirects=0