### qestion regarding "A null-scattering path integral formulation of light transport"

Posted:

**Tue Apr 21, 2020 9:29 am**Hello guys,

I have experimenting with hetero volume pathtracing recently and trying to implement https://cs.dartmouth.edu/~wjarosz/publications/miller19null.html

I started with pure scattering volume , some density in the center of larger volume box( so, many empty areas ). I have matched results with the reference delta-tracker in monochromatic case, however, spectral (RGB actually) version has issues:

https://i.gyazo.com/32dd6d8a42fc54601e2cd62d28185634.png (volume box)

https://i.gyazo.com/3ddf9e9183cd84d54f260f981c2ff200.png (monochrome pure scattering)

https://i.gyazo.com/9bf4f2f997d62366a01058836f54e57c.png ( problematic chromatic pure scattering)

In the last problematic case, i set up my RGB majorant (combined extinction) to somewhat red color dominant value (density in the volume is restricted to [0,1]), and got that weird red filled air.

Once new position x is outside of the volbox, I used the same return value expression as on absorption event : return EnvironmentValue * f / ((p.r + p.g + p.b) / 3)

As i can see from the algorithm

https://i.gyazo.com/c2e70967e1a2c674ca5be5695a0ae57d.png

those air zones without density will be always null-scattered until ray gets outside the box, but according to line 9 and 10 the null Un which equals to Umajorant in the absense of Uabs and Uscatt will influence subpath contribution and pdf, these f and p perfectly cancels each other in the monochromatic case, but when dealing with color case, the average of p is no more red-dominant and cant compensate too much for f . I am sure i got something wrong from the above derivations , but cant understand what exactly.

Just for clarity: i assume p and f is rgb values which gets multiplied each subpath with itself, with T (transmittance with subpath length t and Umajorant rgb extinction) and with rgb extinction sampled from volume (abs, scatt or null selected when the event type is choosen).

And this also produces a one more issue, once i went with scattering/null/abs coeff above 1, p and f will quickly raised so high that float32bit value is not enough to cover (something like 100 bounces and i got INF)

Could anyone advise in the right direction ? ( i have contacted directly with authors but they are busy at the moment and suggest to ask here)

Thanks.

I have experimenting with hetero volume pathtracing recently and trying to implement https://cs.dartmouth.edu/~wjarosz/publications/miller19null.html

I started with pure scattering volume , some density in the center of larger volume box( so, many empty areas ). I have matched results with the reference delta-tracker in monochromatic case, however, spectral (RGB actually) version has issues:

https://i.gyazo.com/32dd6d8a42fc54601e2cd62d28185634.png (volume box)

https://i.gyazo.com/3ddf9e9183cd84d54f260f981c2ff200.png (monochrome pure scattering)

https://i.gyazo.com/9bf4f2f997d62366a01058836f54e57c.png ( problematic chromatic pure scattering)

In the last problematic case, i set up my RGB majorant (combined extinction) to somewhat red color dominant value (density in the volume is restricted to [0,1]), and got that weird red filled air.

Once new position x is outside of the volbox, I used the same return value expression as on absorption event : return EnvironmentValue * f / ((p.r + p.g + p.b) / 3)

As i can see from the algorithm

https://i.gyazo.com/c2e70967e1a2c674ca5be5695a0ae57d.png

those air zones without density will be always null-scattered until ray gets outside the box, but according to line 9 and 10 the null Un which equals to Umajorant in the absense of Uabs and Uscatt will influence subpath contribution and pdf, these f and p perfectly cancels each other in the monochromatic case, but when dealing with color case, the average of p is no more red-dominant and cant compensate too much for f . I am sure i got something wrong from the above derivations , but cant understand what exactly.

Just for clarity: i assume p and f is rgb values which gets multiplied each subpath with itself, with T (transmittance with subpath length t and Umajorant rgb extinction) and with rgb extinction sampled from volume (abs, scatt or null selected when the event type is choosen).

And this also produces a one more issue, once i went with scattering/null/abs coeff above 1, p and f will quickly raised so high that float32bit value is not enough to cover (something like 100 bounces and i got INF)

Could anyone advise in the right direction ? ( i have contacted directly with authors but they are busy at the moment and suggest to ask here)

Thanks.