# Multiple Importance Sampling in Path tracer produces Dark Images

So I recently implemented Multiple Importance Sampling in my path tracer which was based on next event estimation.

The problem is without MIS I get images like,

This is obtained by setting
light_sample *= 1/light_pdf; // Note no mis_weight
and just returning this sample alone. No BRDF sampling.

Where as with MIS as defined above I get darker images like,

The reason is surely the mis_weight factor. From what I gathered over the internet my MIS code is ok but theoretically it doesn't seem right. For example suppose we performed Light Sampling first and obtained a mis_weight. After that when we tried BRDF sampling, the ray didn't intersect any light source resulting in light_pdf = 0. We neglected this estimate. Since we neglected this estimate isn't it wrong to weight our light sample by mis_weight when we didn't even use multiple estimators, plus how is the sum of weights equal to 1 when we didnt even estimate anything using the BRDF pdf?

Imo, mis_weight factor in light_sample should only be used when BRDF sampling also results in a light ray that intersects the light source.

Can anybody explain if these results are ok or there is something wrong with the code?

EDIT:- There is another case which is a little confusing. I am currently using a heuristic (basically power/distance) to choose 1 light out of multiple lights. What if Light sampling and BRDF sampling choose different light sources. Is MIS still valid then? Since the PDF would change resulting the weights not being able to sum to 1 anymore

EDIT2:- So Stefan pointed out a mistake here, that I was clamping radiance. And this solved that issue and changed the results I'm getting for MIS. I have double checked PBRT's implementation and it is similar to mine. I'm still getting darker images using MIS however now I'm getting more fireflies and I think I read that MIS reduces fireflies?. Anyways, I'm removing the snippet and adding a link to github for the whole kernel. The core functions are evaluateDirectLighting, shading, sampleLights.

--Found a mistake. I was using the direct lighting equation when calculating the brdf sample. (multiplying by $$\cos(\theta^{\prime})$$ and dividing by $$r^2$$). Removed it since we initially sampled through BSDF which is integral over solid angle not area. The image got a little brighter but the fireflies still remain. Note the reflection is harder to converge although its 2500spp while the one below is 1500 spp.

• You shouldn't include the cosine foreshortening term in your brdf_pdf. – Hubble Jan 7 at 6:26
• Im using cosine weighted hemispherical sampling so the BRDF PDF is supposed to be cos(theta)/pi – gallickgunner Jan 7 at 9:57
• @PaulHK - What would that imply? I don't think it's actually PI times darker, its just mis_weight times darker/brighter. Because as I said as soon as i remove mis_wieght and just divide by light_pdf I get the brighter image. – gallickgunner Jan 11 at 10:33
One of the first things that many people get wrong with MIS of direct lighting is that you have to always consider the same light source for both light sampling and BSDF sampling. For example, if you sampled Light $$L_i$$ during light sampling and the ray spawned from BSDF sampling hit $$L_j$$, you cannot mix them together since the probabilities cannot be used together for weights.