Implementing Hero Wavelength

[Angom8]

Hello,
I am currently working on implementing Hero Wavelength (Spectral mode,no Polarization) into Mitsuba.
For the moment, I worked around the BDSFs to properly evaluate spectrums and some example materials to illustrate the different noise from a regular mono wavelength/spectrum render (a rework of the very old Mitsuba 0.6 dragon dipole notably). I also modified the sensor's ray generation method to shift independently around the visible spectrum range and have an uniform distribution for the Wavelengths.

My main issue revolves around the integrator's handling of the MIS (path or volpath). From what I understand, the MIS for Hero Wavelength is computed at the end of all ray interactions, according to

where for each Wavelength, the render function is divided by the sum of the paths probabilities. If other techniques are used, we take the sum of probabilities for each technique.

In the current (vol)path integrator, the main steps are :

• Direct emission : MIS from the previous bounce pdf and the current em_pdf. The emitter is evaluated and added to the result depending on the variable Throughput (multiplication of all bsdf_weights i.e. basic reflectance/transmission) and the MIS.
• Emitter sampling for the wo
• eval_pdf_sample returns bsdf_val, bsdf_pdf, bsdf_sample, bsdf_weight
• Emitter sampling contribution : MIS from the Emitter Sampling pdf and bsdf_pdf. The bdsf_val is accumulated according to * em_weight * mis_em, the Troughput and only if the emitter contributes (active_em Mask)
• The Ray is updated
• Throughput is multiplied by the current BSDF weight

Hero Wavelength requires to divide some variables (notably between the hero wavelength and the other sidekicks) and compute the paths according to the Hero Wavelength. However, i do not know at which extend this sampling method could be integrated with the current integrators. Is the MIS / rendering equation used in path/volpath detailed somewhere in the documentation ?
I already plan the following changes :

• RR : The path should only stop if the probability of the Hero Wavelength is cut and keeps going even if a Wavelength is missing otherwise
• Remove the MIS computations (mis_weight(prev_bsdf_pdf, em_pdf) for example) from inside the loop
• Split the variables between the Hero Wavelength and its "sidekicks"
• Have a BSDF and PDF evaluation per Wavelength (a monoband Spectrum and a triband Spectrum might possible instead of multiple Floats?)
• wo should only be directed according to the Hero's BSDF values
• The results should only be computed after the loop. The values (bsdf_val, emitter evaluation) are ponderated by the weights (em, bdsf) for each bounce and then divided by the sum of the Wavelength path probabilities (per Wavelength pdf multiplication)

Am I missing something ? I am still not 100% sure about how to sort and compute the rendering equation by changing the main loop.

[Angom8]

I currently modified the main path integrator to split the variables as mentioned above, with (and without) reporting the MIS after the loop. All pdfs are now sampled per wavelength and etas (from BSDFs) are Spectrums (custom XML definition is possible). Some work still needs to be done in order to fully use Hero Wavelength in a general case. I also need more tests with scattered materials and medias against the base integrator and a mono band variant. For now, i am toying with emitter contribution to the BDSFs (the MIS contribution is off and). The noise is notably more colorful when using dielectrics. It's an in between of mono-wavelength and 4-wavelength spectrum.

Here are zoomed images of the CornellBox scene's background with 2 roughdielectrics to increase the noise. These were rendered with a mono-wavelength spectrum, a 4-wavelength spectrum and a 4-wavelength spectrum at 1024/64/64 SPPs. Two area emitters were tested with a radiance definition of "300:0,400:0, 500:8, 600:15.6, 700:18.4, 800:19.6" for the first one and a global "1" for the second one.

	Uniform light	Non uniform light
Mono-wavelength/1024
Base/4-wavelengths/64spp
Hero/4-wavelengths/64spp

[Angom8]

After some documentation (notably from PBRT), the MIS computation inside the loop is a non problem and setting the correct Hero PDF for the Throughput/Beta while using all PDFs for emitter sampling fixed the colorimetric issues. For now, I use a dual SurfaceInteraction setup, one carrying a spectrum of one active wavelength for Hero directional sampling and another with the other wavelengths to complete emitter/BSDF interactions.
By studying a bit longer the volpath integrator, i noticed that it already partially apply Hero Wavelength, but only for the scattering events. I'll apply the same changes (which seem to work properly before further tests on Dirac materials)