Unable to Reproduce the Volumetric Caustics Example Render

[Disgruntoad]

Hi all, I'm trying to reproduce the Volumetric Caustics demo (under "Simple Scenes") (https://mitsuba.readthedocs.io/en/stable/src/gallery.html)

This is the demo image:

From the author (https://benedikt-bitterli.me/resources/):

Since Mitsuba and pbrt-v4 don't fully support the tonemaps and BRDFs used here, conversion is approximate and Mitsuba/pbrt-v4 output may deviate from the renderings shown here.

To note, this is all done on mitsuba 3.6.4, drjit version 1.0.5, ubuntu 24.04, rendered with a 4090. on driver version 570.133.20 and cuda version 12.8.

I was producing very noisy images that did not approximate the original render, so I modified the xml file in an attempt to more faithfully reproduce the render. This is not exactly the same scene -- the main difference is that the ceiling light is larger and dimmer than the original scene as the small rectangle in the original image was causing too much Monte Carlo noise (or a point source I tried to replace it). The fog also extinguishes slower. So I definitely expect some rendering differences. The other major difference is the addition of a constant emitter. Without it, the scene is much noisier.

<scene version="3.6.4">

  <default name="seed" value="0" />
  
  <integrator type="volpathmis">
    <integer name="max_depth" value="-1"/>
    <integer name="rr_depth" value="32"/>
    <!--<boolean name="hide_emitters" value="true"/>-->
  </integrator>

  <sensor type="perspective">
    <float name="fov" value="19.5" />
    <string name="fov_axis" value="x"/>
    <transform name="to_world">
      <matrix value="-1 0 0 0   0 1 0 1   0 0 -1 7   0 0 0 1" />
    </transform>
	
    <sampler type="orthogonal">
      <integer name="sample_count" value="2209"/>
      <integer name="seed" value="$seed"/>
    </sampler>

    <film type="hdrfilm">
      <integer name="width" value="1024"/>
      <integer name="height" value="1024"/>
      <string name="component_format" value="float16"/>
      <boolean name="sample_border" value="false"/>
      <boolean name="compensate" value="true"/>
      <string name="file_format" value="openexr"/>
      <string name="pixel_format" value="rgb"/>

      <rfilter type="box">
      </rfilter>
    </film>

    <ref id="fog"/>
  </sensor>
  
  <bsdf type="twosided" id="Red">
    <bsdf type="diffuse">
      <rgb name="reflectance" value="0.63, 0.065, 0.05" />
    </bsdf>
  </bsdf>
  
  <bsdf type="twosided" id="Green">
    <bsdf type="diffuse">
      <rgb name="reflectance" value="0.14, 0.45, 0.091" />
    </bsdf>
  </bsdf>
  
  <bsdf type="twosided" id="Yellow">
    <bsdf type="diffuse">
      <rgb name="reflectance" value="0.725, 0.71, 0.68" />
    </bsdf>
  </bsdf>
    
  <bsdf type="roughdielectric" id="Glass">
    <float name="int_ior" value="1.5" />
    <float name="ext_ior" value="1" />
    <string name="distribution" value="ggx"/>
    <float name="alpha" value="0.01"/>
  </bsdf> 

  <shape type="rectangle" name="Floor">
    <ref id="Yellow"/>
    <transform name="to_world">
      <matrix value="0 1 0 0   0 0 2 0   1 0 0 0   0 0 0 1" />
    </transform>
  </shape>
  
  <shape type="rectangle" name="Ceiling">
    <ref id="Yellow"/>
    <transform name="to_world">
      <matrix value="-1 0 0 0   0 0 -2 2   0 -1 0 0   0 0 0 1" />
    </transform>
  </shape>

  <shape type="rectangle" name="Back">
    <ref id="Yellow"/>
    <transform name="to_world">
      <matrix value="0 1 0 0   1 0 0 1   0 0 -2 -1   0 0 0 1" />
    </transform>
  </shape>
  
  <shape type="rectangle" name="Right">
    <ref id="Green"/>
    <transform name="to_world">
      <matrix value="0 0 2 1   1 0 0 1   0 1 0 0   0 0 0 1" />
    </transform>
  </shape>
  
  <shape type="rectangle" name="Left">
    <ref id="Red"/>
    <transform name="to_world">
      <matrix value="0 0 -2 -1   1 0 0 1   0 -1 0 0   0 0 0 1" />
    </transform>
  </shape>
  
  <shape type="sphere" name="Marble">
    <ref id="Glass"/>
    <transform name="to_world">
      <scale x="0.3" y="0.3" z="0.3"/>
      <translate x="-0.25" y="1.2" z="0.15"/>
    </transform>
  </shape> 


  <!-- <shape type="rectangle" name="Lamp">
    <bsdf type="null"/>

    <transform name="to_world">
      <scale x="0.0025" y="0.005" z="0.002"/>
      <translate x="0." y="1.97" z="0."/>
    </transform>
    
    <emitter type="area">
      <rgb name="radiance" value="541127, 381972, 127324"/>
    </emitter>
  </shape> -->


  <shape type="sphere">
    <bsdf type="null"/>
    <float name="radius" value=".1"/>
    <point name="center" value="0., 1.89, 0."/>
    <emitter type="area">
      <rgb name="radiance" value="90, 60, 20"/>
    </emitter>
  </shape>

  <emitter type="constant" name="Sun">
    <rgb name="radiance" value="1.5, 1.05, .36"/>
  </emitter>
  
  <!--<shape type="cube">
    <transform name="to_world">
      <scale value="2.5"/>
    </transform>
    <ref id="fog"/>
    <bsdf type="null"/>
  </shape> -->

  <medium type="homogeneous" id="fog">
    <float name="albedo" value="1." />
    <float name="sigma_t" value=".2" />
    <boolean name="sample_emitters" value="True"/>

    <phase type="isotropic"/>
  </medium>

</scene>

I render by averaging 10 passes to reduce monte carlo noise:

import mitsuba as mi
import numpy as np
mi.set_variant('cuda_rgb')
images = []
for i in range(10):
    scene = mi.load_file('scene_v3-update.xml')
    images.append(np.asarray(mi.render(scene, seed=i)))
images = np.stack(images, axis=0)
image = np.mean(images, axis=0)
bitmap = mi.Bitmap(image)
mi.util.write_bitmap('caustic-10x-fog.png', bitmap)

WARNING: This takes about an hour to process on a 4090.

This is the result:

Here's a single pass render without the constant emitter, sigma_t=0.2 (sigma_t=0.5 is far noisier):

Note that without the area light (just the constant emitter), a single render pass produces:

(This is a single pass with sigma_t=0.5 (as in Bitterli's original render) instead of sigma_t=0.2 as above)

A single pass without the fog and without the area light:

A single pass without the fog but with the area light (hide_emitters=True):

Just to be clear, these are demonstrative renders-- I was messing with the xml file a lot trying to figure out what was going on, so some of the other settings may vary slightly and not be perfectly reproducible with the xml script above.

Note that I am collecting 2209 samples per pixel, or up to 22090 for the 10x pass. Is this all Monte Carlo noise? The image also does not appear to be converging towards the scene rendered by Bitterli.

The rendering result looks so different that I do wonder if there is an issue with the area / point light sources, if this is my fault for setting up the scene incorrectly, or if this is expected behavior for monte carlo noise (based on #1082). Still, I'm unable to recreate the example image, so I thought submitting an issues ticket would help future users to render this scene properly.

[njroussel]

Hi @Disgruntoad

I've moved this to a discussion, because I don't think there is a bug here. I think all of your images can hopefully be useful to someone who runs into the same issue.

A couple of notes:

• The original scene relies on a bidirectional volumetric path tracer. Finding light paths that go though the sphere and then directly hit the emitter is very difficult for a path tracer (impossible if it's a point light) as it cannot use next event estimation. A light tracer will most likely already produce a much better result. Adding participating media to the scene alleviates these issues by making easier to create valid light paths, but it still remains hard to directly sample the high-contribution paths I mentioned at the beginning.
• Having a roughdielectric rather than an ideal dielectric will also help.
• Your scene description has a considerably smaller max_depth (32) than the original (1024).

In any case this is hard scene to render noise-free. I've applied the changes above, and rendered it on a 4090 with 64k samples at 256 x 256 (~4 minutes).