Gradient-Domain Photon Density Estimation

Supplemental material

Binh-Son Hua      Adrien Gruson      Derek Nowrouzezahrai      Toshiya Hachisuka

1. Code and scenes

The source code (Mistuba implementation) with instruction can be found at the following address: Github repo

Scenes (Mitsuba format) and the reference: You can download each scene individually by clicking on the scene's name below.
Please note that some scenes have a Copyright. Refer to the acknowledgment section inside the paper.

2. Comparison

In the rest of this supplemental document, we demonstrate more results of the scenes in the main paper: "Gradient-Domain Photon Density Estimation". Equal-time comparisons are shown for the below scenes. In each result page, we first show interactive 4-way comparisons between our method and other methods. Each visual comparison includes:

• L2 and L1 reconstruction images
• Relative error map: positive (green) or negative (red) relative error to the reference.
• Gradient images (brightened with +3 exposure value)

Scene	Equal-time comparison	Reference image	Comments
Teaser	5 min 30 min		This scene has some near-specular surfaces which make BDPT [VG95,LW93] inefficient due bad performance in vertex connection. GBDPT [MKA*15] also suffers from this issue and makes noisy reconstruction.
Sponza	10 min 30 min		In this scene, all the surfaces are diffuse which is ideal for GBDPT [MKA*15]. Despite that, our technique works comparably to GBDPT and still outperforms SPPM [HJ09].
Bookshelf	10 min 30 min		In this scene, some regions with SDS paths are challenging for GBDPT [MKA*15] to make an efficient reconstruction, e.g., the objects behind the glass on the bookshelf. In contrast, our technique works well for such regions.
Torus	5 min 30 min		This is one of the classic scenes for progressive photon mapping. In this scene, the torus in the glass cube is lit by many SDS paths. This results in poor performance for GBDPT [MKA*15].
Veach-Lamp	10 min 30 min		This scene was originally used in the GBDPT paper [MKA*15]. Their method achieves good performance on this scene except for the glass egg. Our method does not have this issue. Note that to make the glass egg smooth, we compute the reference using SPPM.

We also show an additional experiment where the reference of the Veach-Lamp scene is computed by BDPT. While this reference image has less errors in the corners and thus favoring GBDPT results, the glass egg is noisy due to the inefficiency of sampling SDS paths. To plot the convergence, we followed Manzi et al. [MKA*15] and discarded 0.1% of the highest pixel errors in the relMSE metric. In this way, we can reproduce similar convergence curves as shown in their paper. As can be seen, our method still works efficiently.

Scene	Equal-time comparison	Reference image	Comments
Veach-Lamp	30 min		This scene was originally used in the GBDPT paper [MKA*15].

2. References

[LW93] Lafortune E. P., Willems Y. D.: Bi-directional path tracing (1993).

[VG95] Veach E., Guibas L.: Bidirectional estimators for light transport. Photorealistic Rendering Techniques. Springer, (1995) 145.

[HJ09] Hachisuka T., Jensen H. W.: Stochastic progressive photon mapping. ACM Transactions on Graphics (TOG) 28, 5 (2009), 141.

[MKA*15] Manzi M., Kettunen M., Aittala M., Lehtinen J., Durand F., Zwicker M.: Gradient-domain bidirectional path tracing. Proc. Eurographics Symposium on Rendering (2015).