1. The Next Frontier

2. POTENTIAL RESEARCH IDEAS
Gradient-domain virtual point lights and scalable many lights rendering.
Gradient-domain photon density estimation in splatting style.
There requires further investigation to bring even more integrators to the gradient domain.

3. POTENTIAL RESEARCH IDEAS
Unifying points, beams, and other integrators for volumetric rendering into a single gradient-domain integrator, i.e., gradient-domain UPBP.
Rendering heterogeneous media with gradient-domain techniques.
Volumetric rendering also deserves more studies, particularly for heterogeneous media such as rendering cloud, fire, cloth and fabrics.

4. POTENTIAL RESEARCH IDEAS
Robust shift mapping and reconstruction.
Integrate path guiding.
Very low sample count gradient-domain rendering.
Combine image-space denoisers with gradient-domain rendering.
There is also a need to make gradient-domain rendering itself more robust. More evaluation of its performance and comparing to path guiding and other machine learning based denoisers that are becoming more common in the industry is an important task.

5. POTENTIAL RESEARCH IDEAS
Simpler implementation of gradient-domain bidirectional techniques.
Gradient-domain rendering in production.
Accelerating gradient-domain rendering on the GPU and for real-time applications.
Bringing gradient-domain techniques to production requires significant changes in existing renderers. Researches of techniques to implement gradient-domain rendering as a plugin onto existing renderers will be very useful.

6. Acknowledgement
We are grateful to all authors of gradient-domain rendering for making their source code available.
We also thank the following authors for the permission to include materials from their publications into the course:
Jaakko Lehtinen, Aalto University and NVIDIA
Derek Nowrouzezahrai, McGill University
Elmar Eisemann, Delft University of Technology
Bochang Moon, Gwangju Institute of Science and Technology

7. Acknowledgement We also thank the following researchers:
Wenzel Jakob for the Mitsuba renderer.
Fabrice Rousselle for some presentation slides of image denoisers we derived.

8. Acknowledgement
We thank the following researchers and artists for making the beautiful scenes:
Eric Veach, Leo Guibas, Miika Aittala, Samuli Laine, and Jaakko Lehtinen (the Door scene)
JayArtist (Kitchen)
Wig42 (Staircase)
Mareck (Bathroom)
Chaos Group and Jaroslav Krivanek (Spotlight bathroom)
Marko Dabrovic (Sponza)
Tiziano Portenier (Bookshelf, Bottle, and Bathroom)

9. ACKNOWLEDGEMENT This project was partly funded by
JSPS KAKENHI grant numbers 15H05308 and 17K19958
Swiss National Science Foundation grant number
We hope you find this course material useful. Please feel free to contact us if you have any questions or spot any errors. 