A Practical Introduction to
Frequency Analysis of Light Transport
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Welcome
- About this course
- Result of 11 years of research so far
- Started with Durand et al. [2005]
- About the lecture
- Not targetting completness or details
- Give a taste of different possibilities
Noise: An Issue in Physically Based Rendering
- PBR rely a lot on sampling
- Plagued by noise
- Hard to know a stopping criterion
- Frequency Analysis can solve part of it!
Applications
- Examples of today's lecture's applications
- Adaptive sampling
- Upsampling
- Density estimation
- Anti-aliasing
Frequency Analysis
- In the Signal Processing toolbox
- Study of signals and their transformations
- Application to digitalization, sampling, numerical integration
Example: Nyquist Rate
Distance between samples $ d < \dfrac{1}{2 B_w} $The Fourier Transform
The Fourier Transform
Rendering has a lot to do with Blur
For Example: Defocus Blur
Our Goal
- Use the Fourier Transform
- Predict the smoothness in rendering
- Use it to adapt and optimize rendering
- However
- We cannot fully render the image
- We only need a conservative prediction
- But without limitations
- Be able to treat defocus, motion blur, ...
- Work for offline and real-time contexts
Fourier Transform of Rendering?
Fourier Transform of Rendering?
- Need to go to the fundementals
- Rendering Equation [Kajiya 1986]
- Even a little step further ...
- Break the Rendering Equation into pieces
- Decompose shading, defocus, motion, ...
- To perform and compose the analysis
- First a quick recap of the Rendering Equation
Overview
- Introduction
- Frequency Operators
- Travel & Occlusion
- Reflection & Refraction
- Scattering & Absorption
- Applications
- Adaptive sampling & denoising
- Upsampling
- Density estimation
- Antialiasing
- Conclusion
Break: Questions?
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