Title: Stochastic Light Culling

Authors: Yusuke Tokuyoshi (Square Enix), Takahiro Harada (AMD)

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Overview

The paper introduces a novel unbiased light culling technique for rendering scenes with many light sources, particularly virtual point lights (VPLs). Traditional methods like tiled lighting with clamped light ranges introduce bias and darkening artifacts. The proposed method uses stochastic sampling via Russian roulette to determine light influence ranges, achieving sublinear shading cost and unbiased results.

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Key Contributions

1. Stochastic Fall-off Function:
   • Replaces deterministic clamping with a probabilistic approach.
   • Uses Russian roulette to decide whether a light contributes to a shading point.
   • Ensures unbiased estimation of radiance.
2. Sublinear Shading Cost:
   • Light evaluation cost per shading point becomes sublinear with respect to the total number of lights.
   • Controlled via a user-specified error bound.
3. Integration with Tiled Lighting:
   • Demonstrates how stochastic light culling can be integrated into tiled lighting frameworks (e.g., Forward+, clustered shading).
   • Achieves real-time performance with tens of thousands of VPLs.
4. Point Cloud Culling for Imperfect Shadow Maps (ISMs):
   • Accelerates ISM rendering by culling invisible points based on stochastic light ranges.
   • Reduces splatting cost in ISM generation.
5. Extension to Path Tracing:
   • Introduces a bounding sphere tree for light culling in progressive path tracing.
   • Supports area lights and multi-bounce global illumination.
   • Implements GPU optimizations to reduce divergence and memory usage.

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Technical Details

1. Stochastic Fall-off Function

• Traditional fall-off: \(f(l) = \frac{1}{l^2}\) (infinite range).
• Stochastic version:
  • Probability of evaluating a light:
    \(p_i(l) = \min\left(\frac{f(l)}{\alpha_i}, 1\right)\)
  • Light is culled if \(p_i(l) < \xi_i\) (random number).
  • Effective range:
    \(r_i = \frac{1}{\sqrt{\alpha_i \xi_i}}\)

2. Error Bound-Based Control

• Variance of the estimator:
  \(\sigma_i^2(l) = \left(\frac{1}{p_i(l)} - 1\right)f^2(l)\)
• Error bound per light:
  \(\epsilon_i(x, \hat{\omega}) = \sigma_i(l) \cdot E \cdot I_i \cdot V(x, x_i) \cdot \rho(x, \hat{\omega}, \hat{\omega}_i) \cdot \max(\hat{\omega}_i \cdot \hat{n}, 0)\)
• Solving for α: \(\alpha_i = \frac{2\pi \epsilon_{\text{max}}}{E \cdot \max_{\hat{\omega}'} I_i(\hat{\omega}')}\)

3. Tiled Lighting Integration

• Algorithm consists of:
  1. Light range computation (randomized).
  2. Light culling (same as traditional tiled lighting).
  3. Shading (modified fall-off function).

4. Point Cloud Culling for ISMs

• Uses visibility and stochastic range to cull points before splatting.
• Reduces ISM generation time significantly.

5. Path Tracing with Bounding Sphere Tree

• Builds a tree of lights with stochastic ranges.
• Traverses tree to find overlapping lights.
• Uses reservoir sampling to limit memory usage.
• Applies resampled importance sampling to restrict shadow rays to one per shading point.

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Experimental Results

• Real-time rendering of 65,536 VPLs in ~5 ms.
• AISMs (with shadows) for 16,384 VPLs in ~22 ms.
• Path tracing with 50,000+ area lights shows significant noise reduction and performance gain.
• RMSE comparisons show stochastic method outperforms clamping and uniform sampling.

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Limitations & Future Work

• Banding artifacts due to shared random numbers.
• Directional importance and high-frequency BRDFs not fully addressed.
• Future directions include:
  • Better bounding volumes.
  • Improved ISM performance.
  • Clustering shading points.
  • Integration with bidirectional path tracing.

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