Representativity for robust and adaptive multiple importance sampling.

Area of Science:

• Computer Graphics
• Numerical Analysis
• Scientific Computing

Background:

• Multiple Importance Sampling (MIS) is a technique to reduce variance in estimators for numerical integration.
• However, MIS estimators can suffer from high variance when the sampling configuration is poorly adapted to the integrand.
• This limitation hinders the robustness of rendering algorithms that rely on accurate numerical integration.

Purpose of the Study:

• To develop a general method for enhancing the robustness of MIS-based estimators.
• To introduce and define the concept of "representativity" for sampling strategies.
• To demonstrate the practical application of this method in common rendering algorithms.

Main Methods:

• Introduced the concept of "representativity" to quantify how well a sampling strategy matches an integrand.
• Developed methods to compute representativity using readily available rendering information (e.g., BSDF, photon maps, caches).
• Adapted estimators based on representativity to improve robustness and reduce variance.

Main Results:

• Demonstrated that representativity can be computed using common rendering data.
• Showcased that adapting estimators to the integrand via representativity significantly enhances robustness.
• Validated the method's effectiveness across various common rendering algorithms.

Conclusions:

• The proposed method offers a general approach to improve the robustness of MIS estimators in numerical integration.
• Representativity provides a principled way to select and adapt sampling strategies for reduced variance.
• This technique has broad applicability and can enhance the performance of diverse rendering algorithms.