Imperfect Image-Space Control Variates for Monte Carlo Rendering

Chanu Yang , Bochang Moon

Gwangju Institute of Science and Technology

ACM Transactions on Graphics (SIGGRAPH Asia 2025)

Imperfect Image-Space Control Variates for Monte Carlo Rendering
Results of our image-space control variate method, which utilizes two image inputs: one generated via path tracing with independent sampling (PT) and the other via path tracing with common random numbers (CRN), where identical random seeds are assigned to all pixels, unlike in PT. Both input images are rendered with 96 samples per pixel (spp), and the relative mean squared error (relMSE) is reported to quantify numerical accuracy. Our method reduces the variance of each pixel estimate by exploiting correlations among spatially nearby pixel estimates in the CRN image, treating them as control variates. Since the expectations of these variates are unknown, they are approximated using unbiased pixel estimates from the PT image. The control variate coefficients, which determine their relative contributions, are then optimally adjusted by accounting for heterogeneous errors in the estimated expectations.

Abstract

We present an image-space control variate technique to improve Monte Carlo (MC) integration-based rendering. Our method selects spatially nearby pixel estimates as control variates to exploit spatial coherence among pixel estimates in a rendered image without requiring analytic modeling of the control variate functions. Employing control variates is a classical and well-established technique for variance reduction in MC integration, typically relying on the assumption that the expectations of control variates are readily obtainable. When this condition is met, control variate theory offers a principled framework for optimizing their use by adjusting coefficients that determine the relative contribution of each control variate. However, our image-space approach introduces a technical challenge, as the expectations of the pixel-based control variates are unknown and must be estimated from additional MC samples, which are unbiased but inherently noisy. In this paper, we propose a control variate estimator designed to optimally leverage such imperfect control variates by relaxing the traditional requirement that their expectations are known. We demonstrate that our approach, which estimates the optimal coefficients while explicitly accounting for uncertainty in the expectation estimates, effectively reduces the variance of MC rendering across various test scenes.

Contents

License

This work is licensed under a Creative Commons Atribution International 4.0 License.

Creative Commons Atribution International 4.0 License