A progressive error estimation framework for photon density estimation

1UC San Diego 2Disney Research Zürich

In ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia), 2010

Our error estimation framework takes into account error due to noise and bias in progressive photon mapping. The reference image is rendered using more than one billion photons, and the rendered image is the result using 15M photons. The noise/bias ratio shows the areas of the image dominated by noise (in green) or bias (in red). The bounded pixels images show the results corresponding to a desired confidence in the estimated error value (pixels with bounded error are shown yellow): a higher confidence (90%) provides a conservative per pixel error estimate, and lower confidence (50%) is useful to estimate the average error.


We present an error estimation framework for progressive photon mapping. Although estimating rendering error has been well investigated for unbiased rendering algorithms, there is currently no error estimation framework for biased rendering algorithms. We characterize the error by the sum of a bias estimate and a stochastic noise bound based on stochastic error bounds in biased methods. As a part of our error computation, we extend progressive photon mapping to operate with smooth kernels. This enables the calculation of illumination gradients with arbitrary accuracy, which we use to progressively compute the local bias in the radiance estimate. We also show how variance can be computed in progressive photon mapping, which is used to estimate the error due to noise. As an example application, we show how our stochastic error bound can be used to compute images with a given error threshold. For this example application, our framework only requires the error threshold and a confidence level to automatically terminate rendering. Our results demonstrate how our error estimation framework works well in realistic synthetic scenes.



Toshiya Hachisuka, Wojciech Jarosz, Henrik Wann Jensen. A progressive error estimation framework for photon density estimation. ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia), 29(6):144:1–144:12, December 2010.
    author    = {Hachisuka, Toshiya and Jarosz, Wojciech and Jensen, Henrik Wann},
    title     = {A Progressive Error Estimation Framework for Photon Density Estimation},
    journal   = {ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia)},
    volume    = {29},
    number    = {6},
    month     = dec,
    year      = {2010},
    issn      = {0730-0301},
    pages     = {144:1--144:12},
    articleno = {144},
    doi       = {10/czxq2t}
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