Frequency Analysis and Sheared Reconstruction for Rendering Motion Blur

Abstract : Motion blur is crucial for high-quality rendering but is also very expensive. Our first contribution is a frequency analysis of motion-blurred scenes, including moving objects, specular reflections, and shadows. We show that motion induces a shear in the frequency domain, and that the spectrum of moving scenes is usually contained in a wedge. This allows us to compute adaptive space-time sampling rates, to accelerate rendering. For uniform velocities and standard axis-aligned reconstruction, we show that the product of spatial and temporal bandlimits or sampling rates is constant, independent of velocity. Our second contribution is a novel sheared reconstruction filter that tightly packs the wedge of frequencies in the Fourier domain, and enables even lower sampling rates. We present a rendering algorithm that computes a sheared reconstruction filter per pixel, without any intermediate Fourier representation. This often permits synthesis of motion-blurred images with far fewer rendering samples than standard techniques require.
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ACM Transactions on Graphics, Association for Computing Machinery, 2009, 28 (3), pp.93:1-14. 〈10.1145/1531326.1531399〉
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Kevin Egan, Yu-Ting Tseng, Nicolas Holzschuch, Frédo Durand, Ravi Ramamoorthi. Frequency Analysis and Sheared Reconstruction for Rendering Motion Blur. ACM Transactions on Graphics, Association for Computing Machinery, 2009, 28 (3), pp.93:1-14. 〈10.1145/1531326.1531399〉. 〈inria-00388461〉

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