Frequency Analysis and Sheared Reconstruction for Rendering Motion Blur
Motion blur is crucial for high-quality rendering, but is also very expensive. Our first contribution is a frequency analysis of motionblurred 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 can be approximated by 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 is aligned to the first-order direction of motion 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.
Kevin Egan, Yu-Ting Tseng, Nicolas Holzschuch, Fredo Durand, and Ravi Ramamoorthi. "Frequency Analysis and Sheared Reconstruction for Rendering Motion Blur". ACM Transactions on Graphics (SIGGRAPH 09), 28(3), July 2009.