Frequency Analysis and Sheared Reconstruction for
Rendering Motion Blur

Kevin Egan Yu-Ting Tseng Nicolas Holzschuch Frédo Durand Ravi Ramamoorthi
Columbia University Columbia University INRIA -- LJK MIT CSAIL University of
California, Berkeley


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 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.

    author  = {Kevin Egan and Yu-Ting Tseng and Nicolas Holzschuch and
        Fr{\'{e}}do Durand and Ravi Ramamoorthi},
    title   = {{F}requency {A}nalysis and {S}heared {R}econstruction for {R}endering {M}otion {B}lur},
    journal = {SIGGRAPH (ACM Transactions on Graphics)},
    volume  = {28},
    number  = {3},
    pages   = {93:1--93:13},
    year    = {2009},

After publication we found this additional citation: Shinya, Mikio. Spatial Anti-Aliasing for Animation Sequences with Spatio-Temporal Filtering. SIGGRAPH '93, 1993.


Supplementary Files:
[Images and Shader, 6MB] [Source Code and Scene, 8MB]
[Ballerina Video, 10MB] [Powerpoint presentation, 5MB]

Updated: Dec 13, 2009