A theory of optimal flutter shutter for probabilistic velocity models

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Original languageEnglish
Pages (from-to)445-480
Journal / PublicationSIAM Journal on Imaging Sciences
Issue number1
Publication statusPublished - 23 Mar 2016
Externally publishedYes


Flutter shutter (coded exposure) is a new paradigm for cameras that allows for an arbitrary increase of the exposure time when the relative camera/scene motion is uniform. The photon flux is interrupted according to a flutter shutter code. For arbitrarily severe uniform motion blur a well chosen code guarantees an invertible blur kernel. Yet, when the relative camera/scene velocity is a known constant, a flutter shutter cannot gain more than a 1.17 factor in terms of root mean-squared error compared to the optimal snapshot. In this paper, we prove that this optimality bound can be relaxed under the realistic assumption that a random model for the velocities is available. We give analytical formulae for the optimal flutter shutter code and the optimal snapshots associated with a random velocity distribution. Conversely we also prove formulae that reveal the velocity distribution underlying a given flutter shutter code. © 2016 Society for Industrial and Applied Mathematics.

Research Area(s)

  • Coded exposure, Flutter shutter, Mean-squared error (MSE), Motion blur, Optimization, Poisson noise, Signal-to-noise ratio (SNR), Snapshot, Stochastic motion model

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