A theory of optimal flutter shutter for probabilistic velocity models

Yohann Tendero; Jean-Michel Morel

doi:10.1137/15M1035872

A theory of optimal flutter shutter for probabilistic velocity models

Yohann Tendero
, Jean-Michel Morel

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Abstract

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.

Original language	English
Pages (from-to)	445-480
Journal	SIAM Journal on Imaging Sciences
Volume	9
Issue number	1
DOIs	https://doi.org/10.1137/15M1035872
Publication status	Published - 23 Mar 2016
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Funding

LTCI, CNRS, T´el´ecom ParisTech, Universit´e Paris-Saclay, 75013 Paris, France ([email protected]). The research of this author was partially supported by the grant ONR N000141410683. Part ofthis author’s work was completed at the UCLA Mathematics Department. Centre de Math´ematiques et Leurs Applications (CMLA), ´Ecole Normale Sup´erieure de Cachan, 94235 Cachan,France ([email protected]). The research of this author was partially supported by the European ResearchCouncil (advanced grant Twelve Labours 246961), by the Oﬃce of Naval Research (ONR grant N00014-14-1-0023),and by ANR-DGA project ANR-12-ASTR-0035.

Research Keywords

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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abstract = "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. {\textcopyright} 2016 Society for Industrial and Applied Mathematics.",

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AU - Morel, Jean-Michel

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AB - 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.

KW - Coded exposure

KW - Flutter shutter

KW - Mean-squared error (MSE)

KW - Motion blur

KW - Optimization

KW - Poisson noise

KW - Signal-to-noise ratio (SNR)

KW - Snapshot

KW - Stochastic motion model

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DO - 10.1137/15M1035872

M3 - RGC 21 - Publication in refereed journal

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SP - 445

EP - 480

JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

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ER -

A theory of optimal flutter shutter for probabilistic velocity models

Abstract

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Research Keywords

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