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.
| Original language | English |
|---|---|
| Pages (from-to) | 445-480 |
| Number of pages | 36 |
| Journal | SIAM Journal on Imaging Sciences |
| Volume | 9 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 2016 |
| Externally published | Yes |
Funding
The research of this author was partially supported by the grant ONR N000141410683. Part of this author’s work was completed at the UCLA Mathematics Department The research of this author was partially supported by the European Research Council (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.
Keywords
- Coded exposure
- Flutter shutter
- Mean-squared error (MSE)
- Motion blur
- Optimization
- Poisson noise
- Signal-to-noise ratio (SNR)
- Snapshot
- Stochastic motion model