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# Mathematical theory of the Flutter Shutter : its paradoxes and their solution

Abstract : This thesis provides theoretical and practical solutions to two problems raised by digital photography of moving scenes, and infrared photography. Until recently photographing moving objects could only be done using short exposure times. Yet, two recent groundbreaking works have proposed two new designs of camera allowing arbitrary exposure times. The flutter shutter of Agrawal et al. creates an invertible motion blur by using a clever shutter technique to interrupt the photon flux during the exposure time according to a well chosen binary sequence. The motion-invariant photography of Levin et al. gets the same result by accelerating the camera at a constant rate. Both methods follow computational photography as a new paradigm. The conception of cameras is rethought to include sophisticated digital processing. This thesis proposes a method for evaluating the image quality of these new cameras. The leitmotiv of the analysis is the SNR (signal to noise ratio) of the image after deconvolution. It gives the efficiency of these new camera design in terms of image quality. The theory provides explicit formulas for the SNR. It raises two paradoxes of these cameras, and resolves them. It provides the underlying motion model of each flutter shutter, including patented ones. A shorter second part addresses the the main quality problem in infrared video imaging, the non-uniformity. This perturbation is a time-dependent noise caused by the infrared sensor, structured in columns. The conclusion of this work is that it is not only possible but also efficient and robust to perform the correction on a single image. This permits to ensure the absence of ghost artifacts'', a classic of the literature on the subject, coming from inadequate processing relative to the acquisition model.
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https://theses.hal.science/tel-00752409
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Submitted on : Thursday, November 15, 2012 - 4:03:11 PM
Last modification on : Tuesday, June 8, 2021 - 6:58:01 AM
Long-term archiving on: : Saturday, February 16, 2013 - 3:43:52 AM

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Tendero2012.pdf
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• HAL Id : tel-00752409, version 1

### Citation

Yohann Tendero. Mathematical theory of the Flutter Shutter : its paradoxes and their solution. General Mathematics [math.GM]. École normale supérieure de Cachan - ENS Cachan, 2012. English. ⟨NNT : 2012DENS0029⟩. ⟨tel-00752409⟩

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