Analysis of Motion Blur with a Flutter Shutter Camera for Non-linear Motion

Motion blurs confound many computer vision problems. The fluttered shutter (FS) camera [1] tackles the motion deblurring problem by emulating invertible broadband blur kernels. However, existing FS methods assume known constant velocity motions, e.g., via user specifications. In this paper, we extend the FS technique to general 1D motions and develop an automatic motion-from-blur framework by analyzing the image statistics under the FS. We first introduce a fluttered-shutter point-spread-function (FS-PSF) to uniformly model the blur kernel under general motions. We show that many commonly used motions have closed-form FS-PSFs. To recover the FS-PSF from the blurred image, we present a new method by analyzing image power spectrum statistics. We show that the Modulation Transfer Function of the 1D FS-PSF is statistically correlated to the blurred image power spectrum along the motion direction. We then recover the FS-PSF by finding the motion parameters that maximize the correlation. We demonstrate our techniques on a variety of motions including constant velocity, constant acceleration, and harmonic rotation. Experimental results show that our method can automatically and accurately recover the motion from the blurs captured under the fluttered shutter.