Improved Motion Invariant Deblurring through Motion Estimation

We address the capture of sharp images of fast-moving objects, and build on the Motion Invariant photographic technique. The key advantage of motion invariance is that, unlike other computational photographic techniques, it does not require pre-exposure velocity estimation in order to ensure numerically stable deblurring. Its disadvantage is that the invariance is only approximate objects moving with nonzero velocity will exhibit artifacts in the deblurred image related to tail clipping in the motion Point Spread Function (PSF). We model these artifacts as a convolution of the desired latent image with an error PSF, and demonstrate that the spatial scale of these artifacts corresponds to the object velocity. Surprisingly, despite the use of parabolic motion to capture an image in which blur is invariant to motion, we demonstrate that the motion invariant image can be used to estimate object motion post-capture. With real camera images, we demonstrate significant reductions in the artifacts by using the estimated motion for deblurring. We also quantify a 96% reduction in reconstruction error, relative to a floor established by exact PSF deconvolution, via simulation with a large test set of photographic images.