Richardson-Lucy Deblurring for Scenes under a Projective Motion Path

TLDR: This paper discusses how the blurred image can be modeled as an integration of the clear scene under a sequence of planar projective transformations that describe the camera's path, and describes how to modify the Richardson-Lucy algorithm to incorporate this new blur model.

Abstract: This paper addresses how to model and correct image blur that arises when a camera undergoes ego motion while observing a distant scene. In particular, we discuss how the blurred image can be modeled as an integration of the clear scene under a sequence of planar projective transformations (i.e., homographies) that describe the camera's path. This projective motion path blur model is more effective at modeling the spatially varying motion blur exhibited by ego motion than conventional methods based on space-invariant blur kernels. To correct the blurred image, we describe how to modify the Richardson-Lucy (RL) algorithm to incorporate this new blur model. In addition, we show that our projective motion RL algorithm can incorporate state-of-the-art regularization priors to improve the deblurred results. The projective motion path blur model, along with the modified RL algorithm, is detailed, together with experimental results demonstrating its overall effectiveness. Statistical analysis on the algorithm's convergence properties and robustness to noise is also provided.