Inferring Image Transformation and Structure from Motion-Blurred Images

While capturing images of a scene, the relative motion between the camera and the scene during exposure leads to motion-blur in images. The convolution model for motion-blur is applicable only when the camera motion is restricted to in-plane translations. Blur arising due to rotation and out-of-plane translation of camera cannot be modeled using convolution with a single blur kernel [3, 5, 6]. In this paper, we model the motionblurred image as the weighted average of geometrically transformed versions of the reference image. The model implicitly accounts for the spacevariant nature of blurring that occurs due to unrestricted camera motion. In many applications, motion-blur can occur while capturing scenes with depth variations from a moving camera. During the camera motion, the apparent movement of the scene points in the image is related to the shape of the scene [1]. Consequently the extent of blurring at a point is governed by both the camera motion and the scene structure. Initially, we consider scenes having constant depth and develop an algorithm to estimate the transformations undergone by the reference image during exposure. We next consider images of scenes with depth variations. Based on the estimated transformations, we relate the depth at a scene point to the blurred image intensity through the point spread function. Depth estimation is posed as a state estimation problem and is solved using an unscented Kalman filter (UKF). A motion-blurred image g can be related to the reference image f through the space-variant point spread function (PSF) h as