Motion Blur : Analysis and Restoration

Motion blur is a phenomenon which is corrupting images when, any motion occurs between the camera viewpoint and the captured scene during the acquisition. Rarely this can be described with a shift invariant operator although this is a common assumption in the literature. In a motion blurred image, the Point Spread Function (PSF) of each pixel is determined by the relative motion between the camera viewpoint and the imaged scene point. Therefore the PSF of each pixel may typically vary according to the camera motion and the depths of the imaged scene points. Both the blur analysis (estimation) and the image restoration, become much more challenging issues in case of a shift variant blur operator, than in case of a shift invariant blur operator. As a matter of fact, only few works in literature have considered the shift variant blur. This thesis concerns the analysis and the restoration of single blurred images when the blur is due to a specific camera motions. In particular the focus is on the blur produced by a camera translation. We show that assuming shift variant blur allows us to describe the degradation process more accurately. We derive two descriptions of the degradation process due to camera translation and camera rotation, where the blur is modeled as shift variant and parametric operators. The thesis is divided into two parts. The first part deals with local blur estimation, and presents algorithms devised for estimating blur direction and extent in small image regions containing a corner. The proposed algorithms estimate blur parameters in corner regions where other blur parameters estimation methods typically fail. We devised also a procedure for detecting blurred corners and adaptively select a region where to perform blur estimation. In the second part of the thesis we consider the blurred image as a whole and we address two different issues: the estimation of the camera motion and the image restoration. This part is mostly dedicated to images corrupted by blur due to a pure camera translation. We prove that, although this situation has been always treated assuming the blur shift invariant, the blur becomes shift variant as the camera translation has an essential component perpendicular to the image plane. We devise a single image algorithm for estimating both the camera 3D motion direction and the PSF parameters in every image pixel. We also introduce a restoration algorithm for these kind of images (radial blurred images), which is based on two steps: the blur inversion and the noise removal. The blur is inverted exploiting polar to Cartesian coordinate transformations. We study how the coordinate transformations and the blur inversion affect the noise in order to use a non-linear spatially adaptive filter, the Pointwise ShapeAdaptive DCT to exploit the image structures and attenuate noise and artifacts. Since in radially blurred images, the PSF extent at any image pixel can be related to the depth of the corresponding point in the scene, we also investigate and discuss the capabilities of estimating the scene depth from a single motion blurred image. The blur produced by a camera rotation is also considered in the second part of the thesis. We devise an algorithm for estimating the 3D rotation axis of a camera by analyzing a single blurred image. Contrary to the existing methods, we treat the more general case where the rotation axis is not necessarily orthogonal to the image plane, taking into account the perspective effects that affect the smears. All the proposed algorithms have been tested on synthetically blurred images as well as camera images.