Treffer: Deformation processing for image restoration and retargeting

M.Phil. ; Deformation plays a crucial role in image processing, in particular, when our data is series of image frames or a particular intrinsic deformation is assumed. In this thesis, we develop efficient algorithms to solve different proposed mathematical models involving deformation information captured and represented via quasi-conformal map, low-rank decomposition and miscellaneous image registration techniques with numerous applications. ; We divide this thesis into two parts. In the first part, we propose mathematical models with algorithms considering deformation in two approaches for image restoration. In this part, firstly we address the problem of image restoration with atmospheric turbulence-degraded video by directly obtaining the deformations between the frames by optical flow. The deformation fields are further processed by calculating their Beltrami coefficients and applying Robust Principal Component Analysis (RPCA) to the proposed algorithm. Secondly, we propose a general variational model with different fidelity and regularization terms for image restoration and subsampling. Instead of processing the deformation information directly by the traditional image registration techniques such as optical flow and non-rigid image registration, which are computationally costly, we applied various fidelity terms including 2-norm, TV-norm, and nuclear norm to extract the deformation in different situations. We propose efficient algorithms called Image Restoration and Image Subsampling (IRIS) with its modified version, simultaneously subsample and restore a clear image from the turbulence-degraded video. Both the subsampling stages and the implicit approach to obtain the deformation information remarkably speed up the computation process. ; In the second part, we propose a simple and yet effective algorithm to resize an image, which preserves the geometry of the important content, using the Beltrami representation. We formulate the problem of content-aware image retargeting as a suitable deformation, in ...