Digital inpainting is the reconstruction of a missing or damaged region in a digital image. Intensity values in the missing region are approximated using information near the boundary of the region. Some applications include repair of chipped paintings, repair of rips in paper photographs, and removal of unwanted objects from photographs. In this thesis, we review 2D digital inpainting techniques, examine the application of 3D digital inpainting to cell path reconstruction, and propose a new inpainting technique inspired by the cell path reconstruction problem. Cell path reconstruction is the estimation of the shape and position of living cells in videos recorded using fluorescence microscopy. This procedure is necessary because in a particular phase of the life cycle of some cells, fluorescent light passes through the cells with an undetectable change in wavelength and they vanish from the frame. This leads to misleading results when, for example, the number of cells in a particular frame is counted. We transform the position/shape estimation problem into a 3D shape reconstruction problem by stacking the frames of the video to form a 3D volume. In this volume, cell paths form tubes with missing segments where cells have vanished. We apply elastica inpainting to the 3D tube reconstruction problem and introduce a new 3D inpainting model to overcome difficulties with a direct generalization to 3D of 2D elastica.

Digital inpainting is the reconstruction of a missing or damaged region in a digital image. Intensity values in the missing region are approximated using information near the boundary of the region. Some applications include repair of chipped paintings, repair of rips in paper photographs, and removal of unwanted objects from photographs. In this thesis, we review 2D digital inpainting techniques, examine the application of 3D digital inpainting to cell path reconstruction, and propose a new inpainting technique inspired by the cell path reconstruction problem. Cell path reconstruction is the estimation of the shape and position of living cells in videos recorded using fluorescence microscopy. This procedure is necessary because in a particular phase of the life cycle of some cells, fluorescent light passes through the cells with an undetectable change in wavelength and they vanish from the frame. This leads to misleading results when, for example, the number of cells in a particular frame is counted. We transform the position/shape estimation problem into a 3D shape reconstruction problem by stacking the frames of the video to form a 3D volume. In this volume, cell paths form tubes with missing segments where cells have vanished. We apply elastica inpainting to the 3D tube reconstruction problem and introduce a new 3D inpainting model to overcome difficulties with a direct generalization to 3D of 2D elastica.

Segmentation of an image into individual tree crowns is a key step in the processing of remotely sensed data for forestry practice. The doctoral thesis gives a broad overview of this topic. It comprehends theoretical context from mathematical point of view and defines basic terms from airborne imaging and laser scanning. Mathematical methods of tree detection are focused on a robust adaptation to the actual conditions in a region of interest. A novel approach of crown area delineation is introduced, it combines a seeded region growing technique with an active contour as a crown boundary representation. The parametrisation of all algorithms is analysed in a practical half of the thesis and more application-oriented issues are mentioned. Executable computer programs are attached.