| Two images of the same subject taken under different scenarios (e.g. views, times, devices) need to be spatially aligned before information included can be integrated and compared. The process of searching for the best alignment between two images is called image registration. There exists a large number of work, mainly in the medical field, involving different types of medical image pairs to facilitate diagnosis, observation and treatment. However, industrial field demands applications of image registration as well, and various imaging techniques also bring countless possibilities of image pairs to be registered. In this work, we investigate the complete scheme to register a two dimensional Infrared thermal image with a three dimensional Computed Tomography image for industrial inspection purpose, in which the mathematical optimization process searches for the best alignment based on the design of the objective function. Experiments show that with the proper selection of mathematical optimization method and objective function, final alignment between two images from different modalities containing same imaging subject can be achieved with acceptable spatial error.;Another image processing topic that will be studied in this dissertation is image completion. It involves the issue of filling in values at the regions which lost their original pixel values in images, based on the knowledge of the known regions. Losing partial pixel values is a practical common problem that can happen during image acquisition, transmission and even the storage stage. In this dissertation, we emphasize on the implementation of an existing low rank matrix completion method and consider the images to be matrices with low rank, in such a way that known pixel values can linearly predict the missing pixel values. With real rank unknown, mathematical optimization is used to minimize the estimation error between known pixel values and estimated pixel values. We further improve the completion method, taking advantage of the information redundancy property among neighboring pixels, ensuring the overall completion performance. It works specifically well for images with lost regions that can be abstracted as uniformly distributed square blocks. It requires no domain transformation and no prior knowledge on how the original image is degraded. Results prove that the improved low rank matrix completion method can outperform the original method and one automatic image inpaint method, achieving great visual quality improvement.;Mathematical optimization is used in both applications, being the critical driven component in registration scheme and the mechanism to clean the estimation error in image completion problem. Among various optimization methods, gradient descent optimization is emphasized and implemented in both applications. Evolutionary-based optimization is also introduced as a comparison in image registration application. |
