Dissertation abstract: geometrical wavelets and their generalizations in digital image coding and processing
Agnieszka Lisowska · Machine Graphics & Vision International Journal archive · 2005
Efficient representation of an image plays a crucial role in computer graphics because it forms the foundation for image coding and processing. Recently, it has become evident that separable transforms, e.g., wavelet transformations, are not the best tools for image representation due to their inability to capture line discontinuities present in images in the form of edges. To overcome that problem, a competitive theory of geometrical wavelets has been developed recently.Recent research in psychology of vision and neuropsychology has proven that the amount of information which is gathered by receptors of the retina in the eye is far larger than the dozens of bits per second which are transmitted to the brain from the eye. Additionally, they give us information what kinds of signals are perceived by brain first of all, and which ones are less important. As a result, two practical questions arise. How can we approximate images better, in a more sparse way? And how can we extract, the information which is most important, from the Human Visual System point of viewout of an image in an automatic way? The dissertation has tried to answer both these questions.Thus, firstly, a generalization of wedgelets (the class of geometrical wavelets) to those based on second degree curves has been proposed, and it has been shown that thanks to a better, sparser, approximation of images such wedgelets improve the properties of image coding and processing in comparison with the classical wedgelets. It has been additionally shown that generalized wedgelets give better results in noisy image processing compared to other standard methods.Secondly, a new application of geometrical wavelets to extracting different classes of signals with different importance for perception by human brain has been proposed. With help of such wavelets (especially beamlets), an operator has been defined which extracts such signals automatically in a geometrical multiresolution way. All the results presented in the dissertation appear to improve the results presented so far in literature, which has been confirmed both theoretically and experimentally.