Ανάλυση εικόνων με τη χρήση μη γραμμικών δισδιάστατων απεικονίσεων

Κόντι, Αλέξανδρος; Konti, Alexandros

dc.contributor.author	Κόντι, Αλέξανδρος	el
dc.contributor.author	Konti, Alexandros	en
dc.date.accessioned	2022-02-28T09:34:00Z
dc.date.available	2022-02-28T09:34:00Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/54864
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.22562
dc.rights	Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/gr/	*
dc.subject	Δυναμικά συστήματα	el
dc.subject	Μη γραμμικές απεικονίσεις	el
dc.subject	Νανοτεχνολογία	el
dc.subject	Αναλυση εικόνων	el
dc.title	Ανάλυση εικόνων με τη χρήση μη γραμμικών δισδιάστατων απεικονίσεων	el
dc.contributor.department	Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Μαθηματική Προτυποποίηση σε Σύγχρονες Τεχνολογίες και στα Χρηματοοικονομικά”	el
heal.type	masterThesis
heal.classification	Μαθηματικά	el
heal.language	el
heal.access	campus
heal.recordProvider	ntua	el
heal.publicationDate	2021-07-25
heal.abstract	One challenge in researching and studying complex systems is to nd metrics that di erentiate randomness from complexity. The purpose of this dissertation is to contribute in the direction of nding such a metric that can characterize the complexity of images by proposing a methodology based on a) the use of discrete two-dimensional dynamic transformations on gray (but also multicoloured or black and white) scale images using the image as a collection of initial conditions whose trajectories we observe and b) the use of the discrete Fourier transform for further analysis of the images resulting from step a and drawing conclusions about the complexity. For a more systematic investigation and validation of the methodology, it was applied to synthetic images created by an appropriate algorithm for the production of Gaussian and non-Gaussian surfaces as well as an algorithm for the production of surfaces with more intense periodic behaviour. The produced synthetic images are characterized by various statistical characteristics such as the correlation length, the kurtosis, the skewness, as well as the roughness exponent that is more directly related to the fractal dimension of the produced surfaces and images. From the analysis of the results it was observed that by applying the appropriate metrics a) of the variance of the linear t of the Fourier diagrams and b) of the di erence of the rst from the fth repetition of the angled pro les of the rst ve repetitions of the discrete Arnold's cat transformation, the complexity is maximum in intermediate correlation lengths and minimum in extreme cases. In other words, both noise and full periodical surfaces are less complex than intermediate surfaces.	el
heal.advisorName	Διάκονος, Φώτης	el
heal.committeeMemberName	Κωνσταντούδης, Βασίλειος	el
heal.committeeMemberName	Προβατά, Αστέρω	el
heal.committeeMemberName	Διάκονος, Φώτης	el
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Εφαρμοσμένων Μαθηματικών και Φυσικών Επιστημών	el
heal.academicPublisherID	ntua
heal.numberOfPages	70 σ.	el
heal.fullTextAvailability	false