A digital watermark is a message robustly hidden within another digitized signal such as an image, a piece of music, a video, etc. . The principal applications of this technology are copyright protection and document fingerprinting. The robustness of watermarking algorithms against common geometrical deformations has drawn the attention of many researchers in the last ten years. Such distortions can result from usual processing of the media and/or malicious manipulations. As an example, a major concern for digital cinema industry is the illicit copy of movies with video cameras taking place in movie theaters. In this scenario, severe geometric distortions can jeopardize the retrieval of the watermark message from the illicit copies. The limitations and weaknesses of the previously proposed solutions to fight these distortions are presented. We developed a generalized construction method for periodic pseudo-random patterns. Based on these patterns, we designed a spread spectrum watermarking scheme with enhanced security properties. We investigated the detection probability and the interaction between exhaustive search and informed coding strategies. Finally, a scheme for the detection of a periodic structure and for the inversion of affine distortions was presented. We showed that the choice of the periodic repetition size involves a trade-off between robustness and secrecy. Thereafter, we studied the security flaw caused by the lack of secrecy in pilot-registration approaches. We proposed an innovative hiding scheme to remedy this issue. Our solution involves the extraction of robust local references from the content of the cover signal. Using this content normalized interpretation, we showed how one can design robust secret binary mask and modulate pilot signals in watermarking schemes. The efficiency of the approach is demonstrated on pilots derived from periodic structures. We also addressed the assessment of the degradation introduced by a geometrical distortion. We assume that a global rigid transform does not impair the perceptual value of an image and we propose a new criterion based on a local analysis of the geometrical deformations.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 139-150). Also available in electronic version. Access restricted to campus users.

My dissertation has two main parts. In the first half, I draw out an underlying presupposition of Descartes' philosophy: what I term "atomism of thought." Descartes employs a radical procedure of doubt in order to show that the first principle of his philosophy, the cogito, is an unshakeable foundation of knowledge. In the dialogue that follows his dissemination of the Meditations, Descartes reveals that a whole set of concepts and rational principles innate in our minds are never doubted. These fundamental units of thought are indivisible, distinct, and isolated, and enable the possibility of any rational demonstration. Atoms of thought are perfectly individuated because God has created them as such. Likewise, our minds have been fashioned such that we necessarily have a clear and distinct perception every time we alight upon these simple notions. In the second part of the dissertation, I take up critiques of Descartes' view given by Nietzsche and Heidegger. In the chapter on Nietzsche, I attempt to fill a lacuna in scholarship about Nietzsche's commentary on Descartes. More specifically, I argue that once the foundation of God is displaced, the basis for accepting atomism of thought dissolves. In the final chapter, I analyze Heidegger's critique of Cartesian atomism. I first look at Heidegger's critique of classical truth as correspondence from Being and Time, and show how it is relevant to a critique of atomism. Then I show how the early Heidegger's holistic philosophical framework can provide an alternative that avoids the pitfalls of atomism. While I limit the scope of my analysis to Descartes' particular formulation, atomism of thought was an influential doctrine throughout modern philosophy. This aspect of Cartesianism has persisted and continues to be a significant theoretical underpinning of many contemporary views. It is my contention that Nietzsche and Heidegger have important contributions to make to this area of thought, and the relative neglect of their work in recent scholarship is a detrimental oversight.

Surface tiling, as well as its counterpart in 3D, i.e. volume tiling, is a fundamental research problem in the subject of computer graphics and geometric modeling, which has found applications in numerous areas, such as computer-aided design (CAD), physical simulation, realtime rendering and architectural modeling. The objective of surface tiling is to compute discrete mesh representations for given surfaces which are often required to possess some desirable geometric properties. Likewise, volume tiling focuses on the study of discretizing a given 3D volume with complex boundary into a set of high-quality volumetric elements. This thesis starts with the study of computing optimal sampling for parametric surfaces, that is, decompose the surface into quad patches such that 1) each quad patch should have their sides with equal length; and 2) the shapes and sizes of all the quad patches should be the same as much as possible. Then, the similar idea is applied to the discrete case, i.e. optimizing the face elements of a quad mesh surface with the goal of making it possess, as much as possible, face elements of desired shapes and sizes. This thesis further studies the computation of hexagonal tiling on free-form surfaces, where the planarity of the faces is more concerned. Free-form meshes with planar hexagonal faces, to be called P-Hex meshes, provide a useful surface representation in discrete differential geometry and are demanded in architectural design for representing surfaces built with planar glass/metal panels. We study the geometry of P-Hex meshes and present an algorithm for computing a free-form P-Hex mesh of a specified shape. Lastly, this thesis progresses to 3D volume case and proposes an automatic method for generating boundary-aligned all-hexahedron meshes with high quality, which possess nice numerical properties, such as a reduced number of elements and high approximation accuracy in physical simulation and mechanical engineering. / published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

Inertial measurement units (IMUs) are used in a wide range of applications to estimate position, velocity, and attitude of vehicles. The high cost of tactical grade IMUs makes the low-cost microelectromechanical systems (MEMS) based IMUs appealing. These types of IMUs are less accurate, so to counteract this effect, multiple and different configurations should be used. The work presented here provides efficient and low cost solutions using different configurations of redundant (multiple) MEMS-IMU swarms, which increase the level of accuracy to potentially the order of that of a tactical IMU. Several configurations are presented and compared through different methods. / text

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

Οι γεωμετρικές κατασκευές (με την χρήση κανόνα και διαβήτη) και η παρουσίαση των τριών περίφημων προβλημάτων από την ελληνική αρχαιότητα μέχρι την τελική απάντηση που δόθηκε για αυτά. Η εξιστόρηση της κατασκευής κανονικών πολυγώνων και η διερεύνηση της δυνατό- ητας των μαθητών του Λυκείου να εργαστούν πάνω σε προβλήματα γεωμετρικών κατασκευών, με την αναλυτικο-συνθετική μέθοδο. / Geometrical constructions (using only an unmarked straight edge and compasses)of Euclidean plane geometry and the presentation of the three unsolved famous constructions problems from the greek anciety until the final answer for them. The construction’s narration of regular polygons and the research of high school students possibility to work on geometrical construction problems with the analysis and synthesis method.

No description available.

The field of wireless communications has been experiencing tremendous growth with the ever-increasing dependence on wireless services. In the operation of a communication network, the network coverage and node placement are of profound importance. The network performance metrics can be modeled as nonlinear functions of inter-node distances. Therefore, a geometric abstraction of the distance between wireless devices becomes a prerequisite for accurate system modeling and analysis. A geometrical probability approach is presented in this dissertation to characterize the probabilistic distance properties, for analyzing the location-critical performance metrics through various spatial distance distributions. Ideally, the research in geometrical probability shall give results for the distance distributions 1) over elementary geometries such as a straight line, squares and rectangles, and 2) over complex geometries such as rhombuses and hexagons. Both 1) and 2) are the representative topological shapes for communication networks. The current probability and statistics literature has explicit results for 1), whereas the results for 2) are not in existence. In particular, the absence of the distance distributions for rhombuses and hexagons has posed challenges towards the analytical modeling of location-critical performance metrics in complex geometries. This dissertation is dedicated to the application of existing results in 1) elementary geometries to the networking area, and the development of a new approach to deriving the distance distributions for complex geometries in 2), bridging the gap between the geometrical probability and networking research. The contribution of this dissertation is twofold. First, the one-dimensional Poisson point process in 1) is applied to the message dissemination in vehicular ad-hoc networks, where the network geometry is constrained by highways and city blocks. Second, a new approach is developed to derive the closed-form distributions of inter-node distances associated with rhombuses and hexagons in 2), which are obtained for the first time in the literature. Analytical models can be constructed for characterizing the location-critical network performance metrics, such as connectivity, nearest/farthest neighbor, transmission power, and path loss in wireless networks. Through both analytical and simulation results, this dissertation demonstrates that this geometrical probability approach provides accurate information essential to successful network protocol and system design, and goes beyond the approximations or Monte Carlo simulations by gracefully eliminating the empirical errors. / Graduate

Pacific Rim International Conference on Advanced Materials and Processing <DA14524950> (5th : 2004 : Beijing, China)