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In the early days of computer graphics, research was mainly driven by the goal to create realistic synthetic imagery. By contrast, non-photorealistic computer graphics, established as its own branch of computer graphics in the early 1990s, is mainly motivated by concepts and principles found in traditional art forms, such as painting, illustration, and graphic design, and it investigates concepts and techniques that abstract from reality using expressive, stylized, or illustrative rendering techniques. This thesis focuses on the artistic stylization of two-dimensional content and presents several novel automatic techniques for the creation of simplified stylistic illustrations from color images, video, and 3D renderings. Primary innovation of these novel techniques is that they utilize the smooth structure tensor as a simple and efficient way to obtain information about the local structure of an image. More specifically, this thesis contributes to knowledge in this field in the following ways. First, a comprehensive review of the structure tensor is provided. In particular, different methods for integrating the minor eigenvector field of the smoothed structure tensor are developed, and the superiority of the smoothed structure tensor over the popular edge tangent flow is demonstrated. Second, separable implementations of the popular bilateral and difference of Gaussians filters that adapt to the local structure are presented. These filters avoid artifacts while being computationally highly efficient. Taken together, both provide an effective way to create a cartoon-style effect. Third, a generalization of the Kuwahara filter is presented that avoids artifacts by adapting the shape, scale, and orientation of the filter to the local structure. This causes directional image features to be better preserved and emphasized, resulting in overall sharper edges and a more feature-abiding painterly effect. In addition to the single-scale variant, a multi-scale variant is presented, which is capable of performing a highly aggressive abstraction. Fourth, a technique that builds upon the idea of combining flow-guided smoothing with shock filtering is presented, allowing for an aggressive exaggeration and an emphasis of directional image features. All presented techniques are suitable for temporally coherent per-frame filtering of video or dynamic 3D renderings, without requiring expensive extra processing, such as optical flow. Moreover, they can be efficiently implemented to process content in real-time on a GPU.
By means of the cluster expansion method we show that a recent result of Poghosyan and Ueltschi (2009) combined with a result of Nehring (2012) yields a construction of point processes of classical statistical mechanics as well as processes related to the Ginibre Bose gas of Brownian loops and to the dissolution in R^d of Ginibre's Fermi-Dirac gas of such loops. The latter will be identified as a Gibbs perturbation of the ideal Fermi gas. On generalizing these considerations we will obtain the existence of a large class of Gibbs perturbations of the so-called KMM-processes as they were introduced by Nehring (2012). Moreover, it is shown that certain "limiting Gibbs processes" are Gibbs in the sense of Dobrushin, Lanford and Ruelle if the underlying potential is positive. And finally, Gibbs modifications of infinitely divisible point processes are shown to solve a new integration by parts formula if the underlying potential is positive.
Transport Molecules play a crucial role for cell viability. Amongst others, linear motors transport cargos along rope-like structures from one location of the cell to another in a stochastic fashion. Thereby each step of the motor, either forwards or backwards, bridges a fixed distance. While moving along the rope the motor can also detach and is lost. We give here a mathematical formalization of such dynamics as a random process which is an extension of Random Walks, to which we add an absorbing state to model the detachment of the motor from the rope. We derive particular properties of such processes that have not been available before. Our results include description of the maximal distance reached from the starting point and the position from which detachment takes place. Finally, we apply our theoretical results to a concrete established model of the transport molecule Kinesin V.
We consider systems of Euler-Lagrange equations with two degrees of freedom and with Lagrangian being quadratic in velocities. For this class of equations the generic case of the equivalence problem is solved with respect to point transformations. Using Lie's infinitesimal method we construct a basis of differential invariants and invariant differentiation operators for such systems. We describe certain types of Lagrangian systems in terms of their invariants. The results are illustrated by several examples.
Amongst the many complex processes taking place in living cells, transport of cargoes across the cytosceleton is fundamental to cell viability and activity. To move cargoes between the different cell parts, cells employ Molecular Motors. The motors operate by transporting cargoes along the so-called cellular micro-tubules, namely rope-like structures that connect, for instance, the cell-nucleus and outer membrane. We introduce a new Markov Chain, the killed Quasi-Random-Walk, for such transport molecules and derive properties like the maximal run length and time. Furthermore we introduce permuted balance, which is a more flexible extension of the ordinary reversibility and introduce the notion of Time Duality, which compares certain passage times pathwise. We give a number of sufficient conditions for Time Duality based on the geometry of the transition graph. Both notions are closely related to properties of the killed Quasi-Random-Walk.
Since 2011 the Comorian Island of Mayotte has been France’s 101st département, thereby becoming part of the European Union. As a result, France has consolidated and strengthened its strategic position in the Indian Ocean. With the change of political status in 2011, new developments have occurred in Mayotte. It is still unclear whether the expected economic boom, extensive social benefits or injection of EU regional funds can help to alleviate poverty and raise living standards. There is concern, however, that massive immigration to Mayotte from the surrounding territories is diminishing any progress and will continue to do so. Not only France but also the EU will have to adapt to new immigration problems due to this new external border. In this situation one thing is clear: the language contact between French and the local languages, which is the result of political developments, is leading to new dynamics. The diglossic situation east of Africa, between French as the dominant language and local languages like Shimaoré or Shibushi spoken in Mayotte will become more marked in the next few years.