Approximation learning methods of Harmonic Mappings in relation to Hardy Spaces

A new Hardy space Hardy space approach of Dirichlet type problem based on Tikhonov regularization and Reproducing Hilbert kernel space is discussed in this paper, which turns out to be a typical extremal problem located on the upper upper-high complex plane. If considering this in the Hardy space, the optimization operator of this problem will be highly simplified and an efficient algorithm is possible. This is mainly realized by the help of reproducing properties of the functions in the Hardy space of upper-high complex plane, and the detail algorithm is proposed. Moreover, harmonic mappings, which is a significant geometric transformation, are commonly used in many applications such as image processing, since it describes the energy minimization mappings between individual manifolds. Particularly, when we focus on the planer mappings between two Euclid planer regions, the harmonic mappings are exist and unique, which is guaranteed solidly by the existence of harmonic function. This property is attractive and simulation results are shown in this paper to ensure the capability of applications such as planer shape distortion and surface registration.Comment: 2016 3rd International Conference on Informative and Cybernetics for Computational Social Systems (ICCSS

Perancangan Dan Pembuatan Perangkat Lunak Proses Transformasi Nonlinier Dari Citra Digital Dengan Metode Splitting-Shooting Dan Splitting-Integrating

Untuk merepresentasikan obyek yang terbentuk dari kurva dan permukaan irregular harus dipakai persamaan polinomial parametrik seperti polinom B-Splines. Polinom ini dapat dipakai untuk merepresentasikan dan memanipulasi kurva dan permukaan berbentuk bebas (free form). Beberapa sistem pemodelan dan animasi grafika komputer tiga dimensi manggunakan representasi B-splines untuk kurva dan permukaan karena properti-properti geometrik yang dimiliki seperti kehalusan (smoothness) dan pengontrolan terhadap kontinyuitas parametrik Cfl antar bag ian. Fungsi-fungsi spline memainkan aturan dasar pada beberapa analisa numerik dan pemodelan geometrik. Daerah hierarchical spline didefinisikan sebagai liniar span dari tensor produk B-spline dari grid level yang berbeda. Ide dasar dari metode ini sama dengan pendekatan-pendekatan sebelumnya, khususnya untuk konstruksi dari wavelets spline. Wavelets adalah tool matematik untuk fungsi-fungsi dekomposisi secara hierarchi, yang memungkinkan sebuah fungsi untuk dideskripsikan ke dalam bagian-bagian dari keseluruhan permukaan, dan detail yang dimiliki terbentuk dari permukaan luas ke permukaan sempit. Disini akan diberikan mekanisme seleksi untuk B-Splines, yang menjamin kebebasan liniet dengan menyertakan kontrol lokal secara lengkap dari penghalusan yang dapat dilakukan dengan menambah beberapa B-splines. Penyelesaian ruang spline rata mempunyai persamaan kegunaan dengan pendekatan polinomial diskontinyu. Selain itu, hirarki dasar B-Splines adalah stabil lemah, dimana kestabilannya tumbuh secara konstan seperti O(n), dimana n adalah jumlah level-level grid. Lebih jauh lagi, disini akan didefinisikan quasi interpolant yang didasarkan pada adaptasi prinsip seleksi dan yang menyelesaikan pendekatan lokal optimal. Multilevel dan hirarki ruang B-spline ini sangat sesuai untuk approksimasi dan interpolasi data yang diacak. Approksimasi secara iterasi untuk algoritma dimana ruang spline dapat diadaptasi secara lokal ke dalam data yang diberikan. Tugas akhir ini mengembangkan metode untuk mengotomatisasi pembuatan permukaan B-spline dari himpunan (set) titik kontrol. Hasif dari permukaan hierarachi yang dibuat secara akurat dan ekonomis akan menghasilkan kembali sebuah mesh, yang bebas dari undulasi yang berlebihan pada level-level intermediate dan menghasilkan sebuah gambaran multiresolusi yang tepat untuk animasi dan pemodelan interaktif

Doctor of Philosophy

dissertationTransgressing norms and barriers of mundane digital spaces to seize spotlight in the name of social change is breathtaking. Such are modern-day protest groups as they utilize a special mix of skills, tactics, and resourcefulness to become forces of disruptive tensions in the spectacular seas of image-whirls, sound-waves, and incredible storyscapes in which we live. "Femen and Assemblage Politics of Protest in the Age of Social Media" examines these disruptive tensions as created by the topless female activist group Femen. Specifically, I am interested in how human and nonhuman elements in Femen activism create lasting impressions in the fleeting everyday life of the millions of internet-connected individuals around the globe. I conceptualize these processes under the name of media-activism assemblage and illustrate the work of Femen protest politics through three different case studies. In Chapters 2, 3, and 4, we see the dynamics of the Kiev 2012 cutting down of the crucifix by Femen

Visibility computation through image generalization

This dissertation introduces the image generalization paradigm for computing visibility. The paradigm is based on the observation that an image is a powerful tool for computing visibility. An image can be rendered efficiently with the support of graphics hardware and each of the millions of pixels in the image reports a visible geometric primitive. However, the visibility solution computed by a conventional image is far from complete. A conventional image has a uniform sampling rate which can miss visible geometric primitives with a small screen footprint. A conventional image can only find geometric primitives to which there is direct line of sight from the center of projection (i.e. the eye) of the image; therefore, a conventional image cannot compute the set of geometric primitives that become visible as the viewpoint translates, or as time changes in a dynamic dataset. Finally, like any sample-based representation, a conventional image can only confirm that a geometric primitive is visible, but it cannot confirm that a geometric primitive is hidden, as that would require an infinite number of samples to confirm that the primitive is hidden at all of its points. ^ The image generalization paradigm overcomes the visibility computation limitations of conventional images. The paradigm has three elements. (1) Sampling pattern generalization entails adding sampling locations to the image plane where needed to find visible geometric primitives with a small footprint. (2) Visibility sample generalization entails replacing the conventional scalar visibility sample with a higher dimensional sample that records all geometric primitives visible at a sampling location as the viewpoint translates or as time changes in a dynamic dataset; the higher-dimensional visibility sample is computed exactly, by solving visibility event equations, and not through sampling. Another form of visibility sample generalization is to enhance a sample with its trajectory as the geometric primitive it samples moves in a dynamic dataset. (3) Ray geometry generalization redefines a camera ray as the set of 3D points that project at a given image location; this generalization supports rays that are not straight lines, and enables designing cameras with non-linear rays that circumvent occluders to gather samples not visible from a reference viewpoint. ^ The image generalization paradigm has been used to develop visibility algorithms for a variety of datasets, of visibility parameter domains, and of performance-accuracy tradeoff requirements. These include an aggressive from-point visibility algorithm that guarantees finding all geometric primitives with a visible fragment, no matter how small primitive\u27s image footprint, an efficient and robust exact from-point visibility algorithm that iterates between a sample-based and a continuous visibility analysis of the image plane to quickly converge to the exact solution, a from-rectangle visibility algorithm that uses 2D visibility samples to compute a visible set that is exact under viewpoint translation, a flexible pinhole camera that enables local modulations of the sampling rate over the image plane according to an input importance map, an animated depth image that not only stores color and depth per pixel but also a compact representation of pixel sample trajectories, and a curved ray camera that integrates seamlessly multiple viewpoints into a multiperspective image without the viewpoint transition distortion artifacts of prior art methods

Asteroseismology and Interferometry

Asteroseismology provides us with a unique opportunity to improve our understanding of stellar structure and evolution. Recent developments, including the first systematic studies of solar-like pulsators, have boosted the impact of this field of research within Astrophysics and have led to a significant increase in the size of the research community. In the present paper we start by reviewing the basic observational and theoretical properties of classical and solar-like pulsators and present results from some of the most recent and outstanding studies of these stars. We centre our review on those classes of pulsators for which interferometric studies are expected to provide a significant input. We discuss current limitations to asteroseismic studies, including difficulties in mode identification and in the accurate determination of global parameters of pulsating stars, and, after a brief review of those aspects of interferometry that are most relevant in this context, anticipate how interferometric observations may contribute to overcome these limitations. Moreover, we present results of recent pilot studies of pulsating stars involving both asteroseismic and interferometric constraints and look into the future, summarizing ongoing efforts concerning the development of future instruments and satellite missions which are expected to have an impact in this field of research.Comment: Version as published in The Astronomy and Astrophysics Review, Volume 14, Issue 3-4, pp. 217-36

Advanced Image Acquisition, Processing Techniques and Applications

"Advanced Image Acquisition, Processing Techniques and Applications" is the first book of a series that provides image processing principles and practical software implementation on a broad range of applications. The book integrates material from leading researchers on Applied Digital Image Acquisition and Processing. An important feature of the book is its emphasis on software tools and scientific computing in order to enhance results and arrive at problem solution

Studies in seismic scattering

Modem methods of seismic data analysis are tending to inversion through model fitting, i.e., actually finding the best model of the Earth's subsurface which would produce the amplitude and phase variation in the observed data. An understanding of seismic scattering is fundamental to this form of data analysis. This dissertation involves the study of seismic scattering and its use in the inverse problem, applying full waveform inversion ideas in novel situations. The terminology and methodology of inverse theory may sometimes hide what is going on, and may make it difficult to connect the results with those from more familiar techniques. In Chapter 1 I show that, with the appropriate choice for the model parameters, the first iteration of the nonlinear least-squares seismic waveform inversion algorithm reduces to classical results from linear filter theory. I use the idea of the adjoint of the Frechet derivative linear operator in Chapter 2 to understand smoothing in the waveform inversion, which manifests itself as a new sensitivity function incorporating the smoothing information. This gives us physical intuition into the wave equation based inverse problem. My mathematical analysis is general; however, using sensitivity functions for the paraxial equation in ray centered coordinates, I show a specific application to full waveform imaging in a tomographic experiment where only phase information (travel-time data) is normally used. I consider an inversion of teleseismic data from some deep earthquakes in Chapter 3. I use the phase and amplitude variation in the seismic signals in an imaging technique derived from inverse theory and digital signal analysis, interpreting the coherent energy in the coda of the first arrival as due to scattering from upper mantle discontinuities. Applying an inversion through iterative forward modeling, I measure the depth variation of the spinel-perovskite upper mantle phase transition within the subduction zone region. This measurement allows me to characterize the variation of the transition with respect to pressure and temperature. My results are consistent with convection in a model of a chemically homogeneous mantle, where the presence of the phase transition at around 670 km depth disrupts the full mantle convection patterns.Geological Science