A Generative Model of Natural Texture Surrogates

Natural images can be viewed as patchworks of different textures, where the local image statistics is roughly stationary within a small neighborhood but otherwise varies from region to region. In order to model this variability, we first applied the parametric texture algorithm of Portilla and Simoncelli to image patches of 64X64 pixels in a large database of natural images such that each image patch is then described by 655 texture parameters which specify certain statistics, such as variances and covariances of wavelet coefficients or coefficient magnitudes within that patch. To model the statistics of these texture parameters, we then developed suitable nonlinear transformations of the parameters that allowed us to fit their joint statistics with a multivariate Gaussian distribution. We find that the first 200 principal components contain more than 99% of the variance and are sufficient to generate textures that are perceptually extremely close to those generated with all 655 components. We demonstrate the usefulness of the model in several ways: (1) We sample ensembles of texture patches that can be directly compared to samples of patches from the natural image database and can to a high degree reproduce their perceptual appearance. (2) We further developed an image compression algorithm which generates surprisingly accurate images at bit rates as low as 0.14 bits/pixel. Finally, (3) We demonstrate how our approach can be used for an efficient and objective evaluation of samples generated with probabilistic models of natural images.Comment: 34 pages, 9 figure

Review of steganalysis of digital images

Steganography is the science and art of embedding hidden messages into cover multimedia such as text, image, audio and video. Steganalysis is the counterpart of steganography, which wants to identify if there is data hidden inside a digital medium. In this study, some specific steganographic schemes such as HUGO and LSB are studied and the steganalytic schemes developed to steganalyze the hidden message are studied. Furthermore, some new approaches such as deep learning and game theory, which have seldom been utilized in steganalysis before, are studied. In the rest of thesis study some steganalytic schemes using textural features including the LDP and LTP have been implemented

Self-similarity and wavelet forms for the compression of still image and video data

This thesis is concerned with the methods used to reduce the data volume required to represent still images and video sequences. The number of disparate still image and video coding methods increases almost daily. Recently, two new strategies have emerged and have stimulated widespread research. These are the fractal method and the wavelet transform. In this thesis, it will be argued that the two methods share a common principle: that of self-similarity. The two will be related concretely via an image coding algorithm which combines the two, normally disparate, strategies. The wavelet transform is an orientation selective transform. It will be shown that the selectivity of the conventional transform is not sufficient to allow exploitation of self-similarity while keeping computational cost low. To address this, a new wavelet transform is presented which allows for greater orientation selectivity, while maintaining the orthogonality and data volume of the conventional wavelet transform. Many designs for vector quantizers have been published recently and another is added to the gamut by this work. The tree structured vector quantizer presented here is on-line and self structuring, requiring no distinct training phase. Combining these into a still image data compression system produces results which are among the best that have been published to date. An extension of the two dimensional wavelet transform to encompass the time dimension is straightforward and this work attempts to extrapolate some of its properties into three dimensions. The vector quantizer is then applied to three dimensional image data to produce a video coding system which, while not optimal, produces very encouraging results

Rare-gas clusters in intense VUV laser fields

A hybrid quantum-classical approach to the interaction of atomic clusters with intense laser fields in the vacuum ultra-violet (VUV) has been developed. Much emphasis is put on localized electrons, those quasi-free electrons which localize about the ions and screen them. These electrons set a time scale, which is used to interpolate between the quantum, rate based description of photon absorption by bound electrons and the classical, deterministic description of the cluster nano-plasma. Typical observables such as total energy absorption, electron and ion spectra are in very good agreement with the experimental findings. A scheme to probe the multi-electron motion in clusters with attosecond laser pulses is introduced. Conventional final state measurements in the energy domain cannot provide information about earlier states of the system due to the incoherent nature of the dynamics. Time-delayed attosecond pulses in the extreme ultra-violet (XUV) are used to probe the transient charging of the cluster ions during the interaction with the laser by measuring the kinetic energy of the electrons detached by the probe pulse. This information is otherwise lost at later times due to recombination. Knowledge about the transient charging would also shed more light on the still controversial subject of the energy absorption mechanisms in the VUV regime. Moving to shorter duration of the excitation, the characteristic time-scales for ionization and plasma equilibration are inversed. An attosecond laser pulse in the VUV regime creates a dense, warm nano-plasma far from equilibrium. Time-delayed attosecond pulses in the XUV probe then both the creation and the relaxation. The latter shows the breakup of the Bogoliubov hierarchy of characteristic times, indicating strongly-coupled plasma dynamics and drawing parallels to the relaxation of extended ultra-cold neutral plasmas with millions of particles

Probes of strong-field gravity

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2012.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 221-234).In this thesis, I investigate several ways to probe gravity in the strong-field regime. These investigations focus on observables from the gravitational dynamics, i.e. when time derivatives are large: thus I focus on sources of gravitational waves. Extreme mass-ratio inspirals (EMRIs) can be very sensitive probes of strong-field physics. Predicting observables from EMRIs must be done numerically, so accurate numerical methods are required to ensure that any comparison with measurement is not spoiled by numerical artefacts. The first investigation of this thesis is a spectral (in the angular sector), pseudospectral (in the radial sector) time-domain PDE solver for perturbations of a Kerr black hole (i.e. solving the Teukolsky equation). The method exhibits good convergence and prompts much future investigation. A second approach to probing strong gravity is to consider theories which are general relativity (GR) with a few small corrections and investigate the effect of these corrections on observables. Since gravitational waves are the prime observable and they control the long-term evolution of dynamical systems, I investigate their properties in almost-GR theories. The second investigation of this thesis is a study of the propagation and energy content of gravitational waves in these theories. I find that in a large class of theories, approaching the asymptotically at part of spacetime, gravitational waves propagate in the same fashion as in GR and have the same effective stress-energy tensor as in GR. Next, I study the strong-field correction to the structure of a Schwarzschild black hole in a class of theories. Finally, with these ingredients, I investigate the leading corrections to the dynamics and observables of a comparable mass-ratio inspiral using post-Newtonian techniques. The main result is the appearance of dipolar scalar radiation in this class of theories. The dipolar radiation has a frequency dependence which does not arise in GR and is a distinct signature of corrections. Such signatures should be testable using gravitational wave detection and pulsar timing.by Leo Chaim Stein.Ph.D

3D modelling using partial differential equations (PDEs).

Partial differential equations (PDEs) are used in a wide variety of contexts in computer science ranging from object geometric modelling to simulation of natural phenomena such as solar flares, and generation of realistic dynamic behaviour in virtual environments including variables such as motion, velocity and acceleration. A major challenge that has occupied many players in geometric modelling and computer graphics is the accurate representation of human facial geometry in 3D. The acquisition, representation and reconstruction of such geometries are crucial for an extensive range of uses, such as in 3D face recognition, virtual realism presentations, facial appearance simulations and computer-based plastic surgery applications among others. The principle aim of this thesis should be to tackle methods for the representation and reconstruction of 3D geometry of human faces depending on the use of partial differential equations and to enable the compression of such 3D data for faster transmission over the Internet. The actual suggested techniques are based on sampling surface points at the intersection of horizontal and vertical mesh cutting planes. The set of sampled points contains the explicit structure of the cutting planes with three important consequences: 1) points in the plane can be defined as a one dimensional signal and are thus, subject to a number of compression techniques; 2) any two mesh cutting planes can be used as PDE boundary conditions in a rectangular domain; and 3) no connectivity information needs to be coded as the explicit structure of the vertices in 3D renders surface triangulation a straightforward task. This dissertation proposes and demonstrates novel algorithms for compression and uncompression of 3D meshes using a variety of techniques namely polynomial interpolation, Discrete Cosine Transform, Discrete Fourier Transform, and Discrete Wavelet Transform in connection with partial differential equations. In particular, the effectiveness of the partial differential equations based method for 3D surface reconstruction is shown to reduce the mesh over 98.2% making it an appropriate technique to represent complex geometries for transmission over the network

Spectral features of matrix-sequences, GLT, symbol, and application in preconditioning Krylov methods, image deblurring, and multigrid algorithms.

The final purpose of any scientific discipline can be regarded as the solution of real-world problems. With this aim, a mathematical modeling of the considered phenomenon is often compulsory. Closed-form solutions of the arising functional equations are usually not available and numerical discretization techniques are required. In this setting, the discretization of an infinite-dimensional linear equation via some linear approximation method, leads to a sequence of linear systems of increasing dimension whose coefficient matrices could inherit a structure from the continuous problem. For instance, the numerical approximation by local methods of constant or nonconstant coefficients systems of Partial Differential Equations (PDEs) over multidimensional domains, gives rise to multilevel block Toeplitz or to Generalized Locally Toeplitz (GLT) sequences, respectively. In the context of structured matrices, the convergence properties of iterative methods, like multigrid or preconditioned Krylov techniques, are strictly related to the notion of symbol, a function whose role relies in describing the asymptotical distribution of the spectrum. This thesis can be seen as a byproduct of the combined use of powerful tools like symbol, spectral distribution, and GLT, when dealing with the numerical solution of structured linear systems. We approach such an issue both from a theoretical and practical viewpoint. On the one hand, we enlarge some known spectral distribution tools by proving the eigenvalue distribution of matrix-sequences obtained as combination of some algebraic operations on multilevel block Toeplitz matrices. On the other hand, we take advantage of the obtained results for designing efficient preconditioning techniques. Moreover, we focus on the numerical solution of structured linear systems coming from the following applications: image deblurring, fractional diffusion equations, and coupled PDEs. A spectral analysis of the arising structured sequences allows us either to study the convergence and predict the behavior of preconditioned Krylov and multigrid methods applied to the coefficient matrices, or to design effective preconditioners and multigrid solvers for the associated linear systems