Exposing Digital Forgeries From JPEG Ghosts

When creating a digital forgery, it is often necessary to combine several images, for example, when compositing one person's head onto another person's body. If these images were originally of different JPEG compression quality, then the digital composite may contain a trace of the original compression qualities. To this end, we describe a technique to detect whether the part of an image was initially compressed at a lower quality than the rest of the image. This approach is applicable to images of high and low quality as well as resolution.      

Discrete Copulas

We define discrete copulas on a grid of the unit square and show that with each discrete copula there is associated, in a natural way, a bistochastic matrix. This is used in order to introduce the product of discrete copulas. Discrete copulas of order$n$are the smallest convex set containing the irreducible discrete copulas of order$n$introduced by Mayor .     

Image Restoration in Optical-Acoustic Tomography

We consider the optical-acoustic tomography problem. In the general case, the problem is to reconstruct a real-valued function with a compact support in the n-dimensional Euclidean space via its spherical integrals, i.e., integrals over all (n – 1)-dimensional spheres centered at points on some (n – 1)-dimensional hypersurface. We deal with the cases n = 2 and n = 3, which are of the most practical interest from the standpoint of possible medical applications. We suggest a new effective method of reconstruction, develop restoration algorithms, and investigate the quality of the algorithms for these cases. The main result of the paper is construction of explicit approximate reconstruction formulas; from the mathematical standpoint, these formulas give the parametrix for the optical-acoustic tomography problem. The formulas constructed is a background for the restoration algorithms. We performed mathematical experiments to investigate the quality of the restoration algorithms using the generally accepted tomography quality criteria. The results obtain lead to the general conclusion: the quality of the restoration algorithms developed for optical-acoustic tomography is only slightly lower then the quality of the convolution and back projection algorithm used in Radon tomography, which is a standard de facto.     

Discrete optimization

This paper presents some theoretical ideas for the discrete non-linear programming problem. The main objective in to construct a hypercube inside of which the discrete optimum will lie. It is shown that for quadratic functions this hypercube can be constructed by knowing the inverse of the hessian matrix.     

Discrete models in social sciences

Behaviors of solutions of a differential equation and its discretization sometimes differ greatly from each other. For example, even if a differential equation has no chaotic solution, its discretization happens to have a chaotic solution. In this paper, the meanings of this fact in economics are shown. Also, a finite difference model in sociology is given as a chaotic phenomenon.     

Discrete Events in Power Systems

The relevance of Discrete Event System theory (whether synthetic or analytic) to power system analysis and control is not clear. However, based on several characterizations of the domain of discrete systems set forth in the January 1989 Special Issue of the IEEE Proceedings, on Dynamics of discrete event systems (Ho, 1989), we attempt to delineate several power system control problems that may be amenable to analysis by DEDS methodologies. While the author is not qualified to judge whether the latter can speak to any of the examples, it may be relevant that in all cases the problems are non-trivial and in need of further contributions toward improved solutions, especially in view of the ongoing radical restructuring of the industry. The continuous process that is instantiated in the functioning of a power system is observed via three more or less diverse variables. Two of these, the scaler system frequency and the vector system voltage profile, are in principle mensurable physical phenomena; the third, system security, is a quality represented by a set membership conditioned on an inferred relationship between the two physical system variables and future realizations of one or more classes of autonomous stochastic phenomena. (These latter may be internal or external to the physical system, such as, e.g., respectively, equipment failure mechanisms and weather events.)     

离散数学中的DNA计算

由于电子计算机的存贮量小,运算速度慢,智能化低,特别是制造工艺趋于极限。最近,采用计算的可能性引起了人们的广泛关注,尤其是它的良好的并行性。离散数学中的逻辑演算有着广泛的应用,特别是在信息处理方面。论文给出了一个运用图论和DNA计算的方法,解决较复杂的逻辑演算问题。     

Discrete Positive Realness of The Discrete Min-Max Control Law

It is shown that the discrete state dependent min-maxcontroller for an uncertain discrete system with matched uncertainties,is a Discrete Strictly Positive Real (d.s.p.r.) control law.That is to say that an output may always be defined such thatthe nominal open loop is d.s.p.r., and the min-max control lawmay be realized via that output.     

The Euler Characteristics of Discrete Objects and Discrete Quasi-Objects

Assuming planar 4-connectivity and spatial 6-connectivity, we first introduce the curvature indices of the boundary of a discrete object, and, using these indices of points, we define the vertex angles of discrete surfaces as an extension of the chain codes of digital curves. Second, we prove the relation between the number of point indices and the numbers of holes, genus, and cavities of an object. This is the angular Euler characteristic of a discrete object. Third, we define quasi-objects as the connected simplexes. Geometric relations between discrete quasi-objects and discrete objects permit us to define the Euler characteristic for the planar 8-connected, and the spatial 18- and 26-connected objects using these for the planar 4-connected and the spatial 6-connected objects. Our results show that the planar 4-connectivity and the spatial 6-connectivity define the Euler characteristics of point sets in a discrete space. Finally, we develop an algorithm for the computation of these characteristics of discrete objects.     

An Application of Wavelets in Tomography

A method of tomographic inversion using wavelets is described which relies on the “diagonalization” property of wavelets for the derivative of the Hilber transform. Error bounds are given for reconstruction using the technique and an optimal wavelet which minimizes the error is presented. The method is well suited for inversion of from local data.     

Discrete Sibson interpolation

Natural-neighbor interpolation methods, such as Sibson's method, are well-known schemes for multivariate data fitting and reconstruction. Despite its many desirable properties, Sibson's method is computationally expensive and difficult to implement, especially when applied to higher-dimensional data. The main reason for both problems is the method's implementation based on a Voronoi diagram of all data points. We describe a discrete approach to evaluating Sibson's interpolant on a regular grid, based solely on finding nearest neighbors and rendering and blending d-dimensional spheres. Our approach does not require us to construct an explicit Voronoi diagram, is easily implemented using commodity three-dimensional graphics hardware, leads to a significant speed increase compared to traditional approaches, and generalizes easily to higher dimensions. For large scattered data sets, we achieve two-dimensional (2D) interpolation at interactive rates and 3D interpolation (3D) with computation times of a few seconds.     

Discrete ray tracing

Discrete ray tracing, or 3-D raster ray tracing (RRT), which, unlike existing ray tracing methods that use geometric representation for the 3-D scene employs a 3-D discrete raster of voxels for representing the 3-D scene in the same way a 2-D raster of pixels represents a 2-D image, is discussed. Each voxel is a small quantum unit of volume that has numeric values associated with it representing some measurable properties or attributes of the real object or phenomenon at that voxel. It is shown that RRT operates in two phases: preprocessing voxel and discrete ray tracing. In the voxel phase, the geometric model is digitized using 3-D scan-conversion algorithms that convert the continuous representation of the model into a discrete representation within the 3-D raster. In the second phase, RRT employs a discrete variation of the conventional recursive ray tracer in which 3-D discrete rays are traversed through the 3-D raster to find the first surface voxel. Encountering a nontransparent voxel indicates a ray-surface hit. Results obtained by running the RRT software one one 20-MIPS (25-GHz) processor of a Silicon Graphics 4D/240GTX are presented in terms of CPU time     

Discrete port-Hamiltonian systems

Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling at the discrete level itself. One of the goals of this paper is to model port-Hamiltonian systems at the discrete level. We also show that the dynamics of the discrete models we obtain exactly correspond to the dynamics obtained via a usual discretization procedure. In this sense we offer an alternative to the usual procedure of modeling (at the smooth level) and discretization.