Multiclass Semi-Supervised Learning on Graphs using Ginzburg-Landau Functional Minimization

We present a graph-based variational algorithm for classification of high-dimensional data, generalizing the binary diffuse interface model to the case of multiple classes. Motivated by total variation techniques, the method involves minimizing an energy functional made up of three terms. The first two terms promote a stepwise continuous classification function with sharp transitions between classes, while preserving symmetry among the class labels. The third term is a data fidelity term, allowing us to incorporate prior information into the model in a semi-supervised framework. The performance of the algorithm on synthetic data, as well as on the COIL and MNIST benchmark datasets, is competitive with state-of-the-art graph-based multiclass segmentation methods.Comment: 16 pages, to appear in Springer's Lecture Notes in Computer Science volume "Pattern Recognition Applications and Methods 2013", part of series on Advances in Intelligent and Soft Computin

Information Security for Audio Steganography Using a Phase Coding Method

The art and science of steganography are dedicated to concealing the presence of a secret message from a third party, such that only the sender and recipient are aware of its content. Various types of media can be used to conceal these communications. When information is hidden in an audio signal, this is referred to as audio steganography. In this paper, two distinct steganography techniques are combined with a multi-level steganography approach: the initial message is embedded in an audio cover at the initial stage, employing, a modified LSB technique, additionally, the second message is embedded in the output from the first level, using a phase coding approach at the second level. A stego audio file is the second level's output containing two audio covers with secret messages. The message is split in multiple ways, with varying proportions between the two levels, in order to investigate how the message's size affects the two procedures used here as well as the levels. The PSNR, MSE, and histogram metrics are used to compare the original and stego audio, in order to assess the effectiveness of the suggested approach. The optimum outcome is achieved when the message is divided in the ratio (1:1). The worst outcome is achieved when the message is divided in the ratio (3:1)&nbsp

A Second Order Fully-discrete Linear Energy Stable Scheme for a Binary Compressible Viscous Fluid Model

We present a linear, second order fully discrete numerical scheme on a staggered grid for a thermodynamically consistent hydrodynamic phase field model of binary compressible fluid flow mixtures derived from the generalized Onsager Principle. The hydrodynamic model not only possesses the variational structure, but also warrants the mass, linear momentum conservation as well as energy dissipation. We first reformulate the model in an equivalent form using the energy quadratization method and then discretize the reformulated model to obtain a semi-discrete partial differential equation system using the Crank-Nicolson method in time. The numerical scheme so derived preserves the mass conservation and energy dissipation law at the semi-discrete level. Then, we discretize the semi-discrete PDE system on a staggered grid in space to arrive at a fully discrete scheme using the 2nd order finite difference method, which respects a discrete energy dissipation law. We prove the unique solvability of the linear system resulting from the fully discrete scheme. Mesh refinements and two numerical examples on phase separation due to the spinodal decomposition in two polymeric fluids and interface evolution in the gas-liquid mixture are presented to show the convergence property and the usefulness of the new scheme in applications

Medical Image Segmentation Using Phase-Field Method based on GPU Parallel Programming

The use of a Phase Field method for medical image segmentation is proposed in this paper. The Allen-Cahn equation, a mathematical model equation, is used in this method. The Finite Difference method is used for numerical discretization of model equations and semi-algebraic equations integrated over time using the second -order Runge-Kutta method. Numerical algorithms are implemented into computer programming using the serial and parallel C programming language based on GPU CUDA. Based on image segmentation calculations, the Phase Field method has high accuracy. It is indicated by the Jaccard Index and Dice Similarity values that are close to one. The range of Jaccard Index values is 0.859 - 0.952, while the Dice Similarity value range is 0.926 - 0.976. In addition, it is shown that parallel programming with GPU CUDA can accelerate 45.72 times compared to serial programming

Second Order Fully Discrete Energy Stable Methods on Staggered Grids for Hydrodynamic Phase Field Models of Binary Viscous Fluids

We present second order, fully discrete, energy stable methods on spatially staggered grids for a hydrodynamic phase field model of binary viscous fluid mixtures in a confined geometry subject to both physical and periodic boundary conditions. We apply the energy quadratization strategy to develop a linear-implicit scheme. We then extend it to a decoupled, linear scheme by introducing an intermediate velocity term so that the phase variable, velocity field, and pressure can be solved sequentially. The two new, fully discrete linear schemes are then shown to be unconditionally energy stable, and the linear systems resulting from the schemes are proved uniquely solvable. Rates of convergence of the two linear schemes in both space and time are verified numerically. The decoupled scheme tends to introduce excessive dissipation compared to the coupled one. The coupled scheme is then used to simulate fluid drops of one fluid in the matrix of another fluid as well as mixing dynamics of binary polymeric, viscous solutions. The numerical results in mixing dynamics reveals the dramatic difference between the morphology in the simulations obtained using the two different boundary conditions (physical vs. periodic), demonstrating the importance of using proper boundary conditions in fluid dynamics simulations

Thermodynamically Consistent Hydrodynamic Phase Field Models and Numerical Approximation for Multi-Component Compressible Viscous Fluid Mixtures

Material systems comprising of multi-component, some of which are compressible, are ubiquitous in nature and industrial applications. In the compressible fluid flow, the material compressibility comes from two sources. One is the material compressibility itself and another is the mass-generating source. For example, the compressibility in the binary fluid flows of non-hydrocarbon (e.g. Carbon dioxide) and hydrocarbons encountered in the enhanced oil recovery (EOR) process, comes from the compressibility of the gas-liquid mixture itself. Another example of the mixture of compressible fluids is growing tissue, in which cell proliferation and cell migration make the material volume changes so that it cannot be described as incompressible. We present a systematic derivation of thermodynamically consistent hydrodynamic phase field models for compressible viscous fluid mixtures using the generalized Onsager principle along with the one fluid multi-component formulation. By maintaining momentum conservation while enforcing mass conservation at different levels, we obtain two compressible models. When the fluid components in the mixture are incompressible, we show that one compressible model reduces to the quasi-incompressible model via a Lagrange multiplier approach. Several different approaches to arriving at the quasi-incompressible model are discussed. Then, we conduct a linear stability analysis on all the binary models derived in the thesis and show the differences of the models in near equilibrium dynamics. We present a linear, second order fully discrete numerical scheme on a staggered grid for a thermodynamically consistent hydrodynamic phase field model of binary compressible flows of fluid mixtures derived from the generalized Onsager Principle. v The hydrodynamic model not only possesses the variational structure, but also warrants the mass, linear momentum conservation as well as energy dissipation. We first reformulate the model in an equivalent form using the energy quadratization method and then discretize the reformulated model to obtain a semi-discrete partial differential equation system using the Crank-Nicolson method in time. The numerical scheme so derived preserves the mass conservation and energy dissipation law at the semi-discrete level. Then, we discretize the semi-discrete PDE system on a staggered grid in space to arrive at a fully discrete scheme using the 2nd order finite difference method, which respects a discrete energy dissipation law. We prove the unique solvability of the linear system resulting from the fully discrete scheme. Mesh refinements are presented to show the convergence property of the new scheme. In the compressible polymer mixtures, we first construct a Flory-Huggins type of free energy and explore the phase separation phenomena due to spinodal decomposition. We investigate the phase separation with and without hydrodynamics, respectively. It tells us that hydrodynamics indeed changes local densities, the path of phase evolution and even the final energy steady states of fluid mixtures. This is alarming, indicating that hydrodynamic effects are instrumental in determining the correct spatial phase diagram for the binary fluid mixture. Finally, we study the interface dynamics and investigate the mass adsorption phenomena of one component at the interface, to show the performance of our model and the numerical scheme in simulating hydrodynamics of the hydrocarbon mixture