Blind document image enhancement based on diffusion process

This paper introduces a new method for analyzing solution-gas production to determine the ultimate recovery of a well or a field. The procedure developed and outlined in this paper requires very little input data and is easily implemented. By modifiying the equations for dimensionless rate and dimensionless cumulative production derived for the single phase model, a new set of equations is developed to approximate the ultimate recovery of a solution-gas well. Using the approximate material balance equation based on numerical results by Vogel1 and the equation for the production rate derived by Fetkovich et al.2,3,4, this new set of dimensionless rate and dimensionless cumulative production equations are derived. Using the relationship between these equations and an iterative calculation procedure, the ultimate recovery for the solution-gas well can be easily determined. All that is needed as input is the producing bottom-hole pressure, the initial pressure, and the oil production data. The method has been validated with twelve simulator cases, six under constant bottom hole pressure production constraint and six under variable bottom hole pressure production constraint. Furthermore, several field cases have been analyzed. The synthetic and field cases validate the procedure. Using the early pseudo-steady state production data in the analysis the results generated by the method are consistent with the actual ultimate recoveries.

We present a new complete set of Lagrangian relativistic hydrodynamical equations describing the transfer of energy and momentum between a standard fluid and a radiation fluid in a general non-stationary spherical flow. The new set of equations has been derived for a particular application in the study of the cosmological quark--hadron transition, but can also be used in other contexts.

A new noise reduction and edge enhancement method, i.e., Laplacian pyramid-based nonlinear diffusion and shock filter (LPNDSF), is proposed for medical ultrasound imaging. In the proposed LPNDSF, a coupled nonlinear diffusion and shock filter process is applied in Laplacian pyramid domain of an image, to remove speckle and enhance edges simultaneously. The performance of the proposed method was evaluated on a phantom and a real ultrasound image. In the phantom study, we obtained an average gain of 0.55 and 1.11 in contrast-to-noise ratio compared to the speckle reducing anisotropic diffusion (SRAD) and nonlinear coherent diffusion (NCD), respectively. Also, the proposed LPNDSF showed clearer boundaries on the phantom and the real ultrasound image. These preliminary results indicate that the proposed LPNDSF can effectively reduce speckle noise while enhancing image edges for retaining subtle features.

This work includes some new aspects of motion estimation by the optic flow method in scale spaces. The usual techniques for motion estimation are limited to the application of coarse to fine strategies. The coarse to fine strategies can be successful only if there is enough information in every scale. In this work we investigate the motion estimation in the scale space more basically. The wavelet choice for scale space decomposition of image sequences is discussed in the first part of this work. We make use of the continuous wavelet transform with rotationally symmetric wavelets. Bandpass decomposed sequences allow the replacement of the structure tensor by the phase invariant energy operator. The structure tensor is computationally more expensive because of its spatial or spatio-temporal averaging. The energy operator needs in general no further averaging. The numerical accuracy of the motion estimation with the energy operator is compared to the results of usual techniques, based on the structure tensor. The comparison tests are performed on synthetic and real life sequences. Another practical contribution is the accuracy measurement for motion estimation by adaptive smoothed tensor fields. The adaptive smoothing relies on nonlinear anisotropic diffusion with discontinuity and curvature preservation. We reached an accuracy gain under properly chosen parameters for the diffusion filter. A theoretical contribution from mathematical point of view is a new discontinuity and curvature preserving regularization for motion estimation. The convergence of solutions for the isotropic case of the nonlocal partial differential equation is shown. For large displacements between two consecutive frames the optic flow method is systematically corrupted because of the violence of the sampling theorem. We developed a new method for motion analysis by scale decomposition, which allows to circumvent the systematic corruption without using the coarse to fine strategy. The underlying assumption is, that in a certain neighborhood the grey value undergoes the same displacement. If this is fulfilled, then the same optic flow should be measured in all scales. If there arise inconsistencies in a pixel across the scale space, so they can be detected and the scales containing this inconsistencies are not taken into account.

A new dynamic theory of die swell for entangled polymeric liquids in a steady simple shear flow is proposed which can be used to predict the correlation of the time-dependent and time-independent extrudate swelling behaviors to the molecular parameters of polymers and the operational variables. The theory is based on the O-W-F constitutive equation and the free recovery from Poioeuille flow with different ratios. Experiments show that the magnitudes of the simple shear in the steady simple shear flow may be resolved into the free recoil resulting from the recoverable elastic strains and the viscous heating resulting from the unrecoverable viscoelastic strains. For distinguishing the recoil from the viscous heating, a partition function and two exponential fractions of conformation for the recoil and the viscous heating were defined. Thus the instantaneous, delayed and ultimate recoverable strain, and recoil in the free recovery were correlated to the partition function, the fraction of recoverable conformation, the molecular parameters, and the operational variables. Also the dynamics of the growth equation on the delayed viscoelastic strain and the delayed recoil in free state were deduced. After introducing the condition of uniform two dimensional extensions, the definition of swell ratio and the operational variables into the above correlation expressions and growth equations, then the correlations of the delayed extrudate swelling effect and the ultimate extrudate swelling effects to the molecular parameters and the operational variables were derived. Finally, two new sets of equations on the growth variables and ultimate extrudate swelling ratios under the dynamic and equilibrium states were also deduced from this dynamic theory of die swell. The first set of equations on the ultimate extrudate swelling ratio under the free and equilibrium states was verified by HDPE experimental data at two temperatures and different operational variables. The second set of equations on the growth extrudate swelling ratios under free and dynamic states was verified by PBD experimental data with different molecular weights and different operational variables. An excellent agreement is obtained, which shows that the two sets of equations for the growth and ultimate extrudate swelling ratios can be used directly to predict the correlation of extrudate swelling ratios to the molecular parameters and the operational variables.

A new set of equations is introduced for the analysis of the evacuation process. The equations are based on the surface processes of adsorption and desorption of gas molecules taking place on the inhomogeneous metal surface but not on the diffusion process. Because the equations are nonlinear, it is difficult to get the analytic solution, and numerical calculations, as well as analytic considerations were made. The results tell us that (i) the outgassing phenomena can only be understood under nonequilibrium conditions, (ii) the evacuation time dependence of the outgassing rate depends on the distribution function of the adsorbing site, i.e., the adsorption site density as a function of the activation energy of desorption E, and (iii) a pressure buildup phenomenon, which is accompanied by a sudden stop of evacuation, can be easily understood. Finally, a new measurement method is proposed for the investigation of surface properties. In this method, a chamber made of a test material is evacuated for a long time and then a measurement follows. In the measurement, one adjusts the pumping speed so as to keep the vacuum pressure in the chamber constant. The amount of outgas is determined as a function of time by knowing the pumping speed. By this method, one can get quite new information concerning the surface properties.

Edge noise is generated if turbulence interacts with solid edges. Reduction of trailing edge noise of airfoils can be achieved by replacing the solid material at the trailing edge by inlays of porous permeable material. The acoustic benefit of approximately 6 dB of such treatment is known from experiments. Enroute to numerically optimized porous properties, this paper presents a first principle based Computational Aeroacoustics (CAA) method for predicting the acoustic effect of a porous NACA0012 trailing edge. In a hybrid two-step CFD/CAA procedure the turbulence statistics from a solution of the Volume Averaged Navier-Stokes (VANS) equations is used as a basis for the prediction of turbulent-boundary-layer trailing-edge noise (TBL-TEN). For the acoustic part of the calculation, the Acoustic Perturbation Equations (APE) are solved in the flow field. Inside the porous regions, a different set of governing equations, referred to as Linear Perturbation Equations (LPE) will be solved. The LPE represent a modified form of the Linearized Euler Equations (LEE) with the APE vorticity source term shifted to the right-hand side. The new set of equations is derived by volume averaging the Navier-Stokes equations and decomposing the flow variables into a time-averaged mean part and a fluctuating part and isolating the vorticity source term to the right-hand side of the momentum equation. The LPE are verified by an analytical solution. The simulation results of a NACA0012 airfoil geometry with and without porous trailing edge treatment are compared to wind tunnel measurements. The noise reduction effect of such a trailing edge treatment is successfully demonstrated.

The basic problem of order reduction of nonlinear systems with time periodic coefficients is considered in state space and in direct second order (structural) form. In state space order reduction methods, the equations of motion are expressed as a set of first order equations and transformed using the Lyapunov–Floquet (L–F) transformation such that the linear parts of new set of equations are time invariant. At this stage, four order reduction methodologies, namely linear, nonlinear projection via singular perturbation, post-processing approach and invariant manifold technique, are suggested. The invariant manifold technique yields a unique ‘reducibility condition’ that provides the conditions under which an accurate nonlinear order reduction is possible. Unlike perturbation or averaging type approaches, the parametric excitation term is not assumed to be small. An alternate approach of deriving reduced order models in direct second order form is also presented. Here the system is converted into an equivalent second order nonlinear system with time invariant linear system matrices and periodically modulated nonlinearities via the L–F and other canonical transformations. Then a master-slave separation of degrees of freedom is used and a nonlinear relation between the slave coordinates and the master coordinates is constructed. This method yields the same ‘reducibility conditions’ obtained by invariant manifold approach in state space. Some examples are given to show potential applications to real problems using above mentioned methodologies. Order reduction possibilities and results for various cases including ‘parametric’, ‘internal’, ‘true internal’ and ‘true combination resonances’ are discussed. A generalization of these ideas to periodic-quasiperiodic systems is included and demonstrated by means of an example.

Global and localised temporal structures in driven ring quantum cascade lasers

Nonlinear structure tensors

This study aims at developing a new set of equations of mean motion in the presence of surface waves, which is practically applicable from deep water to the coastal zone, estuaries, and outflow areas. The generalized Lagrangian mean (GLM) method is employed to derive a set of quasi-Eulerian mean three-dimensional equations of motion, where effects of the waves are included through source terms. The obtained equations are expressed to the second-order of wave amplitude. Whereas the classical Eulerian-mean equations of motion are only applicable below the wave trough, the new equations are valid until the mean water surface even in the presence of finite-amplitude surface waves. A two-dimensional numerical model (2DV model) is developed to validate the new set of equations of motion. The 2DV model passes the test of steady monochromatic waves propagating over a slope without dissipation (adiabatic condition). This is a primary test for equations of mean motion with a known analytical solution. In addition to this, experimental data for the interaction between random waves and a mean current in both non-breaking and breaking waves are employed to validate the 2DV model. As shown by this successful implementation and validation, the implementation of these equations in any 3D model code is straightforward and may be expected to provide consistent results from deep water to the surf zone, under both weak and strong ambient currents.

The method of moments is employed to extend the validity of continuum-hydrodynamic models into the transition-flow regime. An evaluation of the regularized 13 moment equations for two confined flow problems, planar Couette and Poiseuille flows, indicates some important limitations. For planar Couette flow at a Knudsen number of 0.25, they fail to reproduce the Knudsen-layer velocity profile observed using a direct simulation Monte Carlo approach, and the higher-order moments are not captured particularly well. Moreover, for Poiseuille flow, this system of equations creates a large slip velocity leading to significant overprediction of the mass flow rate for Knudsen numbers above 0.4. To overcome some of these difficulties, the theory of regularized moment equations is extended to 26 moment equations. This new set of equations highlights the importance of both gradient and non-gradient transport mechanisms and is shown to overcome many of the limitations observed in the regularized 13 moment equations. In particular, for planar Couette flow, they can successfully capture the observed Knudsen-layer velocity profile well into the transition regime. Moreover, this new set of equations can correctly predict the Knudsen layer, the velocity profile and the mass flow rate of pressure-driven Poiseuille flow for Knudsen numbers up to 1.0 and captures the bimodal temperature profile in force-driven Poiseuille flow. Above this value, the 26 moment equations are not able to accurately capture the velocity profile in the centre of the channel. However, they are able to capture the basic trends and successfully predict a Knudsen minimum at the correct value of the Knudsen number.

Fingerprint enhancement is a critical step in a fingerprint identific ation system. Recently, some anisotropic nonlinear diffusion filter is applied to the fingerprint preprocessed. Impressive results are main reason for using nonlinear diffusion filtering in image processing. Poor efficiency, especially the computational load, is the main reason for not using nonlinear diffusion filtering. In order to improve the efficie ncy, a novel piecewise nonlinear diffusion for fingerprint enhancement is presented. It shows anisotropic diffusion equation using diffusion tensor which continuously depends on the gradient is not necessary to smooth the fingerprint. We simplify the anisotropic nonlinear-diffusion in order to satisfy a real-time fingerprint recognition system. According to the local character of the fingerprint, the diffusion filter is steered by the orientation of ridge. Experimental results illustrate that our enhancement algorithm can satisfy the requirement of an AFIS.

In this work, facial thermal infrared images are employed for intoxicated person discrimination. The activity of the facial blood vessels of sober and intoxicated people comes into sight when nonlinear anisotropic diffusion and top-hat transformation are applied to enhance and isolate the vessels from the rest of the information on the face. For an intoxicated person, vessels around the nose and eyes as well as on the forehead become more active, whereas for a person who is sober the vessels’ activity is smoother all over the face’s thermal image. Accordingly, drunkenness can be ascertained by only using the thermal infrared image of the intoxicated person. The proposed method can be incorporated into a non-invasive inspection system used by the police as a first step for intoxicated person detection. The Student’s t-test is employed to assess the degree of confidence in separating the thermal images corresponding to sober and intoxicated people. The 40 participants in the experiment have contributed to the creation of the unique sober–drunk database available on the web.

Two-dimensional weakly nonlinear surface gravity–capillary waves in an ideal fluid of finite water depth are considered and nonlinear evolution equations which are correct up to the third order of wave steepness are derived including the applied pressure on the free surface. Since no assumptions are made on the length scales, the equations can be applied to a fluid of arbitrary depth and to disturbances with arbitrary wavelength. For one-dimensional gravity waves, these evolution equations are reduced to those derived by Matsuno (1992). Most of the known equations for surface waves are recovered from the new set of equations as special cases. It is shown that one set of equations has a Hamiltonian formulation and conserves mass, momentum and energy. The analysis for irrotational flow is extended to two-dimensional uniform shear flow.