Academic literature on the topic 'Extended moment invariants'

This article examines the Bouton–Lie group invariants of the Navier–Stokes equation (NSE) for incompressible fluids. The theory is applied to the general scaling transformation admitted by the NSE: it adds new partial differential equations to the Navier–Stokes system of equations and is used to derive all self-similar solutions. This method can be applied to any differential equation exhibiting scaling invariance. The solutions are found to be based on isobaric polynomials, which can be smooth and nonzero at the initial moment. The non-self-similar velocity and pressure fields in the case of constant viscosity at all scales are studied and also found to be polynomials, nonzero, and smooth at the initial moment; they vanish far away from the origin and are not increasing in time. For a subset of the solutions, the cavitation number is shown to be a conserved quantity; the invariant analysis is extended to higher-dimensioned manifolds for the purpose of finding additional conserved quantities.

t has been shown that the traditional seven Hu invariant moment does not have scaling invariance with low recognition rate in human behavior recognition. In order to improve the recognition rate, a human behavior recognition method will be put forward in this paper based on weighted modified Hu moments. Firstly, the traditional seven Hu moments will be extended to ten Hu moments to get more image details. Then, the extended Hu moments will be modified to make the Hu moments has the feature of scaling invariance. Lastly, the weighted modified Hu moment will be obtained through least squares method based on minimum variance criterion. The simulation of the sequence images shows that the weighted modified Hu moment can improve the recognition rate effectively.

It is known that Kolmogorov's four-fifths law for statistically homogeneous and isotropic turbulence can be generalized to anisotropic turbulence. This fundamental result for homogeneous anisotropic turbulence says that in the inertial range the divergence of the vector third-order moment 〈|δv(r)|2δv(r)〉 is constant and is equal to -4ϵ, where ϵ is the dissipation rate of the turbulence. This law can be extended to incompressible magnetohydrodyamic (MHD) turbulence where statistical isotropy is often not valid due, for example, to the presence of a large-scale magnetic field. Laws for anisotropic incompressible MHD turbulence were first derived by Politano and Pouquet. In this paper, the laws for vector third-order moments in homogeneous non-isotropic incompressible MHD turbulence are derived by a technique due to Frisch that clarifies the relationship between the energy flux in Fourier space and the vector third-order moments in physical space. This derivation is different from the original derivation of Politano and Pouquet which is based on the Kármán–Howarth equation, and provides some new physical insights. Separate laws are derived for the cascades of energy, cross-helicity and magnetic-helicity, the three ideal invariants of incompressible MHD for flows in three dimensions. These laws are of fundamental importance in the theory of MHD turbulence where non-isotropic turbulence is much more prevalent than isotropic turbulence.

Abstract In this paper a single camera vision guidance system for fixed wing UAV is developed. This system searches for and identifies a target object with known colour and shape from images captured by an onboard camera. HSV colour space and moment invariants are utilised to describe the colour and shape features of the target object. Position, area and rotation angle of the target object in the image plane are collected. This information is then processed by the Extended Kalman Filter to estimate the relative positions and attitudes of the UAV. The vision guidance system guides the UAV towards the target object automatically based on these estimated states by using a proportional controller. A Senior Telemaster aircraft model kit installed with an onboard camera and computer is used for flight test. The target object for the flight test is a white flag with a red cross. Flight simulations and flight tests results are presented in this paper, showing that the vision guidance system can recognise the target object and guide the UAV effectively.

Script identification is an appealing research interest in the field of document image analysis during the last few decades. The accurate recognition of the script is paramount to many post-processing steps such as automated document sorting, machine translation and searching of text written in a particular script in multilingual environment. For automatic processing of such documents through Optical Character Recognition (OCR) software, it is necessary to identify different script words of the documents before feeding them to the OCR of individual scripts. In this paper, a robust word-level handwritten script identification technique has been proposed using texture based features to identify the words written in any of the seven popular scripts namely, Bangla, Devanagari, Gurumukhi, Malayalam, Oriya, Telugu, and Roman. The texture based features comprise of a combination of Histograms of Oriented Gradients (HOG) and Moment invariants. The technique has been tested on 7000 handwritten text words in which each script contributes 1000 words. Based on the identification accuracies and statistical significance testing of seven well-known classifiers, Multi-Layer Perceptron (MLP) has been chosen as the final classifier which is then tested comprehensively using different folds and with different epoch sizes. The overall accuracy of the system is found to be 94.7% using 5-fold cross validation scheme, which is quite impressive considering the complexities and shape variations of the said scripts. This is an extended version of the paper described in (Singh et al., 2014).

AbstractWe present a systematic derivation of a model based on the central moment lattice Boltzmann equation that rigorously maintains Galilean invariance of forces to simulate inertial frame independent flow fields. In this regard, the central moments, i.e. moments shifted by the local fluid velocity, of the discrete source terms of the lattice Boltzmann equation are obtained by matching those of the continuous full Boltzmann equation of various orders. This results in an exact hierarchical identity between the central moments of the source terms of a given order and the components of the central moments of the distribution functions and sources of lower orders. The corresponding source terms in velocity space are then obtained from an exact inverse transformation due to a suitable choice of orthogonal basis for moments. Furthermore, such a central moment based kinetic model is further extended by incorporating reduced compressibility effects to represent incompressible flow. Moreover, the description and simulation of fluid turbulence for full or any subset of scales or their averaged behavior should remain independent of any inertial frame of reference. Thus, based on the above formulation, a new approach in lattice Boltzmann framework to incorporate turbulence models for simulation of Galilean invariant statistical averaged or filtered turbulent fluid motion is discussed.

Hydrocarbon dipole moments are calculated by means of correlation weighting of local graph invariants within the context of QSPR theory. This sort of flexible topological descriptor is used for several parameters: local invariants of k th vertex in the labeled hydrogen filled graph extended connectivity of zero-, first- and second-orders, number of paths of length 2 at k th vertex and valence shell of the k th vertex. The models predict hydrocarbon dipole moments in a quite sensible way. The best model is that one based upon numbers of path length 2 correlation weighting.

Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.

AbstractIn this paper we propose a novel method for invariant image reconstruction with the properly selected degree of symmetry. We make use of Zernike radial moments to represent an image due to their invariance properties to isometry transformations and the ability to uniquely represent the salient features of the image. The regularized ridge regression estimation strategy under symmetry constraints for estimating Zernike moments is proposed. This extended regularization problem allows us to enforces the bilateral symmetry in the reconstructed object. This is achieved by the proper choice of two regularization parameters controlling the level of reconstruction accuracy and the acceptable degree of symmetry. As a byproduct of our studies we propose an algorithm for estimating an angle of the symmetry axis which in turn is used to determine the possible asymmetry present in the image. The proposed image recovery under the symmetry constraints model is tested in a number of experiments involving image reconstruction and symmetry estimation.

Canonical analysis of constraint structure of Einstein–Hilbert action in (1+1) dimensions possesses a mixed constrained model. By means of finite order BFT approach in the extended phase space, it converts to a fully gauge-invariant model. Embedded Hamiltonian in this extended phase space is independent of momenta similar to the classical Hamiltonian.

We discuss theoretical methods with which the effects of static, homogenous, electromagnetic fields can be determined for systems that are extended and in the ultimate limit are infinite and periodic. We focus here on the finite field (FF) method, but there are obvious implications for perturbation theory approaches as well. The fact that including finite fields in electronic-structure calculations simultaneously introduces the coordinate r→ means that the translational invariance of the potential would be violated and therefore without modification this approach would be inapplicable to infinite, periodic systems. One such long-standing approach is to replace r→ by an operator that involves the derivative with respect to the crystal momentum k→. This is the primary procedure for electrostatic fields. For magnetostatic fields a number of suggestions have been made, all of which are or may be related to changing the gauge used to describe the fields. In the case of a large finite system, for non-vanishing electrostatic and/or magnetostatic field, the lowest energy orbitals are unbound. Thus, the bound states become resonances and the bound-state variational principle can no longer be applied. Instead, special methods for identifying the changes in the system properties due to the presence of these fields are evaluated. Our own simple method based on identifying those orbitals in the field-containing case that are most similar to the occupied orbitals in the field-free case seems to be a promising approach. Since methods for finite molecular systems exposed to static electromagnetic fields are more mature than those for the infinite, periodic crystals, an important issue is to establish that these methods give identical results when treating a crystal as being either large and finite or infinite and periodic. Finally it shall be mentioned that our presentation focuses on methods rather than results. Moreover, it concentrates on our own work that, in some cases, is not yet complete.

Image moments are invariant under certain coordinate transformations. In practical use, the classical invariant moments are sensitive to noise and to measurement errors if the moments are generated by optical methods. The effects of noise on image moments decrease with the moment order. Low-order invariant moments may be expressed in terms of the radial moments of circular harmonic functions or extended complex moments. For the purpose of invariant pattern recognition, these moments may be used for image description followed by a statistical classification in feature space. They may also be used for image normalization followed by a classification using image correlation. For image normalization the use of low-order moments of circular harmonic functions yields an image mean direction which is more robust against background noise than the classical principal axes.

The invariant integrals are being widely used in the study of defects and fracture mechanics, mostly in elastostatics. However, the properties and the interpretation of these integrals in elastodynamics, especially in the case of time-harmonic excitation, have remained unexplored. Their study has a variety of engineering and geophysical implications, in particular, for the further development of non-destructive evaluation techniques. This contribution is focused on the derivation of the time average J integral for a cylindrical inhomogeneity and M integral for a cylindrical cavity placed in a monochromatic plane elastic wave of arbitrary wavelength. It is shown in the context of antiplane linear elasticity, that the J integral or the material force acting on the inhomogeneity resembles the radiation pressure force exerted on a dielectric cylinder by the normally incident electromagnetic wave. Based on the existing solution of this electrodynamic problem and the corresponding acoustic problem, the J integral is expressed as a function of the nondimensional wave number in the form of the partial wave expansion of the scattering theory. Employing the same classical method as for the J integral, the closed-form solution for the time average M integral for a traction-free cavity is also obtained as a function of the nondimensional wave number. The M integral, i.e., the expansion moment per unit length on an infinitely long circular cavity, is represented in terms of the scattering phase shifts as in the case of the J integral. Rather different expressions for the cavity are also derived for both integrals, which can be used more conveniently for numerical calculations, and these calculations are carried out for J and M integrals in a wide spectrum of frequencies. Asymptotic approximations of both integrals for low and high frequencies are presented. The long wavelength approximation, including the monopole and dipole contributions, has been provided for the J integral in the form of simple analytical expression. The value of M integral in the vanishing frequency limit is also presented. In the opposite short wavelength limit, the corresponding asymptotic values are derived for both integrals. These solutions which are valid for the empty cavity are extended to the case of inviscid fluid-filled cavity. The obtained results can be used in the area of non-destructive evaluation for the flaw characterization by ultrasonic scattering methods. The derived frequency dependence of the J and M integral can be related to the measurable far-field scattering amplitudes. This relationship is relevant to the inverse-scattering approach, which can be applied to the characterization of materials in an attempt to infer geometrical characteristics of flow structures.

The paper proposes an e-learning model which uses the concepts and the methods of the systems theory. The first level of the model is the "black box" representation in which the system is characterized by its input and output terminals. The input terminals correspond to different types of e-learning methods, for instance e-courses, self-study materials, media means, virtual classrooms, interactive e-lessons, video/audio conferences, web-based training, mobile learning, social learning, chat, wiki, blog and personal site, simulation, serious game-based learning. The output terminals correspond to various kinds of examinations, for instance, tests, midterm tests, final exams and results of pairwork and groupwork activities, homework. On the second level, the state, input and output variables of the system are defined and one provides the mathematical model in terms of the state and output equations. Finally, the considered variables are organized into three kinds of vectors, which are the states, inputs and outputs of the model and the coefficients of the obtained equations form three matrices of appropriate dimensions. One obtains the state-space representation of the e-learning process in the form of a linear, discrete-time, time-invariant control system. This representation, which is at the interface between e-learning, systems theory and mathematics, enables the description of the system behaviour by two formulas, one for the state of the system at any moment of time and another one (called the general response or the input-output map) for the output of the system. The main advantage of this model is that one can apply the theory of the linear control systems to solve some problems. For instance, the fundamental concept of controllability and the corresponding techniques give the possibility of establishing a policy of learning so that a student's (or a group of students') state of knowledge comes at a given level at a given time. The dual concept of observability provides methods to estimate the state by knowing the values of the input and output. One can apply the optimal control to minimize or maximize an evaluation functional and obtain solutions in the form of a state feedback. An application to foreign languages e-learning is provided. The four macro language skills have been considered: the productive skills, i.e. writing and speaking and the receptive ones, i.e. reading and listening. This choice is influenced by their important position in foreign languages e-learning (and generally in learning), by the fact that nowadays they are considered skills in their own right, not only support for learning vocabulary or grammar. Another argument is that these skills are commonly used in combination and their learning processes should work interactively. The state-space representation of the e-learning process is obtained, by defining the state variables by the skills acquired at an interval of time. The Control Systems Toolbox of the Matlab software is used to generate and to study the corresponding control system. The given model can be extended to time-varying or to stochastic systems. The model can also be extended by introducing some micro skills, for instance pre-, while- and post-listening skills, email skills or the understanding and the use of specialized terms in a domain (such as engineering, economics, medicine etc.). For the research in the preparation of the paper, the author has received advice within the collective Systems Theory and Optimal Control at the Applied Sciences Faculty, University Politehnica of Bucharest.