Learnable three-dimensional Gabor convolutional network with global affinity attention for hyperspectral image classification

Benefiting from the development of hyperspectral imaging technology, hyperspectral image (HSI) classification has become a valuable direction in remote sensing image processing. Recently, researchers have found a connection between convolutional neural networks (CNNs) and Gabor filters. Therefore, some Gabor-based CNN methods have been proposed for HSI classification. However, most Gabor-based CNN methods still manually generate Gabor filters whose parameters are empirically set and remain unchanged during the CNN learning process. Moreover, these methods require patch cubes as network inputs. Such patch cubes may contain interference pixels, which will negatively affect the classification results. To address these problems, in this paper, we propose a learnable three-dimensional (3D) Gabor convolutional network with global affinity attention for HSI classification. More precisely, the learnable 3D Gabor convolution kernel is constructed by the 3D Gabor filter, which can be learned and updated during the training process. Furthermore, spatial and spectral global affinity attention modules are introduced to capture more discriminative features between spatial locations and spectral bands in the patch cube, thus alleviating the interfering pixels problem. Experimental results on three well-known HSI datasets (including two natural crop scenarios and one urban scenario) have demonstrated that the proposed network can achieve powerful classification performance and outperforms widely used machine-learning-based and deep-learning-based methods.     

Modular invariance in N=2 superconformal field theories

The modular invariance properties of two-dimensional N=2 superconformal field theories are studied. It is shown that the character formulae of the central charge c<3 unitary highest weight representation for the untwisted algebras can be written in terms of the string functions and the theta functions of the affine su(2) Kac-Moody algebra. Deriving the modular transformation of the characters we construct the modular invariant partition functions on a torus. The character relation corresponding to the coset space construction of the unitary discrete series in the N=2 algebra is also obtained.     

基于局部Gabor二进制模式的高光谱伪装目标图像分类(英文)

为提高光谱伪装目标图像分类精度,提出了一种基于局部Gabor二进制模式(LGBP)的空间分类方法。LGBP作为一种多尺度算法,被用来提取高光谱图像的纹理特征。然后高光谱图像中的每一个像元可以用一个光谱特征向量及一个纹理特征向量表示。通过这种方法,增大类间距离。最后使用多核支持向量机结合光谱信息和空间纹理信息实现对高光谱伪装目标图像的分类。实验证明了该方法的有效性,分类总体精度和Kappa系数分别达到了95.6%和0.937。所提出的方法对于提高分类精度及鲁棒性具有重要意义。     

Unified theory of weak,strong, and electromagnetic interactions: Gauge transformation groups and gauge fields

An attempt is made to construct a unified theory of the weak, strong, and electro-magnetic interactions, based on a generalization of the Weinberg-Salam theory [1]. The groups of gauge transformations leaving the Lagrangian of the bispinor field invariant are discussed. It is shown that in order to preserve this invariance in transition from global to local transformations it is necessary to introduce seven gauge compensation fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 19–23, May, 1982.     

Lorentz invariance and origin of symmetries

We reconsider the role of Lorentz invariance in the dynamical generation of the observed internal symmetries. We argue that, generally, Lorentz invariance can be imposed only in the sense that all Lorentz noninvariant effects caused by the spontaneous breakdown of Lorentz symmetry are physically unobservable. The application of this principle to the most general relativistically invariant Lagrangian, with arbitrary couplings for all the fields involved, leads to the appearance of a symmetry and, what is more, to the massless vector fields gauging this symmetry in both Abelian and non-Abelian cases. In contrast, purely global symmetries are generated only as accidental consequences of the gauge symmetry.     

General relativity as a conformally invariant scalar gauge field theory

The global symmetry implied by the fact that one can multiply all masses with a common constant is made into a local, gauge symmetry. The matter action then becomes Conformally invariant and it seems natural to choose for the corresponding scalar gauge field the action for a conformally invariant (massless) scalar field. The resulting conformally invariant theory turns out to be equivalent to general relativity. Since this means that the usual Einstein-Hilbert action is not, in fact, a true gauge action for the space-time geometry, the full theory ought to be supplied with such a term. Gauge-theoretic arguments and conformal invariance requirements dictate its form.     

Constrained systems,OSP(1,1|2) and string theory

The underlying OSP invariance of the Fradkin-Vilkovisky formalism is discussed. Ghost degrees of freedom are interpreted as negative dimensional phase space variables that eliminate unphysical degrees of freedom by the Parisi-Sourlas mechanism, ensuring manifest covariance. The formalism makes use of subsidiary constraints, extending the usual algebra of constraints. A relations between abelian and nonabelian constraint algebras is established, and exploited to construct a nonabelian representation of the OSP generators. For theories based entirely on constraints such as string theories, the natural Fradkin-Vilkovisky hamiltonian is a manifestly OSP invariant squared length of a graded phase space vector. As an application, the OSP covariant formulation of bosonic strings is discussed.     

On global attractors for a class of nonhyperbolic piecewise affine maps

Dynamical behavior of a class of nonhyperbolic discrete systems are considered. These systems are generated by iterating planar maps that are piecewise isometries, and they arise as mathematical models for signal processing, digital filters and modulator dynamics. Planar piecewise isometries may be discontinuous and/or non-invertible. First, the authors consider attraction caused by discontinuity in planar piecewise isometries. Namely, they have shown that the maximal invariant set can induce an invariant measure, and all the Lyapunov exponents are zero under this invariant measure. Second, they discuss various definitions of global attractors and their existence and uniqueness for discontinuous maps, and introduce a few examples in which the attractors are created due to discontinuity. Third, they study the relation between invariance and invertibility for various nonhyperbolic maps, and finally they investigate decomposability of global attractors for certain nonhyperbolic systems.     

Gauge invariance based on the extrinsic geometry in the rigid string

The string model with the extrinsic curvature is studied which is a gauge invariant field theory with higher order derivatives. We present an equivalent action without any higher order derivatives which keeps the gauge invariance. We point out the difficulty caused by the second class constraints in Dirac's canonical method. Following a new method for dynamical systems with second class constraints, we construct an equivalent model which has no second class constrants but as a new gauge invariance. This gauge invariance guarantees the equivalence between the original model and the new one. We show that the model can be quantized in this formalism. We find the unitarity violation of the model.     

A C*-algebra approach to the Schwinger model

If cutoffs are introduced then existing results in the literature show that the Schwinger model is dynamically equivalent to a boson model with quadratic Hamiltonian. However, the process of quantising the Schwinger model destroys local gauge invariance. Gauge invariance is restored by the addition of a counterterm, which may be seen as a finite renormalisation, whereupon the Schwinger model becomes dynamically equivalent to a linear boson gauge theory. This linear model is exactly soluble. We find that different treatments of the supplementary (i.e. Lorentz) condition lead to boson models with rather different properties. We choose one model and construct, from the gauge invariant subalgebra, a class of inequivalent charge sectors. We construct sectors which coincide with those found by Lowenstein and Swieca for the Schwinger model. A reconstruction of the Hilbert space on which the Schwinger model exists is described and fermion operators on this space are defined.     

Shape invariant potentials in higher dimensions

In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended to arrive at a large class of new shape invariant potentials in arbitrary dimensions. A reformulation of the shape invariance property and possible generalizations are proposed. These may lead to an important extension of the shape invariance property to Hamiltonians that are related to standard potential problems via space time transformations, which are found useful in path integral formulation of quantum mechanics.     

Obtaining gauge invariant actions via symplectic embedding formalism

The concept of gauge invariance is one of the most subtle and useful concepts in modern theoretical physics. It is one of the Standard Model cornerstones. The main benefit due to the gauge invariance is that it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every instant of time. It is the objective of this work to show a path of obtaining gauge invariant theories from non‐invariant ones. Both are named also as first‐ and second‐class theories respectively, obeying Dirac's formalism. Namely, it is very important to understand why it is always desirable to have a bridge between gauge invariant and non‐invariant theories. Once established, this kind of mapping between first‐class (gauge invariant) and second‐class systems, in Dirac's formalism can be considered as a sort of equivalence. This work describe this kind of equivalence obtaining a gauge invariant theory starting with a non‐invariant one using the symplectic embedding formalism developed by some of us some years back. To illustrate the procedure it was analyzed both Abelian and non‐Abelian theories. It was demonstrated that this method is more convenient than others. For example, it was shown exactly that this embedding method used here does not require any special modification to handle with non‐Abelian systems.     

基于局部尺度不变特征的快速目标识别

介绍了图像局部尺度不变特征的提取方法,将局部尺度不变特征用于目标识别,为提高识别实时性,提出利用金字塔和尺度空间的混合多尺度表示方法,按照从大尺度到小尺度的顺序对待识别图像的特征点进行检测与匹配,直到完成识别为止,有效地提高了识别速度。     

Optimal Gabor Kernel's Scale and orientation selection for face classification

2D Gabor-based face representation has attracted much attention. However, owing to the fact that Gabor features are redundant and too high-dimensional, appropriate feature dimension reduction appears to be much more paramount. Allowing for each individual Gabor feature constructed by a combination of scale and orientation pair, we equate feature dimension reduction problem to optimal Gabor kernels’ scales and orientation selection problem. Genetic algorithms (GAs) have represented a useful tool for optimal subset selection. However, population premature and optimization stagnancy problems exist in traditional GAs. Here we present an improved algorithm: Hybrid Genetic algorithms-based (HGAsb), which introduces the concept of the simulated annealing into traditional GAs to effectively solve the problems mentioned above and to improve optimization efficiency. Experimental results on IMM face database demonstrate that in contrast to GAs, our proposed algorithm can provide 4.25 improvements. The distributions of orientations and scales of the selected features by HGAsb are also analyzed. Results indicate that the features in the larger scales have equal importance as those in the smaller scales in discriminating nuance of faces. The features in horizontal, vertical and 225° orientations have more discriminative power.     

Invariance of interval and length in the theory of relativity

Two representations are discussed: the standard representation regarding the contraction of a moving body, and a locational representation regarding its elongation. It is shown that the first representation is not relativistically invariant, but the second is and is unique, being consistent with the invariance of interval under a Lorentz transformation.Joint Institute of Nuclear Research. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 125–128, February, 1995.     

非中心力场中经典粒子的轨道参数方程与对称性

把非中心力场中经典粒子运动微分方程写成Ermakov方程的形式，得到Ermakov不变量.用改变时间坐标标度的方法得到用能量H和Ermakov不变量表示的轨道参数方程，并研究两守恒量（能量和Ermakov不变量）相应的无限小变换的Noether对称性、Lie对称性和形式不变性.研究结果表明：与两守恒量相应的无限小变换既具有Noether对称性，也具有Lie对称性和形式不变性. 关键词： 非中心力场 轨道参数方程 守恒量 对称性     

The pursuit of invariance in speech signals

The search for the acoustic properties useful to the listener in extracting the linguistic message from a speech signal is often construed as the task of matching invariant physical properties to invariant phonological percepts; the discovery of the former will explain the latter. These phonological percepts are essentially the phonemes of pregenerative phonology, and they are more or less faithfully reflected in standard alphabetic writing. Thus English deep and doom are supposed to be perceptually identical in their initial /d/s; the orthographic similarity is in agreement with the linguist's "representation" of these forms. The partial identity in spelling is only weak evidence for perceptual invariance, however. First, while some phonemes may comprise a single "sound," others are said by linguists to include phonetically distinct ones. Thus English /p/includes both aspirated and unaspirated voiceless labial stops. The view that it is not the phoneme, but rather the phonetic feature, to which an acoustic invariant might be attributed, raises two questions: (a) Since segments sharing a feature are rarely judged to constitute a single sound, the search for a feature-specific invariant, whose function is to explain perceptual constancy, is deprived of its essential motivation, and (2) there is no more reason to expect the acoustic cues to a feature to be context-independent than is the case with the phoneme. What seems more likely is to find that some phonemes, and some features, are more invariantly marked in the speech signal than others.     

一种抗姿态与表情变化的三维人脸识别方法

为了提高人脸在姿态和表情变化下的识别率,结合局部平面距离(DLP)对曲面局部凹凸性优良的判断能力,提出了一种采用人脸的等距不变表示形式来匹配的人脸识别方法。首先,对深度摄像头采集到的深度图像进行距离约束、位置约束、转换等操作,得到干净完整的三维人脸,利用三维人脸上每一点DLP值确定鼻尖点,利用聚类的思想确定鼻根点;其次,采用改进的快速推进算法计算人脸的测地距矩阵,设置阈值并切割出有效的人脸区域;最后,计算有效的人脸区域的高阶矩特征,作为人脸的特征向量进行匹配。实验结果表明,对于不同的数据库,本文算法的识别率接近97%;将本文算法与基于轮廓线特征的人脸识别算法以及基于Gabor特征的人脸识别算法进行比较,其识别率分别提高了14.1%和8.3%,同时有着较高的运算效率。     

Finite matrix models with continuous local gauge invariance

We construct a hamiltonian lattice gauge theory which possesses local SU (2) gauge invariance and yet is defined on a Hilbert space of 5-dimensional real vectors for every link. This construction does not allow for generalization to arbitrary SU(N), but a small variation of it can be generalized to an SU(N) × U(1) local gauge invariant model. The latter is solvable in simple gauge sectors leading to trivial spectra. We display these by studying a U(1) local gauge invariant model with similar characteristics.     

Field theory of the interacting string: The closed string

We recast dual models in the language of a quantum field theory of functional fields, restricting ourselves for simplicity to the closed string model. We derive the dynamics for both scalar and spinor functional fields from a unique parametrization invariant action. Passages to the Hamiltonian formalism and second quantization are explicitly worked out for the closed mesonic string in the front form. The results are equivalent to those obtained earlier by GGRT, i.e. no ghost fields at the price of an anomalous number of space-time dimensions and a tachyon. Finally, we use the parametrization invariance requirement on the action to derive couplings of closed strings to local fields by extending a global U(1) invariance built in the free action into a local one in the functional sense. We construct the self-couplings of closed string fields by requiring these to be consistent with the gauge invariance of the external fields. This procedure uniquely leads (for the open string) to the string splitting picture of Nambu and Mandelstam. The closed string is found to cross itself and then split up into two others. Both open and closed strings have quartic interactions corresponding to strand (for the open string) and lobe (for the closed string) exchanges. The case of the interacting fermionic model is not treated here.