Simulation and analysis of images using spectral characteristics

Methods intended for the analysis and simulation of microstructure images using integral spectral characteristics of orthogonal transformations are proposed. The described methods, algorithms, and software tools allow the primary processing of such images, along with identifying the correlation spectrum characteristics of microstructures and eliminating distortions related to smearing, blurring, and defocusing.     

一种图像非线性形变的恢复方法

几何成像系统中非线性形变图像的恢复仍是一个未能很好解决的课题。针对常见的双二次、双三次形变图像,提出了以不完全双二次、双三次插值法拟合形变图像,根据形变的特点采用牛顿迭代法和双线性灰度插值法对图像进行恢复。用所提出的方法对失真图像进行恢复,结果表明,仅选用少量参考点便可得到良好的效果。     

Pseudo-three-dimensional reconstruction of ultrasonic images of the tongue

The purpose of the present investigation was to develop a method for the three-dimensional reconstruction of the surface of the tongue using serial ultrasonic images gathered during the production of the sustained fricative /s/. Using a phased linear array ultrasonic monitoring system, transducer position, subject position, and ultrasonic scan data were recorded simultaneously on composite video for off-line analysis. Reconstruction of a series of ultrasound images was completed using a microcomputer programmed to transform the ultrasonic image contours into three-dimensional space. Additional transformations converting the three-dimensional tongue contours into two dimensions for screen plotting were also developed. Results are discussed in light of previously reported models of the tongue surface.     

Relativistic aberrations in quantum phase space

A phase space treatment of special relativity of quantum systems is developed. In this approach a quantum particle remains localized if subject to inertial transformations, the localization occurring in a finite phase space area. Unlike in the non-relativistic case, relativistic transformations generally distort the phase space distribution function, being equivalent to aberrations in optics. The relativistic aberrations of massive particles are in general different from those of optical images.     

Segmentation of holographic images using the level set method

Image segmentation, which is to distinguish objects from background, has played an important role in holographic image processing. In this work, we propose a technique that uses the combination of rough segmentation and the level set methods for segmentation of holographic images with zero-order diffraction interference. To improve the image quality, we eliminate the interference of zero-order diffraction in digital holography using Sobel differential gradient algorithm based on digital image processing. After reconstruction, the rough segmentation including intensity transformations and Morphology methods is applied to acquire the rough contour of the reconstruction image. Finally, we adopt level set methods to smooth the object contour and improve its accuracy. Segmentation results for objects in holographic images are presented.     

Transformation properties and third-order aberrations of thin dynamic χ<Superscript>(2)</Superscript> holograms

The results of a theoretical study of the transformation properties of thin dynamic χ⁽²⁾ holograms for all frequency mixing versions are generalized, and a general pattern of transformations of reconstructed images (recorded and read at different frequencies) is developed. The principles of ray geometric construction of reconstructed images are determined. The theory of thin dynamic χ⁽²⁾ holograms is extended to the range of third-order aberrations.     

Transformation properties of dynamic χ<Superscript>(2)</Superscript> holograms generating at the difference frequency

The transformation properties of dynamic χ⁽²⁾ holograms generating at the difference frequency are analyzed as applied to the position and scales of reconstructed images. Some regularities are established for the spatial localization and scales of images for different combinations of frequencies and positions of the reference and object point sources, involved in the formation of a holographic image. The formation of amplitude transparency images, reconstructed by dynamic χ⁽²⁾ holograms with a decrease or conservation of the object beam frequency, and their transformations are experimentally demonstrated.     

On dynamic plane elasticity problems of 2D quasicrystals

In this Letter, the dynamic plane elasticity problems of 2D quasicrystals is considered. By use of the Fourier transform and matrix transformations the system is reduced to uncoupled ordinary differential equations. Fourier images of Green's functions for dynamic plane elasticity problems of 2D dodecagonal, pentagonal and decagonal quasicrystals are obtained explicitly by the suggested method.     

A method for automatic correction of drift-distorted SPM images

A method for automatic correction of drift-distorted surface images obtained using a scanning probe microscope is developed. For the case of slowly varying drifts, simple linear transformations describing the observed distortions are constructed. One or two pairs of counter-scanned images (CSIs) are used as initial data. A system of linear equations is solved by finding the coordinate of the same surface feature in each CSI. The solutions obtained, i.e., linear transformation coefficients, are used to correct drift-induced distortions in horizontal and vertical planes. Two nonlinear drift correction methods are proposed, which provide a better accuracy in comparison with the linear correction method. The developed method can be used in feature-oriented scanning of the surface.     

Coherent State Representation for a Kind of Operator Disentangling Formulae

We derive a kind of operator disentangling formulae and their coherent state represen tation by virtue of the correspondence be tween symplectic transformations and their quantum mechanical images. The application of the formulae in calculating Feynman transformation matrix elements is discussed.     

Quaternion higher-order spectra and their invariants for color image recognition

This paper describes an invariants generation method for color images, which could be a useful tool in color object recognition tasks. First, by using the algebra of quaternions, we introduce the definition of quaternion higher-order spectra (QHOS) in the spatial domain and derive its equivalent form in the frequency domain. Then, QHOS invariants with respect to rotation, translation, and scaling transformations for color images are constructed using the central slice theorem and quaternion bispectral analysis. The feature data are further reduced to a smaller set using quaternion principal component analysis. The proposed method can deal with color images in a holistic manner, and the constructed QHOS invariants are highly immune to background noise. Experimental results show that the extracted QHOS invariants form compact and isolated clusters, and that a simple minimum distance classifier can yield high recognition accuracy.     

Quantum Image Encryption and Decryption Algorithms Based on Quantum Image Geometric Transformations

Cryptography is the essential subject for network information security to protect important data. Although following the symmetric cryptosystem for which the participations in the communication keep exactly the same keys, the special for the encryption and decryption algorithms proposed in this paper lays in the operational objectives, the quantum image. Firstly, extracts the properties of gray-scale and position from the quantum gray-scale image which the storage expression of image in quantum states is achieved. Along with the geometric transformations in classical images, this article realizes the quantum image geometric transforms by means of designing quantum circuits. Eventually, through a combination of the proposals in previous, the encryption and decryption algorithms on quantum gray-scale images is finally accomplished, which could ensure the confidentiality and security of the information in delivery. The algorithms belong to the application of quantum image geometric transformations, for further, the new explorations for quantum image cryptography researches.     

Generalized Lorentz transformations in the general theory of relativity and the behavior of certain physical quantities at the boundary of the R and T regions

The transition between diagonal metrics is considered. The transformations are written in generalized Lorentzian form. This form of coordinate transformations is used to obtain transformations for the velocity, acceleration, force, momentum, energy, and the components of the energy-momentum tensor. The relations obtained are used to estimate the physical quantities at the boundary of the R and T regions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 13–18, March, 1978.     

Certain properties of the externally invariant Maxwell equations and physical meaning of the external-transformation group

A general vector potential derived for the Maxwell equations in their general form is used to find and analyze the tensor for the angular momentum density. With j = 0, the general Maxwell equations are invariant with respect to a four-parameter group of external displacement, whose addition to the group of external transformations leads to field equations which are invariant with respect to the ten-parameter group of external transformations. For integral quantities, the vector of the total field energy-momentum and the tensor of the total angular momentum, transformations from the inhomogeneous group of external transformations are equivalent to transformations from the inhomogeneous Lorentz group.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 53–57, November, 1969.The authors thank D. D. Ivanenko, A. E. Levashov, and the participants of the Ivanovo interinstitute seminar on mathematical physics for discussion of these results.     

A set of the Lie symmetrical conservation laws for the rotational relativistic Birkhoffian system

For a rotational relativistic Birkhoffian system a set of the Lie symmetries and conservation laws is given under infinitesimal transformation. On the basis of the invariance of rotational relativistic Birkhoffian equations under infinitesimal transformations,Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The determining equations of Lie symmetries are given, and a new type of non-noether conserved quantities are directly obtained from Lie symmetries of the system. An example given to illustrate the application of the results.     

Nonlinear transformations and logarithmic filtering in coherent optical systems

While photographic film allows only a limited class of nonlinear transformations to be applied to pictures, a much wider class can be realized by use of halftone contact screens. A contact screen which performs a logarithmic transformation has been studied both theoretically and experimentally. The screen performs properly over two log units of exposure. Multiplicatively formed images have been subjected to logarithmic filtering with good results. Possible applications include removal of speckle, extraction of images from multiplicative noise, and biomedical image processing.     

基于特征点的对数极坐标变换图像配准算法

介绍了一种新的图像配准算法,可以很好地解决图像配准中的平移、旋转和缩放问题。算法的实现是首先使用SUSAN算子提取两幅图像的特征角点,剔除虚假的特征点(噪声点),然后使用改进对数极坐标变换和投影相关匹配算法实现特征点匹配;结合亚像素定位技术,可以进一步提高算法的精度。     

Reciprocal transformations of the space-time shifted nonlocal short pulse equations

Reciprocal transformations of the space-time shifted nonlocal short pulse equations are elaborated. Covariance of dependent and independent variables involved in the reciprocal transformations is investigated. Exact solutions of the space-time shifted nonlocal short pulse equations are given in terms of double Wronskians. Realness of independent variables involved in the reciprocal transformations is verified. Dynamics of some obtained solutions are illustrated.