scholarly journals METHOD FOR ASSESSING THE SYMMETRY OF OBJECTS ON DIGITAL BINARY IMAGES BASED ON FOURIER DESCRIPTOR

2019 ◽  
Vol XLII-2/W12 ◽  
pp. 143-148
Author(s):  
L. Mestetskiy ◽  
A. Zhuravskaya
Keyword(s):  
Symmetry Axis ◽  
Fourier Descriptor ◽  
Earth Remote Sensing ◽  
Discrete Object ◽  
Binary Images ◽  
Special Cases ◽  
Exact Symmetry ◽  
Measure Of Asymmetry ◽  
Axis Of Symmetry ◽  
High Computational Complexity

<p><strong>Abstract.</strong> In this paper we solve the problem of finding the symmetry axis of the object in a digital binary image. A new axial symmetry criterion is formulated for a connected discrete object. The problem of determining the symmetry measure and finding the symmetry axes arises in a variety of applications. In discrete images, exact symmetry is possible only in special cases. The disadvantage of the existing methods solving this problem is the high computational complexity. To improve computational efficiency, it is proposed to use the so-called Fourier descriptor. A new method for estimating the asymmetry of a discrete silhouette is proposed. The described algorithm for calculating the measure of asymmetry and determining the axis of symmetry is quadratic by the number of contour points. Methods for reducing the volume of calculations using a convex hull and taking into account the values of the modules of Fourier coefficients are proposed. Computational experiments are conducted with silhouettes of aircraft extracted from earth remote sensing images. The reliability of the described solution is established.</p>

Radon–Fourier descriptor for invariant pattern recognition

2019 ◽  
Vol 17 (02) ◽  
pp. 1940004 ◽  
Author(s):  
Jianwei Yang ◽  
Liang Zhang ◽  
Peiyao Li
Keyword(s):  
Pattern Recognition ◽  
Radon Transform ◽  
Mellin Transform ◽  
Closed Curve ◽  
Fourier Descriptor ◽  
Binary Images ◽  
Invariant Features ◽  
Special Cases ◽  
Robust To Noise

Radon transform is not only robust to noise, but also independent on the calculation of pattern centroid. In this paper, Radon–Mellin transform (RMT), which is a combination of Radon transform and Mellin transform, is proposed to extract invariant features. RMT converts any object into a closed curve. Radon–Fourier descriptor (RFD) is derived by applying Fourier descriptor to the obtained closed curve. The obtained RFD is invariant to scaling and rotation. (Generic) R-transform and some other Radon-based methods can be viewed as special cases of the proposed method. Experiments are conducted on some binary images and gray images.

scholarly journals The Stationary Concentrated Vortex Model

Climate ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 39
Author(s):  
Oleg Onishchenko ◽  
Viktor Fedun ◽  
Wendell Horton ◽  
Oleg Pokhotelov ◽  
Natalia Astafieva ◽  
...  
Keyword(s):  
Vortex Structure ◽  
Radial Direction ◽  
Symmetry Axis ◽  
Outer Part ◽  
Vertical Direction ◽  
Axially Symmetric ◽  
New Model ◽  
Vortex Model ◽  
Axis Of Symmetry ◽  
Good Agreement

A new model of an axially-symmetric stationary concentrated vortex for an inviscid incompressible flow is presented as an exact solution of the Euler equations. In this new model, the vortex is exponentially localised, not only in the radial direction, but also in height. This new model of stationary concentrated vortex arises when the radial flow, which concentrates vorticity in a narrow column around the axis of symmetry, is balanced by vortex advection along the symmetry axis. Unlike previous models, vortex velocity, vorticity and pressure are characterised not only by a characteristic vortex radius, but also by a characteristic vortex height. The vortex structure in the radial direction has two distinct regions defined by the internal and external parts: in the inner part the vortex flow is directed upward, and in the outer part it is downward. The vortex structure in the vertical direction can be divided into the bottom and top regions. At the bottom of the vortex the flow is centripetal and at the top it is centrifugal. Furthermore, at the top of the vortex the previously ascending fluid starts to descend. It is shown that this new model of a vortex is in good agreement with the results of field observations of dust vortices in the Earth’s atmosphere.

scholarly journals INCOMPLETENESS IN THE FINITE DOMAIN

2017 ◽  
Vol 23 (4) ◽  
pp. 405-441 ◽  
Author(s):  
PAVEL PUDLÁK
Keyword(s):  
Computational Complexity ◽  
Proof Complexity ◽  
Finite Domain ◽  
Semantic Concept ◽  
Syntactic Complexity ◽  
Special Cases ◽  
Incompleteness Theorems ◽  
High Computational Complexity

AbstractMotivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyondNP≠coNP. These conjectures formally connect computational complexity with the difficulty of proving some sentences, which means that high computational complexity of a problem associated with a sentence implies that the sentence is not provable in a weak theory, or requires a long proof. Another reason for putting forward these conjectures is that some results in proof complexity seem to be special cases of such general statements and we want to formalize and fully understand these statements. Roughly speaking, we are trying to connect syntactic complexity, by which we mean the complexity of sentences and strengths of the theories in which they are provable, with the semantic concept of complexity of the computational problems represented by these sentences.We have introduced the most fundamental conjectures in our earlier works [27, 33–35]. Our aim in this article is to present them in a more systematic way, along with several new conjectures, and prove new connections between them and some other statements studied before.

SYMMETRY AXIS BASED OBJECT RECOGNITION UNDER TRANSLATION, ROTATION AND SCALING

2009 ◽  
Vol 19 (01) ◽  
pp. 25-42 ◽  
Author(s):  
MASHUD HYDER ◽  
MD. MONIRUL ISLAM ◽  
M. A. H. AKHAND ◽  
KAZUYUKI MURASE
Keyword(s):  
Feature Extraction ◽  
Object Recognition ◽  
Symmetry Axis ◽  
Recognition Performance ◽  
Recognition System ◽  
New Approach ◽  
Invariant Object Recognition ◽  
Different Shapes ◽  
Axis Of Symmetry ◽  
Concentric Circles

This paper presents a new approach, known as symmetry axis based feature extraction and recognition (SAFER), for recognizing objects under translation, rotation and scaling. Unlike most previous invariant object recognition (IOR) systems, SAFER puts emphasis on both simplicity and accuracy of the recognition system. To achieve simplicity, it uses simple formulae for extracting invariant features from an object. The scheme used in feature extraction is based on the axis of symmetry and angles of concentric circles drawn around the object. SAFER divides the extracted features into a number of groups based on their similarity. To improve the recognition performance, SAFER uses a number of neural networks (NNs) instead of single NN are used for training and recognition of extracted features. The new approach, SAFER, has been tested on two of real world problems i.e., English characters with two different fonts and images of different shapes. The experimental results show that SAFER can produce good recognition performance in comparison with other algorithms.

Analytic study of the geometrical spreading of P-waves in a layered transversely isotropic medium with a vertical symmetry axis

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1305-1315 ◽  
Author(s):  
Hongbo Zhou ◽  
George A. McMechan
Keyword(s):  
Isotropic Medium ◽  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Analytical Formula ◽  
Transversely Isotropic ◽  
P Wave ◽  
Geometrical Spreading ◽  
Transversely Isotropic Medium ◽  
Weak Anisotropy ◽  
Special Cases

An analytical formula for geometrical spreading is derived for a horizontally layered transversely isotropic medium with a vertical symmetry axis (VTI). With this expression, geometrical spreading can be determined using only the anisotropy parameters in the first layer, the traveltime derivatives, and the source‐receiver offset. Explicit, numerically feasible expressions for geometrical spreading are obtained for special cases of transverse isotropy (weak anisotropy and elliptic anisotropy). Geometrical spreading can be calculated for transversly isotropic (TI) media by using picked traveltimes of primary nonhyperbolic P-wave reflections without having to know the actual parameters in the deeper subsurface; no ray tracing is needed. Synthetic examples verify the algorithm and show that it is numerically feasible for calculation of geometrical spreading. For media with a few (4–5) layers, relative errors in the computed geometrical spreading remain less than 0.5% for offset/depth ratios less than 1.0. Errors that change with offset are attributed to inaccuracy in the expression used for nonhyberbolic moveout. Geometrical spreading is most sensitive to errors in NMO velocity, followed by errors in zero‐offset reflection time, followed by errors in anisotropy of the surface layer. New relations between group and phase velocities and between group and phase angles are shown in appendices.

scholarly journals THE PARALLEL IMPLEMENTATION OF ALGORITHMS FOR FINDING THE REFLECTION SYMMETRY OF THE BINARY IMAGES

2017 ◽  
Vol XLII-2/W4 ◽  
pp. 179-184
Author(s):  
S. Fedotova ◽  
O. Seredin ◽  
O. Kushnir
Keyword(s):  
Symmetry Axis ◽  
Parallel Implementation ◽  
Search Algorithm ◽  
Experimental Studies ◽  
Ground Truth ◽  
Approximate Symmetry ◽  
Brute Force ◽  
Brute Force Search ◽  
Binary Images ◽  
The Common

In this paper, we investigate the exact method of searching an axis of binary image symmetry, based on brute-force search among all potential symmetry axes. As a measure of symmetry, we use the set-theoretic Jaccard similarity applied to two subsets of pixels of the image which is divided by some axis. Brute-force search algorithm definitely finds the axis of approximate symmetry which could be considered as ground-truth, but it requires quite a lot of time to process each image. As a first step of our contribution we develop the parallel version of the brute-force algorithm. It allows us to process large image databases and obtain the desired axis of approximate symmetry for each shape in database. Experimental studies implemented on “Butterflies” and “Flavia” datasets have shown that the proposed algorithm takes several minutes per image to find a symmetry axis. However, in case of real-world applications we need computational efficiency which allows solving the task of symmetry axis search in real or quasi-real time. So, for the task of fast shape symmetry calculation on the common multicore PC we elaborated another parallel program, which based on the procedure suggested before in (Fedotova, 2016). That method takes as an initial axis the axis obtained by superfast comparison of two skeleton primitive sub-chains. This process takes about 0.5 sec on the common PC, it is considerably faster than any of the optimized brute-force methods including ones implemented in supercomputer. In our experiments for 70 percent of cases the found axis coincides with the ground-truth one absolutely, and for the rest of cases it is very close to the ground-truth.

scholarly journals Image skeletonization based on combination of one- and two-sub-iterations models

Informatics ◽  
2020 ◽  
Vol 17 (2) ◽  
pp. 25-35
Author(s):  
J. Ma ◽  
V. Yu. Tsviatkou ◽  
V. K. Kanapelka
Keyword(s):  
Mathematical Model ◽  
Computational Complexity ◽  
Relative Position ◽  
Binary Image ◽  
Iteration Algorithm ◽  
Layer By Layer ◽  
Original Image ◽  
High Quality ◽  
Binary Images ◽  
High Computational Complexity

This paper is focused on the field of the skeletonization of the binary image. Skeletonization makes it possible to represent a binary image in the form of many thin lines, the relative position, sizes and shape of which adequately describe the size, shape and orientation in space of the corresponding image areas. Skeletonization has many variety methods. Iterative parallel algorithms provide high quality skeletons. They can be implemented using one or more sub-iterations. In each iteration, redundant pixels, the neighborhoods of which meet certain conditions, are removed layer by layer along the contour and finally they leave only the skeleton. Many one-sub-iterations algorithms are characterized by a breakdown in connectivity and the formation of excess skeleton fragments. The highest-quality skeletons are formed by the well-known single-iteration OPTA algorithm, which based on 18 binary masks, but it is sensitive to contour noise and has a high computational complexity. The Zhang and Suen two-iteration algorithm (ZS), which is based on 6 logical conditions, is widely used due to its relative simplicity. But it suffers from the problem of the blurs of the diagonal lines with a thickness of 2 pixels and the lost of the square which size is 2×2 pixels. Besides, both algorithms mentioned above do not achieve the unit pixel thickness of the skeleton lines (many non-node pixels have more than two neighbors). Mathematical model and OPCA (One-Pass Combination Algorithm) algorithm which is based on a combination and simplification of single-iterative OPTA and two-iterative ZS are proposed for constructing extremely thin bound skeletons of binary images with low computational complexity. These model and algorithm also made it possible to accelerate the speed of skeletonization, to enhance recoverability of the original image on the skeleton and to reduce the redundancy of the bonds of the skeleton elements.

scholarly journals Relativistic Rotating Electromagnetic Fields

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
H. Vargas-Rodríguez ◽  
A. Gallegos ◽  
M. A. Muñiz-Torres ◽  
H. C. Rosu ◽  
P. J. Domínguez
Keyword(s):  
Electromagnetic Field ◽  
Electromagnetic Fields ◽  
Symmetry Axis ◽  
Poynting Vector ◽  
Momentum Density ◽  
Axially Symmetric ◽  
Speed Of Light ◽  
Vector Form ◽  
Magnetic Dipoles ◽  
Axis Of Symmetry

In this work, we consider axially symmetric stationary electromagnetic fields in the framework of special relativity. These fields have an angular momentum density in the reference frame at rest with respect to the axis of symmetry; their Poynting vector form closed integral lines around the symmetry axis. In order to describe the state of motion of the electromagnetic field, two sets of observers are introduced: the inertial set, whose members are at rest with the symmetry axis; and the noninertial set, whose members are rotating around the symmetry axis. The rotating observers measure no Poynting vector, and they are considered as comoving with the electromagnetic field. Using explicit calculations in the covariant 3 + 1 splitting formalism, the velocity field of the rotating observers is determined and interpreted as that of the electromagnetic field. The considerations of the rotating observers split in two cases, for pure fields and impure fields, respectively. Moreover, in each case, each family of rotating observers splits in two subcases, due to regions where the electromagnetic field rotates with the speed of light. These regions are generalizations of the light cylinders found around magnetized neutron stars. In both cases, we give the explicit expressions for the corresponding velocity fields. Several examples of relevance in astrophysics and cosmology are presented, such as the rotating point magnetic dipoles and a superposition of a Coulomb electric field with the field of a point magnetic dipole.

scholarly journals Efficient Kernel Selection via Spectral Analysis

2017 ◽  
Author(s):  
Jian Li ◽  
Yong Liu ◽  
Hailun Lin ◽  
Yinliang Yue ◽  
Weiping Wang
Keyword(s):  
Spectral Measure ◽  
Fundamental Problem ◽  
Selection Criterion ◽  
Data Sets ◽  
Maximum Mean Discrepancy ◽  
Generalization Bounds ◽  
Kernel Selection ◽  
Special Cases ◽  
High Computational Efficiency ◽  
High Computational Complexity

Kernel selection is a fundamental problem of kernel methods. Existing measures for kernel selection either provide less theoretical guarantee or have high computational complexity. In this paper, we propose a novel kernel selection criterion based on a newly defined spectral measure of a kernel matrix, with sound theoretical foundation and high computational efficiency. We first show that the spectral measure can be used to derive generalization bounds for some kernel-based algorithms. By minimizing the derived generalization bounds, we propose the kernel selection criterion with spectral measure. Moreover, we demonstrate that the popular minimum graph cut and maximum mean discrepancy are two special cases of the proposed criterion. Experimental results on lots of data sets show that our proposed criterion can not only give the comparable results as the state-of-the-art criterion, but also significantly improve the efficiency.

Non-Double-Couple Components of the Moment Tensor in a Transversely Isotropic Medium

2020 ◽  
Vol 110 (3) ◽  
pp. 1125-1133
Author(s):  
William Menke ◽  
Joshua B. Russell
Keyword(s):  
Symmetry Axis ◽  
Fault Plane ◽  
Moment Tensor ◽  
Source Region ◽  
Transversely Isotropic ◽  
Earth Model ◽  
Double Couple ◽  
Axis Of Symmetry ◽  
The Moment ◽  
Insight Into

ABSTRACT The non-double-couple (non-DC) components of the moment tensor provide insight into the earthquake processes and anisotropy of the near-source region. We investigate the behavior of the isotropic (ISO) and compensated linear vector dipole (CLVD) components of the moment tensor for shear faulting in a transversely ISO medium with an arbitrarily oriented symmetry axis. Analytic formulas for ISO and CLVD depend on the orientation of the fault relative to the anisotropy symmetry axis as well as three anisotropic parameters, which describe deviations of the medium from isotropy. Numerical experiments are presented for the preliminary reference Earth model. Both ISO and CLVD components are zero when the axis of symmetry is within the fault plane or the auxiliary plane. For any orientation in which the ISO component is zero, the CLVD component is also zero, but the opposite is not always true (e.g., for strong anisotropy). The relative signs of the non-DC components of neighboring earthquakes may help distinguish source processes from source-region anisotropy. We prove that an inversion of ISO and CLVD components of a set of earthquakes with different focal mechanisms can uniquely determine the orientation and strength of anisotropy. This study highlights the importance of the ISO component for constraining deep slab anisotropy and demonstrates that it cannot be neglected.

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