Research on Copy-Move Image Forgery Detection Using Features of Discrete Polar Complex Exponential Transform

2015 ◽  
Vol 25 (14) ◽  
pp. 1540018 ◽  
Author(s):  
Yanfen Gan ◽  
Junliu Zhong
Keyword(s):  
Coordinate System ◽  
Polar Coordinate System ◽  
Forgery Detection ◽  
Rotation Invariant ◽  
Image Forgery ◽  
Polar Coordinate ◽  
Exponential Transform ◽  
Cartesian Coordinate ◽  
Polar Complex Exponential Transform ◽  
Complex Exponential

With the aid of sophisticated photo-editing software, such as Photoshop, copy-move image forgery operation has been widely applied and has become a major concern in the field of information security in the modern society. A lot of work on detecting this kind of forgery has gained great achievements, but the detection results of geometrical transformations of copy-move regions are not so satisfactory. In this paper, a new method based on the Polar Complex Exponential Transform is proposed. This method addresses issues in image geometric moment, focusing on constructing rotation invariant moment and extracting features of the rotation invariant moment. In order to reduce rounding errors of the transform from the Polar coordinate system to the Cartesian coordinate system, a new transformation method is presented and discussed in detail at the same time. The new method constructs a [Formula: see text] shrunk template to transform the Cartesian coordinate system back to the Polar coordinate system. It can reduce transform errors to a much greater degree. Forgery detection, such as copy-move image forgery detection, is a difficult procedure, but experiments prove our method is a great improvement in detecting and identifying forgery images affected by the rotated transform.

Vehicle Kinematic State Estimation Using Passive Sensor Fusion Approach

2012 ◽  
Vol 271-272 ◽  
pp. 1709-1712 ◽  
Author(s):  
Li Wei Fong ◽  
Pi Ching Lou ◽  
Ke Jia Tang
Keyword(s):  
Coordinate System ◽  
Autonomous Navigation ◽  
Weighted Least Squares ◽  
Hierarchical Architecture ◽  
Estimation Accuracy ◽  
Polar Coordinate System ◽  
Global Estimate ◽  
Polar Coordinate ◽  
Passive Sensor ◽  
Cartesian Coordinate

The main issue addressed here is that of estimating the kinematic state components of a vehicle in autonomous navigation using landmark angle-only measurements from an onboard passive sensor. The estimates of the absolute position and velocity of the vehicle are provided by a hybrid coordinate fusion filter. The hierarchical architecture of the filter which consists of a group of local processors and a global processor is developed for improving estimation accuracy. In each local processor, an extended Kalman filter uses hybrid information from the reference Cartesian coordinate system and the modified polar coordinate system for state and state error covariance extrapolation and updating. In the global processor, a weighted least squares estimator is utilized to combine the outputs of local processors to form a global estimate. By using only two landmarks simulation results show that proposed algorithm improves the estimation accuracy drastically.

scholarly journals Determination of Ship Approach Parameters in the Polar Coordinates System

2014 ◽  
Vol 96 (1) ◽  
pp. 1-8
Author(s):  
Andrzej Banachowicz ◽  
Adam Wolski
Keyword(s):  
Coordinate System ◽  
Target Position ◽  
Geometric Interpretation ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Polar Coordinate ◽  
Radar Measurements ◽  
Cartesian Coordinate ◽  
Radar Antenna

Abstract An essential aspect of the safety of navigation is avoiding collisions with other vessels and natural or man made navigational obstructions. To solve this kind of problem the navigator relies on automatic anti-collision ARPA systems, or uses a geometric method and makes radar plots. In both cases radar measurements are made: bearing (or relative bearing) on the target position and distance, both naturally expressed in the polar coordinates system originating at the radar antenna. We first convert original measurements to an ortho-Cartesian coordinate system. Then we solve collision avoiding problems in rectangular planar coordinates, and the results are transformed to the polar coordinate system. This article presents a method for an analysis of a collision situation at sea performed directly in the polar coordinate system. This approach enables a simpler geometric interpretation of a collision situation

Using a Polar Coordinate System in the Classroom

1990 ◽  
Vol 37 (8) ◽  
pp. 42-45
Author(s):  
William M. Carroll
Keyword(s):  
Elementary School ◽  
Coordinate System ◽  
School Level ◽  
Polar Coordinate System ◽  
School Students ◽  
Rectangular Coordinate System ◽  
Polar Coordinate ◽  
Supplementary Material ◽  
Cartesian Coordinate ◽  
Additional Exposure

Most elementary school students have experiences with a rectangular graphing system that helps to prepare them for ideas in algebra and analytic geometry. Mathematics books at the elementary school level contain a section on graphing, though it is often one of the later chapters, where it may be treated as supplementary material. In science and in social studies, students may find various data graphed or may have a project in which they have to graph daily temperatures, rainfall, or test scores. Biorhythms, record sales charts, or, for the more ambitious, the daily stock market give additional exposure. Designing graphics on the computer monitor often requires some placement by a rectangular coordinate system. By the time students meet the Cartesian coordinate system with its x- and y-axes and use it to graph equations, the idea and techniques should be somewhat familiar.

Stress Calculation of Gravity Dam Based on Elastic Mechanics

2012 ◽  
Vol 238 ◽  
pp. 256-259
Author(s):  
Hai Bo Cui ◽  
Hai Tang Zhu ◽  
Jin Chao Yue
Keyword(s):  
Coordinate System ◽  
Superposition Principle ◽  
Equivalent Stress ◽  
Gravity Dam ◽  
Polar Coordinate System ◽  
Polar Coordinate ◽  
Cartesian Coordinate ◽  
Dimensional Analysis Method ◽  
Water Lever ◽  
Elastic Mechanics

Based on the elastic mechanics theory, combined with Saint-Venant principle and the superposition principle, the calculating method for the stress of gravity dam in arbitrary storage water lever were put forward by means of the equivalent stress method and the dimensional analysis method through the conversion between a Cartesian coordinate system and Polar coordinate system. The method not only offers a new idea for calculating the stress of gravity dam, but also presents research bases for evaluating synthetically the strength of gravity dam.

Research on improved hough algorithm and its application in lunar crater

2021 ◽  
pp. 1-9
Author(s):  
Lanfeng Zhou ◽  
Ling Li
Keyword(s):  
Coordinate System ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Detection Algorithm ◽  
Polar Coordinate System ◽  
Circle Center ◽  
Traditional Algorithm ◽  
Polar Coordinate ◽  
Cartesian Coordinate ◽  
Three Dimensional Space

Traditional Hough circle detection algorithm usually determines the center and radius of a circle by mapping points in cartesian coordinate system to polar coordinate system. Since it accumulates in the three-dimensional space, it requires more calculation consumption. In this paper, we solve the problem of high time complexity of Hough algorithm in judging circle radius and circle center from two aspects of circle angle and circle radius according to the geometric features of quasi-circles. A large number of experiments show that, compared with the traditional algorithm, this algorithm can not only identify quasi-circles, but also improve the detection success rate of circles by about 10%, with efficient running speed, and obtain good experimental results in the detection of craters.

Geometrically Invariant NSCT–GPCET-Based Image Watermarking with Accurate Moment Calculation

2021 ◽  
pp. 2150284
Author(s):  
Wenbing Wang ◽  
Shengli Liu ◽  
Liu Feng
Keyword(s):  
Calculation Method ◽  
Image Watermarking ◽  
Robust Watermarking ◽  
Exponential Transform ◽  
Computational Simplicity ◽  
Polar Complex Exponential Transform ◽  
Watermarking Scheme ◽  
Complex Exponential ◽  
Grid Division ◽  
Geometrical Attacks

Generic polar complex exponential transform (GPCET), as continuous orthogonal moment, has the advantages of computational simplicity, numerical stability, and resistance to geometric transforms, which make it suitable for watermarking. However, errors in kernel function discretization can degrade these advantages. To maximize the GPCET utilization in robust watermarking, this paper proposes a secondary grid-division (SGD)-based moment calculation method that divides each grid corresponding to one pixel into nonoverlapping subgrids and increases the number of sampling points. Using the accurate moment calculation method, a nonsubsampled contourlet transform (NSCT)–GPCET-based watermarking scheme with resistance to image processing and geometrical attacks is proposed. In this scheme, the accurate moment calculation can reduce the numerical error and geometrical error of the traditional methods, which is verified by an image reconstruction comparison. Additionally, NSCT and accurate GPCET are utilized to achieve watermark stability. Subsequent experiments test the proposed watermarking scheme for its invisibility and robustness, and verify that the robustness of the proposed scheme outperforms that of other schemes when its level of invisibility is significantly higher.

Natural Frequencies and Mode Shapes of Elliptic Plates With Boundary Characteristic Orthogonal Polynomials As Assumed Shape Functions

1991 ◽  
Author(s):  
C. Rajalingham ◽  
R. B. Bhat ◽  
G. D. Xistris
Keyword(s):  
Coordinate System ◽  
Orthogonal Polynomials ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Mode Shapes ◽  
Polar Coordinate System ◽  
Free Boundaries ◽  
Natural Modes ◽  
Polar Coordinate ◽  
Boundary Characteristic

Abstract The natural frequencies and natural modes of vibration of uniform elliptic plates with clamped, simply supported and free boundaries are investigated using Rayleigh-Ritz method. A modified polar coordinate system is used to investigate the problem. Energy expressions in Cartesian coordinate system are transformed into the modified polar coordinate system. Boundary characteristic orthogonal polynomials in the radial direction, and trigonometric functions in the angular direction are used to express the deflection of the plate. These deflection shapes are classified into four basic categories, depending on its symmetrical or antisymmetrical property about the major and minor axes of the ellipse. The first six natural modes in each of the above categories are presented in the form of contour plots.

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