THE BACK-PROJECTION METHOD FOR CONSTRUCTING 3D NON-TENSOR PRODUCT MOTHER WAVELETS AND THE APPLICATION IN IMAGE EDGE DETECTION

2012 ◽  
Vol 10 (03) ◽  
pp. 1250026 ◽  
Author(s):  
LI ZENG ◽  
JIQIANG GUO ◽  
CHENCHENG HUANG
Keyword(s):  
Tensor Product ◽  
Computational Cost ◽  
Three Dimension ◽  
Back Projection ◽  
Mother Wavelet ◽  
3D Images ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Directional Wavelets ◽  
Mother Wavelets

In this paper, a non-tensor product method for constructing three-dimension (3D) mother wavelets by back-projecting two dimension (2D) mother wavelets is presented. We have proved that if a 2D mother wavelet satisfies certain conditions, the back-projection of the 2D mother wavelet is a 3D mother wavelet. And the construction instances of 3D Mexican-hat wavelet and 3D Meyer wavelet are given. These examples imply that we can get some new 3D mother wavelets from known 1D or 2D mother wavelets by using back-projecting method. This method inaugurates a new approach for constructing non-tensor product 3D wavelet. In addition, the non-tensor product 3D Mexican-hat wavelet is used for detecting the edge of two 3D images in our experimental section. Compared with the Mallat's maximum wavelet module approach which uses 3D directional wavelets, experimental results show it can obtain better outcome especial for the edge which the orientation is not along the coordinate axis. Furthermore, the edge is more fine, and the computational cost is much smaller. The non-tensor product mother wavelets constructed by using the method of this paper also can be widely used for compression, filtering and denoising of 3D images.

scholarly journals Comparison of Various Mother Wavelets for Fault Classification in Electrical Systems

2020 ◽  
Vol 10 (4) ◽  
pp. 1203 ◽  
Author(s):  
Chaichan Pothisarn ◽  
Jittiphong Klomjit ◽  
Atthapol Ngaopitakkul ◽  
Chaiyan Jettanasen ◽  
Dimas Anton Asfani ◽  
...  
Keyword(s):  
Power System ◽  
Fault Location ◽  
Classification Algorithm ◽  
Fault Classification ◽  
Discrete Wavelet ◽  
Mother Wavelet ◽  
System Protection ◽  
Fault Type ◽  
Zero Sequence ◽  
Mother Wavelets

This paper presents a comparative study on mother wavelets using a fault type classification algorithm in a power system. The study aims to evaluate the performance of the protection algorithm by implementing different mother wavelets for signal analysis and determines a suitable mother wavelet for power system protection applications. The factors that influence the fault signal, such as the fault location, fault type, and inception angle, have been considered during testing. The algorithm operates by applying the discrete wavelet transform (DWT) to the three-phase current and zero-sequence signal obtained from the experimental setup. The DWT extracts high-frequency components from the signals during both the normal and fault states. The coefficients at scales 1–3 have been decomposed using different mother wavelets, such as Daubechies (db), symlets (sym), biorthogonal (bior), and Coiflets (coif). The results reveal different coefficient values for the different mother wavelets even though the behaviors are similar. The coefficient for any mother wavelet has the same behavior but does not have the same value. Therefore, this finding has shown that the mother wavelet has a significant impact on the accuracy of the fault classification algorithm.

UAS Mission Path Planning System (MPPS) Using Hybrid-Game Coupled to Multi-Objective Optimiser

2009 ◽  
Author(s):  
DongSeop Lee ◽  
Jacques Periaux ◽  
Luis Felipe Gonzalez
Keyword(s):  
Path Planning ◽  
Computational Cost ◽  
Optimization Techniques ◽  
Planning System ◽  
Unmanned Aerial Systems ◽  
Three Dimension ◽  
Design Quality ◽  
Nsga Ii ◽  
Start Position ◽  
Multi Objective

This paper presents the application of advanced optimization techniques to Unmanned Aerial Systems (UAS) Mission Path Planning System (MPPS) using Multi-Objective Evolutionary Algorithms (MOEAs). Two types of multi-objective optimizers are compared; the MOEA Non-dominated Sorting Genetic Algorithms II (NSGA-II) and a Hybrid Game strategy are implemented to produce a set of optimal collision-free trajectories in three-dimensional environment. The resulting trajectories on a three-dimension terrain are collision-free and are represented by using Be´zier spline curves from start position to target and then target to start position or different position with altitude constraints. The efficiency of the two optimization methods is compared in terms of computational cost and design quality. Numerical results show the benefits of adding a Hybrid-Game strategy to a MOEA and for a MPPS.

Three-Dimensional Profilometry Based on Mexican Hat Wavelet Transform

2009 ◽  
Vol 29 (1) ◽  
pp. 197-202 ◽  
Author(s):  
周翔 Zhou Xiang ◽  
赵宏 Zhao Hong
Keyword(s):  
Wavelet Transform ◽  
Three Dimensional ◽  
Mexican Hat Wavelet ◽  
Mexican Hat

Foreground Separation Methods for Satellite and Balloon Experiments

2005 ◽  
Vol 201 ◽  
pp. 71-74
Author(s):  
R. Belén Barreiro ◽  
Michael P. Hobson ◽  
Anthony N. Lasenby ◽  
Patricio Vielva ◽  
Enrique Martínez-González ◽  
...  
Keyword(s):  
Point Source ◽  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Balloon Experiments ◽  
Combined Technique ◽  
Physical Components ◽  
Planck Satellite

A combined technique using the maximum-entropy method (MEM) and the mexican hat wavelet (MHW) to separate and reconstruct the physical components of the microwave sky is presented. We apply this method to simulated observations by the ESA Planck satellite in small patches of the sky. The reconstructed maps of the CMB and foregrounds are improved as compared to those obtained with MEM on its own. Moreover, more accurate point source catalogues are produced at each observing frequency. This technique may also be extended to deal with other multifrequency CMB experiments, including all-sky data.

scholarly journals Identification and Representation of Multi-Pulse Near-Fault Strong Ground Motion Using Adaptive Wavelet Transform

2019 ◽  
Vol 9 (2) ◽  
pp. 259 ◽  
Author(s):  
Chunxu Xia ◽  
Chunguang Liu
Keyword(s):  
Wavelet Transform ◽  
Pulse Energy ◽  
Horizontal Direction ◽  
Mother Wavelet ◽  
Adaptive Wavelet ◽  
Near Fault ◽  
Seismic Motion ◽  
Adaptive Wavelet Transform ◽  
Mother Wavelets ◽  
Strong Ground

In order to identify the horizontal seismic motion owning the largest pulse energy, and represent the dominant pulse-like component embedded in this seismic motion, we used the adaptive wavelet transform algorithm in this paper. Fifteen candidate mother wavelets were evaluated to select the optimum wavelet based on the similarities between the candidate mother wavelet and the target seismic motion, evaluated by the minimum cross variance. This adaptive choosing algorithm for the optimum mother wavelet was invoked before identifying both the horizontal direction owning the largest pulse energy and every dominant pulse, which provides the optimum mother wavelet for the continuous wavelet transform. Each dominant pulse can be represented by its adaptively selected optimum mother wavelet. The results indicate that the identified multi-pulse component fits well with the seismic motion. In most cases, mother wavelets in one multi-pulse seismic motion were different from each other. For the Chi-Chi event (1999-Sep-20 17:47:16 UTC, Mw = 7.6), 62.26% of the qualified pulse-like earthquake motions lay in the horizontal direction ranging from ±15° to ±75°. The Daubechies 6 (db6) mother wavelet was the most frequently used type for both the first and second pulse components.

Ca2+ Sparks Detection and Classification using Gaussian-Mexican Hat Wavelet

2007 ◽  
Author(s):  
Zhi Zhou ◽  
Yingzi Du ◽  
George G. Rodney ◽  
Martin F. Schneider
Keyword(s):  
Mexican Hat Wavelet ◽  
Mexican Hat

scholarly journals Combining maximum-entropy and the Mexican hat wavelet to reconstruct the microwave sky

2001 ◽  
Vol 328 (1) ◽  
pp. 1-16 ◽  
Author(s):  
P. Vielva ◽  
R.B. Barreiro ◽  
M.P. Hobson ◽  
E. Martínez-González ◽  
A.N. Lasenby ◽  
...  
Keyword(s):  
Maximum Entropy ◽  
Mexican Hat Wavelet ◽  
Mexican Hat

scholarly journals Explorations into 3D Doppler Tomography of Interacting Binaries

2012 ◽  
Vol 8 (S290) ◽  
pp. 301-302
Author(s):  
Mercedes T. Richards ◽  
Alexander S. Cocking
Keyword(s):  
Gamma Ray ◽  
Cataclysmic Variables ◽  
Magnetic Loop ◽  
Compact Stars ◽  
Gas Flows ◽  
Central Plane ◽  
Back Projection ◽  
Doppler Tomography ◽  
3D Images ◽  
2D Images

AbstractOver the past twenty-five years, the technique of Doppler tomography has produced many 2D images of the accretion structures and other gas flows in a range of systems containing compact and non-compact stars, including cataclysmic variables, polars, Algols, x-ray, and gamma-ray binaries. Recent 3D images derived from the Radio astronomical Approach (RA) have revealed prominent gas motions beyond the central plane, and display the usual characteristics found in 2D images, as well as new evidence of tilted or precessing accretion disks around the mass gainer, and magnetic loop prominences and coronal mass ejections associated with the donor star. In this work, we have compared new 3D images derived from the back projection tomography technique with those derived from the RA method. In general, back projection produces sharper and more distinctive images than the RA method, thereby permitting a more detailed study of the physical properties of the accretion sources.

scholarly journals The De-Noising of Sonic Echo Test Data through Wavelet Transform Reconstruction

1999 ◽  
Vol 6 (5-6) ◽  
pp. 267-272 ◽  
Author(s):  
J.N. Watson ◽  
P.S. Addison ◽  
A. Sibbald
Keyword(s):  
Wavelet Transform ◽  
Test Data ◽  
Discrete Wavelet ◽  
Non Destructive Testing ◽  
Destructive Testing ◽  
Transform Method ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Non Destructive

This paper presents the results of feasibility study into the application of the wavelet transform signal processing method to sonic based non-destructive testing techniques. Finite element generated data from cast in situ foundation piles were collated and processed using both continuous and discrete wavelet transform techniques. Results were compared with conventional Fourier based methods. The discrete Daubechies wavelets and the continuous Mexican hat wavelet were used and their relative merits investigated. It was found that both the continuous Mexican hat and discrete Daubechies D8 wavelets were significantly better at locating the pile toe compared than the Fourier filtered case. The wavelet transform method was then applied to field test data and found to be successful in facilitating the detection of the pile toe.

scholarly journals Features Determination from Super-Voxels Obtained with Relative Linear Interactive Clustering

2016 ◽  
Vol 21 (3) ◽  
pp. 69-79 ◽  
Author(s):  
Abdelkhalek Bakkari ◽  
Anna Fabijańska
Keyword(s):  
Computational Cost ◽  
Brain Images ◽  
3D Images ◽  
New Approach ◽  
Magnetic Resonance Imaging Mri ◽  
Ct Brain ◽  
Interactive Clustering ◽  
The Brain ◽  
Low Computational Cost ◽  
3D Magnetic Resonance Imaging

Abstract In this paper, the problem of segmentation of 3D Magnetic Resonance Imaging (MRI) and Computed Tomography (CT) brain images is considered. A supervoxel-based segmentation is regarded. In particular, a new approach called Relative Linear Interactive Clustering (RLIC) is introduced. The method, dedicated to image division into super-voxels, is an extension of the Simple Linear Interactive Clustering (SLIC) super-pixels algorithm. During RLIC execution firstly, the cluster centres and the regular grid size are initialized. These are next clustered by Fuzzy C-Means algorithm. Then, the extraction of the super-voxels statistical features is performed. The method contributes with 3D images and serves fully volumetric image segmentation. Five cases are tested demonstrating that our Relative Linear Interactive Clustering (RLIC) is apt to handle huge size of images with a significant accuracy and a low computational cost. The results of applying the suggested method to segmentation of the brain tumour are exposed and discussed.

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