scholarly journals EIKONAL-BASED MODELS OF RANDOM TESSELLATIONS

2019 ◽  
Vol 38 (1) ◽  
pp. 15 ◽  
Author(s):  
Bruno Figliuzzi
Keyword(s):  
Efficient Method ◽  
Eikonal Equation ◽  
Velocity Model ◽  
Local Velocity ◽  
Implicit Functions ◽  
Multi Scale ◽  
Random Tessellation ◽  
Straight Line ◽  
Random Tessellations ◽  
Roughness Amplitude

In this article, we propose a novel, efficient method for computing a random tessellation from its vectorial representation at each voxel of a discretized domain. This method is based upon the resolution of the Eikonal equation and has a complexity in O(N log N), N being the number of voxels used to discretize the domain. By contrast, evaluating the implicit functions of the vectorial representation at each voxel location has a complexity of O(N²) in the general case. The method also enables us to consider the generation of tessellations with rough interfaces between cells by simulating the growth of the germs on a domain where the velocity varies locally. This aspect constitutes the main contribution of the article. A final contribution is the development of an algorithm for estimating the multi-scale tortuosity of the boundaries of the tessellation cells. The algorithm computes the tortuosity of the boundary at several scales by iteratively deforming the boundary until it becomes a straight line. Using this algorithm, we demonstrate that depending on the local velocity model, it is possible to control the roughness amplitude of the cells boundaries.

Finite‐difference calculation of direct‐arrival traveltimes using the eikonal equation

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1270-1274 ◽  
Author(s):  
Le‐Wei Mo ◽  
Jerry M. Harris
Keyword(s):  
Finite Difference ◽  
Ray Tracing ◽  
Finite Differences ◽  
Eikonal Equation ◽  
Velocity Model ◽  
Uniform Grid ◽  
Square Grid ◽  
Kirchhoff Migration ◽  
Difference Calculation

Traveltimes of direct arrivals are obtained by solving the eikonal equation using finite differences. A uniform square grid represents both the velocity model and the traveltime table. Wavefront discontinuities across a velocity interface at postcritical incidence and some insights in direct‐arrival ray tracing are incorporated into the traveltime computation so that the procedure is stable at precritical, critical, and postcritical incidence angles. The traveltimes can be used in Kirchhoff migration, tomography, and NMO corrections that require traveltimes of direct arrivals on a uniform grid.

Random mosaics with cells of general topology

1996 ◽  
Vol 28 (02) ◽  
pp. 332
Author(s):  
Richard Cowan ◽  
Albert K. L. Tsang
Keyword(s):  
Euler Characteristic ◽  
Ergodic Theory ◽  
General Topology ◽  
Traditional Theory ◽  
Random Partition ◽  
Random Tessellation ◽  
Random Tessellations ◽  
Partition Process

This paper considers a structure, named a ‘random partition process’, which is a generalisation of a random tessellation. The cells, possibly multi-part and with holes, have a general topology summarised by the Euler characteristic. Vertices of all orders are allowed. Using the tools of ergodic theory, all of the formulae, from the traditional theory of random tessellations with convex cells, are generalised. Some motivating examples are given.

scholarly journals An Efficient Method to Learn Overcomplete Multi-Scale Dictionaries of ECG Signals

2018 ◽  
Vol 8 (12) ◽  
pp. 2569 ◽  
Author(s):  
David Luengo ◽  
David Meltzer ◽  
Tom Trigano
Keyword(s):  
Efficient Method ◽  
Real World ◽  
Digital Signal ◽  
Point Of View ◽  
Computational Point ◽  
Ecg Signals ◽  
Multi Scale ◽  
Multiple Alternative ◽  
St Segments ◽  
Processing Techniques

The electrocardiogram (ECG) was the first biomedical signal for which digital signal processing techniques were extensively applied. By its own nature, the ECG is typically a sparse signal, composed of regular activations (QRS complexes and other waveforms, such as the P and T waves) and periods of inactivity (corresponding to isoelectric intervals, such as the PQ or ST segments), plus noise and interferences. In this work, we describe an efficient method to construct an overcomplete and multi-scale dictionary for sparse ECG representation using waveforms recorded from real-world patients. Unlike most existing methods (which require multiple alternative iterations of the dictionary learning and sparse representation stages), the proposed approach learns the dictionary first, and then applies a fast sparse inference algorithm to model the signal using the constructed dictionary. As a result, our method is much more efficient from a computational point of view than other existing algorithms, thus becoming amenable to dealing with long recordings from multiple patients. Regarding the dictionary construction, we located first all the QRS complexes in the training database, then we computed a single average waveform per patient, and finally we selected the most representative waveforms (using a correlation-based approach) as the basic atoms that were resampled to construct the multi-scale dictionary. Simulations on real-world records from Physionet’s PTB database show the good performance of the proposed approach.

Further random tessellations with the classic Poisson polygon distributions

1996 ◽  
Vol 28 (02) ◽  
pp. 338-339 ◽  
Author(s):  
Roger E. Miles ◽  
Margaret S. Mackisack
Keyword(s):  
Orientation Distribution ◽  
Convex Polygons ◽  
Random Tessellation ◽  
Random Tessellations ◽  
Random Convex

It is well-known that Poisson lines in the plane, with orientation distribution Θ on [0, π), generate a (random) tessellation M 0 of (random) convex polygons whose characteristics (area, perimeter, etc.) conform, in an ergodic sense, to a certain class {D Θ} of distributions.

Moho Topography and Velocity/Density Model for the Hedmarken area, Eastern Norway, using Receiver Function Analysis and Rj-McMC

2020 ◽  
Author(s):  
Claudia Pavez ◽  
Marco Brönner ◽  
Odleiv Olesen ◽  
Arne Bjørlykke
Keyword(s):  
Receiver Function ◽  
Function Analysis ◽  
Seismic Station ◽  
Velocity Model ◽  
Density Model ◽  
Local Velocity ◽  
Anomalous Density ◽  
Receiver Function Analysis ◽  
Mohorovičić Discontinuity ◽  
Eastern Norway

<p>A Receiver Function Analysis was carried out in the Mjøsa area, Eastern Norway, in order to better image this tectonically complex area, understand the crustal contrasts and complement geological analysis that were made previously in the area. For this, we used seismic traces received for seven broadband stations from the NORSAR permanent array. The H-K (depth vs Vp/Vs) stacking procedure and a Reversible jump Markov chain Monte Carlo (Rj-McMC) inversion were developed independently. The first analysis allows us to obtain a model with the Mohorovicic discontinuity values under each seismic station and the average Vp/Vs crustal ratio. With the inversion, it was possible to develop a 1D local velocity model. Applying the Nafe-Drake relationship, a 2D density model was obtained and tested against observed gravity. Results indicate the presence of a low anomalous density layer that is located to the NNW of the study area, which is probably related to low-density meta-sediments in the Åsta Basin located above the basement. A main crustal fault is also indicated from the density model, spatially coinciding with faults grown during the Sveconorwegian orogenic process.</p><p> </p>

An Efficient Retinal Vessels Biometric Recognition System by Using Multi-Scale Local Binary Pattern Descriptor

2020 ◽  
Vol 10 (10) ◽  
pp. 2481-2489
Author(s):  
Muhammad Sheraz Arshad Malik ◽  
Qoseen Zahra ◽  
Imran Ullah Khan ◽  
Muhammad Awais ◽  
Gang Qiao
Keyword(s):  
Feature Extraction ◽  
Random Forest ◽  
Efficient Method ◽  
Large Scale ◽  
Local Binary Pattern ◽  
Evaluation Criteria ◽  
Recognition System ◽  
Suggested Approach ◽  
Multi Scale ◽  
Biometric Systems

Biometric systems are technically used for human recognition by identifying the unique features of an individual. Many security issues are found related to biometric systems such as voice, fingerprints, face, iris, signatures, etc., but the retina is a unique and efficient method to identify valid one. The aim of this paper is provided with an efficient method to recognize someone based on unique retina features. A proposed system based on retinal blood vessel pattern by using multi-scale local binary pattern (MSLBP) and random forest (Bagging tree) as feature extraction and classification. MSLBP is an efficient method to extracted features at six scales perpixel level, earlier work found the deficiency based on simple binary pattern with coverage of small areas and per-pixel level in the surrounding. MSLBP and random forest classifier suggested approach use for improving usability, perceivability, and sensitivity on large scale areas. It is the fastest method to get features accurately in an efficient way at every level of pixels. This method based on deep learning evaluation (criteria) parameter selection that provides more significant influence with sharp feature extraction on large scale areas based on seconds and improves the efficiency of images. MSLBP overcomes the problem of image sizing, pixel levels and efficiently provide accurate results.

New Classes of Random Tessellations Arising from Iterative Division of Cells

2010 ◽  
Vol 42 (1) ◽  
pp. 26-47 ◽  
Author(s):  
Richard Cowan
Keyword(s):  
Probability Distribution ◽  
Mathematical Formalism ◽  
Simulation Methods ◽  
Vast Number ◽  
Random Tessellation ◽  
Random Tessellations ◽  
Typical Cell ◽  
New Ideas ◽  
Successive Division

We present new ideas about the type of random tessellation which evolves through successive division of its cells. These ideas are developed in an intuitive way, with many pictures and only a modicum of mathematical formalism–so that the wide application of the ideas is clearly apparent to all readers. A vast number of new tessellation models, with known probability distribution for the volume of the typical cell, follow from the concepts in this paper. There are other interesting models for which results are not presented (or presented only through simulation methods), but these models have illustrative value. A large agenda of further research is opened up by the ideas in this paper.

scholarly journals MSTD: an efficient method for detecting multi-scale topological domains from symmetric and asymmetric 3D genomic maps

2018 ◽  
Author(s):  
Yusen Ye ◽  
Lin Gao ◽  
Shihua Zhang
Keyword(s):  
Efficient Method ◽  
Three Dimensional ◽  
Cell Types ◽  
Cell Type ◽  
Range Interaction ◽  
Distinct Cell Type ◽  
Chromosome Conformation ◽  
Topological Domains ◽  
Multi Scale ◽  
Cell Type Specific

AbstractThe chromosome conformation capture (3C) technique and its variants have been employed to reveal the existence of a hierarchy of structures in three-dimensional (3D) chromosomal architecture, including compartments, topologically associating domains (TADs), sub-TADs and chromatin loops. However, existing methods for domain detection were only designed based on symmetric Hi-C maps, ignoring long-range interaction structures between domains. To this end, we proposed a generic and efficient method to identify multi-scale topological domains (MSTD), including cis- and trans-interacting regions, from a variety of 3D genomic datasets. We first applied MSTD to detect promoter-anchored interaction domains (PADs) from promoter capture Hi-C datasets across 17 primary blood cell types. The boundaries of PADs are significantly enriched with one or the combination of multiple epigenetic factors. Moreover, PADs between functionally similar cell types are significantly conserved in terms of domain regions and expression states. Cell type-specific PADs involve in distinct cell type-specific activities and regulatory events by dynamic interactions within them. We also employed MSTD to define multi-scale domains from typical symmetric Hi-C datasets and illustrated its distinct superiority to the-state-of-art methods in terms of accuracy, flexibility and efficiency.

Least-squares fitting of a straight line

1968 ◽  
Vol 46 (16) ◽  
pp. 1845-1847 ◽  
Author(s):  
J. H. Williamson
Keyword(s):  
Least Squares ◽  
Efficient Method ◽  
Least Squares Fitting ◽  
Statistical Errors ◽  
Straight Line

An efficient method is given for computing the best straight line by least squares when there are statistical errors in both coordinates. Exact expressions are obtained for the variances of the slope and intercept.

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