scholarly journals On the Generalized Essential Matrix Correction: An Efficient Solution to the Problem and Its Applications

2020 ◽  
Vol 62 (8) ◽  
pp. 1107-1120
Author(s):  
Pedro Miraldo ◽  
João R. Cardoso
Keyword(s):  
Original Problem ◽  
Synthetic Data ◽  
Real Data ◽  
Optimization Method ◽  
Computational Effort ◽  
Optimization Techniques ◽  
Steepest Descent ◽  
Frobenius Norm ◽  
Essential Matrix ◽  
Nonlinear Constrained Optimization

Abstract This paper addresses the problem of finding the closest generalized essential matrix from a given $$6\times 6$$ 6 × 6 matrix, with respect to the Frobenius norm. To the best of our knowledge, this nonlinear constrained optimization problem has not been addressed in the literature yet. Although it can be solved directly, it involves a large number of constraints, and any optimization method to solve it would require much computational effort. We start by deriving a couple of unconstrained formulations of the problem. After that, we convert the original problem into a new one, involving only orthogonal constraints, and propose an efficient algorithm of steepest descent type to find its solution. To test the algorithms, we evaluate the methods with synthetic data and conclude that the proposed steepest descent-type approach is much faster than the direct application of general optimization techniques to the original formulation with 33 constraints and to the unconstrained ones. To further motivate the relevance of our method, we apply it in two pose problems (relative and absolute) using synthetic and real data.

The three‐parameter equation: An efficient tool to enhance the stack

Geophysics ◽  
1994 ◽  
Vol 59 (2) ◽  
pp. 297-308 ◽  
Author(s):  
Pierre D. Thore ◽  
Eric de Bazelaire ◽  
Marisha P. Rays
Keyword(s):  
Synthetic Data ◽  
Real Data ◽  
Least Square Method ◽  
Maximum Energy ◽  
Computational Effort ◽  
Velocity Estimation ◽  
Least Square ◽  
Waveform Data ◽  
Interval Velocity ◽  
Parameter Equation

We compare the three‐term equation to the normal moveout (NMO) equation for several synthetic data sets to analyze whether or not it is worth making the additional computational effort in the stacking process within various exploration contexts. In our evaluation we have selected two criteria: 1)The quality of the stacked image. 2) The reliability of the stacking parameters and their usefulness for further computation such as interval velocity estimation. We have simulated the stacking process very precisely, despite using only the traveltimes and not the full waveform data. The procedure searches for maximum coherency along the traveltime curve rather than a least‐square regression to it. This technique, which we call the Gaussian‐weighted least square, avoids most of the shortcomings of the least‐square method. The following are our conclusions: 1) The three term equation gives a better stack than the regular NMO. The increase in stacking energy can be more than 30 percent. 2)The calculation of interval velocities using a DIX formula rewritten for the three‐parameter equation is much more stable and accurate than the standard DIX formula. 3) The search for the three parameters is feasible in an efficient way since the shifted hyperbola requires only static corrections rather than dy namic ones. 4) Noise alters the parameters of the maximum energy stack in a way that depends on the noise type. The estimates obtained remain accurate enough for interval velocity estimation (where only two parameters are needed), but the use of the three parameters in direct inversion may be hazardous because of noise corruption. These conclusions should, however, be verified on real data examples.

Method of determination of the text direction on the image with the use of convolutional neural network

2020 ◽  
pp. 96-99
Author(s):  
P.L. Nikolaev
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Deep Neural Network ◽  
Binary Classification ◽  
Synthetic Data ◽  
Real Data ◽  
Method Of Determination ◽  
Classification Of Images

This article deals with method of binary classification of images with small text on them Classification is based on the fact that the text can have 2 directions – it can be positioned horizontally and read from left to right or it can be turned 180 degrees so the image must be rotated to read the sign. This type of text can be found on the covers of a variety of books, so in case of recognizing the covers, it is necessary first to determine the direction of the text before we will directly recognize it. The article suggests the development of a deep neural network for determination of the text position in the context of book covers recognizing. The results of training and testing of a convolutional neural network on synthetic data as well as the examples of the network functioning on the real data are presented.

scholarly journals G-Tric: generating three-way synthetic datasets with triclustering solutions

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
João Lobo ◽  
Rui Henriques ◽  
Sara C. Madeira
Keyword(s):  
State Of The Art ◽  
Synthetic Data ◽  
Ground Truth ◽  
Real Data ◽  
Three Dimensions ◽  
Additional Advantage ◽  
Urban Dynamics ◽  
Data Generator ◽  
Real World Datasets ◽  
Synthetic Datasets

Abstract Background Three-way data started to gain popularity due to their increasing capacity to describe inherently multivariate and temporal events, such as biological responses, social interactions along time, urban dynamics, or complex geophysical phenomena. Triclustering, subspace clustering of three-way data, enables the discovery of patterns corresponding to data subspaces (triclusters) with values correlated across the three dimensions (observations $$\times$$ × features $$\times$$ × contexts). With increasing number of algorithms being proposed, effectively comparing them with state-of-the-art algorithms is paramount. These comparisons are usually performed using real data, without a known ground-truth, thus limiting the assessments. In this context, we propose a synthetic data generator, G-Tric, allowing the creation of synthetic datasets with configurable properties and the possibility to plant triclusters. The generator is prepared to create datasets resembling real 3-way data from biomedical and social data domains, with the additional advantage of further providing the ground truth (triclustering solution) as output. Results G-Tric can replicate real-world datasets and create new ones that match researchers needs across several properties, including data type (numeric or symbolic), dimensions, and background distribution. Users can tune the patterns and structure that characterize the planted triclusters (subspaces) and how they interact (overlapping). Data quality can also be controlled, by defining the amount of missing, noise or errors. Furthermore, a benchmark of datasets resembling real data is made available, together with the corresponding triclustering solutions (planted triclusters) and generating parameters. Conclusions Triclustering evaluation using G-Tric provides the possibility to combine both intrinsic and extrinsic metrics to compare solutions that produce more reliable analyses. A set of predefined datasets, mimicking widely used three-way data and exploring crucial properties was generated and made available, highlighting G-Tric’s potential to advance triclustering state-of-the-art by easing the process of evaluating the quality of new triclustering approaches.

Single Depth View Based Real-Time Reconstruction of Hand-Object Interactions

2021 ◽  
Vol 40 (3) ◽  
pp. 1-12
Author(s):  
Hao Zhang ◽  
Yuxiao Zhou ◽  
Yifei Tian ◽  
Jun-Hai Yong ◽  
Feng Xu
Keyword(s):  
Real Time ◽  
Synthetic Data ◽  
Real Data ◽  
Depth Image ◽  
Real Time System ◽  
The Real ◽  
Time Performance ◽  
Contact Constraint ◽  
Object Shapes ◽  
Object Interactions

Reconstructing hand-object interactions is a challenging task due to strong occlusions and complex motions. This article proposes a real-time system that uses a single depth stream to simultaneously reconstruct hand poses, object shape, and rigid/non-rigid motions. To achieve this, we first train a joint learning network to segment the hand and object in a depth image, and to predict the 3D keypoints of the hand. With most layers shared by the two tasks, computation cost is saved for the real-time performance. A hybrid dataset is constructed here to train the network with real data (to learn real-world distributions) and synthetic data (to cover variations of objects, motions, and viewpoints). Next, the depth of the two targets and the keypoints are used in a uniform optimization to reconstruct the interacting motions. Benefitting from a novel tangential contact constraint, the system not only solves the remaining ambiguities but also keeps the real-time performance. Experiments show that our system handles different hand and object shapes, various interactive motions, and moving cameras.

scholarly journals Real UAV-Bird Image Classification Using CNN with a Synthetic Dataset

2021 ◽  
Vol 11 (9) ◽  
pp. 3863
Author(s):  
Ali Emre Öztürk ◽  
Ergun Erçelebi
Keyword(s):  
Deep Learning ◽  
Image Classification ◽  
Synthetic Data ◽  
Real Data ◽  
Corner Detection ◽  
Batch Size ◽  
Test Accuracy ◽  
Classification Problems ◽  
Auc Value ◽  
Classification Test

A large amount of training image data is required for solving image classification problems using deep learning (DL) networks. In this study, we aimed to train DL networks with synthetic images generated by using a game engine and determine the effects of the networks on performance when solving real-image classification problems. The study presents the results of using corner detection and nearest three-point selection (CDNTS) layers to classify bird and rotary-wing unmanned aerial vehicle (RW-UAV) images, provides a comprehensive comparison of two different experimental setups, and emphasizes the significant improvements in the performance in deep learning-based networks due to the inclusion of a CDNTS layer. Experiment 1 corresponds to training the commonly used deep learning-based networks with synthetic data and an image classification test on real data. Experiment 2 corresponds to training the CDNTS layer and commonly used deep learning-based networks with synthetic data and an image classification test on real data. In experiment 1, the best area under the curve (AUC) value for the image classification test accuracy was measured as 72%. In experiment 2, using the CDNTS layer, the AUC value for the image classification test accuracy was measured as 88.9%. A total of 432 different combinations of trainings were investigated in the experimental setups. The experiments were trained with various DL networks using four different optimizers by considering all combinations of batch size, learning rate, and dropout hyperparameters. The test accuracy AUC values for networks in experiment 1 ranged from 55% to 74%, whereas the test accuracy AUC values in experiment 2 networks with a CDNTS layer ranged from 76% to 89.9%. It was observed that the CDNTS layer has considerable effects on the image classification accuracy performance of deep learning-based networks. AUC, F-score, and test accuracy measures were used to validate the success of the networks.

scholarly journals sepal: identifying transcript profiles with spatial patterns by diffusion-based modeling

2021 ◽  
Author(s):  
Alma Andersson ◽  
Joakim Lundeberg
Keyword(s):  
Spatial Patterns ◽  
Expression Profiles ◽  
Synthetic Data ◽  
Real Data ◽  
Cell Types ◽  
Statistical Hypothesis ◽  
Supplementary Information ◽  
Statistical Hypothesis Testing ◽  
Transcriptomics Data ◽  
Transcript Profiles

Abstract Motivation Collection of spatial signals in large numbers has become a routine task in multiple omics-fields, but parsing of these rich datasets still pose certain challenges. In whole or near-full transcriptome spatial techniques, spurious expression profiles are intermixed with those exhibiting an organized structure. To distinguish profiles with spatial patterns from the background noise, a metric that enables quantification of spatial structure is desirable. Current methods designed for similar purposes tend to be built around a framework of statistical hypothesis testing, hence we were compelled to explore a fundamentally different strategy. Results We propose an unexplored approach to analyze spatial transcriptomics data, simulating diffusion of individual transcripts to extract genes with spatial patterns. The method performed as expected when presented with synthetic data. When applied to real data, it identified genes with distinct spatial profiles, involved in key biological processes or characteristic for certain cell types. Compared to existing methods, ours seemed to be less informed by the genes’ expression levels and showed better time performance when run with multiple cores. Availabilityand implementation Open-source Python package with a command line interface (CLI), freely available at https://github.com/almaan/sepal under an MIT licence. A mirror of the GitHub repository can be found at Zenodo, doi: 10.5281/zenodo.4573237. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Surrogate-Based Optimization of Horizontal Axis Hydrokinetic Turbine Rotor Blades

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 4045
Author(s):  
David Menéndez Arán ◽  
Ángel Menéndez
Keyword(s):  
Turbine Blade ◽  
Design Method ◽  
Optimization Method ◽  
Turbine Rotor ◽  
Computational Effort ◽  
Rotor Blades ◽  
Linear Functions ◽  
Cavitation Inception ◽  
Hydrokinetic Turbine ◽  
Blade Geometry

A design method was developed for automated, systematic design of hydrokinetic turbine rotor blades. The method coupled a Computational Fluid Dynamics (CFD) solver to estimate the power output of a given turbine with a surrogate-based constrained optimization method. This allowed the characterization of the design space while minimizing the number of analyzed blade geometries and the associated computational effort. An initial blade geometry developed using a lifting line optimization method was selected as the base geometry to generate a turbine blade family by multiplying a series of geometric parameters with corresponding linear functions. A performance database was constructed for the turbine blade family with the CFD solver and used to build the surrogate function. The linear functions were then incorporated into a constrained nonlinear optimization algorithm to solve for the blade geometry with the highest efficiency. A constraint on the minimum pressure on the blade could be set to prevent cavitation inception.

scholarly journals Benchmarking Unsupervised Outlier Detection with Realistic Synthetic Data

2021 ◽  
Vol 15 (4) ◽  
pp. 1-20
Author(s):  
Georg Steinbuss ◽  
Klemens Böhm
Keyword(s):  
Outlier Detection ◽  
Synthetic Data ◽  
Real Data ◽  
Detection Methods ◽  
Quality Of Data ◽  
Benchmark Data ◽  
Core Idea ◽  
Generic Process ◽  
Unsupervised Outlier Detection

Benchmarking unsupervised outlier detection is difficult. Outliers are rare, and existing benchmark data contains outliers with various and unknown characteristics. Fully synthetic data usually consists of outliers and regular instances with clear characteristics and thus allows for a more meaningful evaluation of detection methods in principle. Nonetheless, there have only been few attempts to include synthetic data in benchmarks for outlier detection. This might be due to the imprecise notion of outliers or to the difficulty to arrive at a good coverage of different domains with synthetic data. In this work, we propose a generic process for the generation of datasets for such benchmarking. The core idea is to reconstruct regular instances from existing real-world benchmark data while generating outliers so that they exhibit insightful characteristics. We propose and describe a generic process for the benchmarking of unsupervised outlier detection, as sketched so far. We then describe three instantiations of this generic process that generate outliers with specific characteristics, like local outliers. To validate our process, we perform a benchmark with state-of-the-art detection methods and carry out experiments to study the quality of data reconstructed in this way. Next to showcasing the workflow, this confirms the usefulness of our proposed process. In particular, our process yields regular instances close to the ones from real data. Summing up, we propose and validate a new and practical process for the benchmarking of unsupervised outlier detection.

Regularization and datuming of seismic data by weighted, damped least squares

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. U67-U76 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Structural Data ◽  
Irregular Sampling ◽  
Data Set ◽  
Near Surface ◽  
Damped Least Squares ◽  
Wavefield Extrapolation

The possibility of improving regularization/datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem. Weighted, damped least squares is then used to produce the regularized/datumed wavefield. Regularization/datuming is extremely costly because of computing the Hessian, so an efficient approximation is introduced. Approximation is achieved by computing a limited number of diagonals in the operators involved. Real and synthetic data examples demonstrate the utility of this approach. For synthetic data, regularization/datuming is demonstrated for large extrapolation distances using a highly irregular recording array. Without approximation, regularization/datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation (PSPI). Approximate regularization/datuming returns a regularized wavefield for approximately two orders of magnitude less in cost; but it is dip limited, though in a controllable way, compared to the full method. The Foothills structural data set, a freely available data set from the Rocky Mountains of Canada, demonstrates application to real data. The data have highly irregular sampling along the shot coordinate, and they suffer from significant near-surface effects. Approximate regularization/datuming returns common receiver data that are superior in appearance compared to conventional datuming.

scholarly journals A Bayesian Approach to Estimation and Testing in Time-course Microarray Experiments

2007 ◽  
Vol 6 (1) ◽  
Author(s):  
Claudia Angelini ◽  
Daniela De Canditiis ◽  
Margherita Mutarelli ◽  
Marianna Pensky
Keyword(s):  
Time Course ◽  
Expression Profiles ◽  
Cancer Cell Line ◽  
Real Data ◽  
Microarray Experiment ◽  
Computational Effort ◽  
Microarray Experiments ◽  
Analytic Expressions ◽  
Sampling Intervals ◽  
Nonparametric Techniques

The objective of the present paper is to develop a truly functional Bayesian method specifically designed for time series microarray data. The method allows one to identify differentially expressed genes in a time-course microarray experiment, to rank them and to estimate their expression profiles. Each gene expression profile is modeled as an expansion over some orthonormal basis, where the coefficients and the number of basis functions are estimated from the data. The proposed procedure deals successfully with various technical difficulties that arise in typical microarray experiments such as a small number of observations, non-uniform sampling intervals and missing or replicated data. The procedure allows one to account for various types of errors and offers a good compromise between nonparametric techniques and techniques based on normality assumptions. In addition, all evaluations are performed using analytic expressions, so the entire procedure requires very small computational effort. The procedure is studied using both simulated and real data, and is compared with competitive recent approaches. Finally, the procedure is applied to a case study of a human breast cancer cell line stimulated with estrogen. We succeeded in finding new significant genes that were not marked in an earlier work on the same dataset.

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