A topographic method for fingerprint segmentation

The paper compares three methods of coding nominal variables in regression analysis: coding of each level as a separate variable, coding with binary code, numbering of factor levels. Although these methods have existed for a long time and even have a theoretical justification (except for encoding with binary code), there were no recommendations and comparisons for their practical application. The features of the application of each method and the existing limitations are analyzed. In the article, there are considered two examples that provide a detailed comparison of these three methods. Comparative analysis has been carried out in the following areas: the presence of restrictions in use; statistical properties of plans; labour intensity and difficulty of obtaining mathematical models and the final result of their building; convenience of semantic analysis and use. Additionally, there have been made comparisons with models based on Chebyshev orthogonal polynomials. It has been established that different methods of coding nominal variables, when used correctly, lead to regression models that are approximately identical in their properties. Moreover, the method of encoding each level as a separate variable is possible only if there are experiments in which there is no nominal variable as an influence effect. The binary coding method is inconvenient to use with a large number of levels of variation of the nominal variable and inconvenient to analyze. When coding by level numbering, it is necessary that the average response values, according to the dispersion diagram of this factor, are sorted by value in accordance with the assigned numbers. With this encoding method, a natural number of factors is preserved. Sharply distinguishable best results are achieved with this coding method using Chebyshev orthogonal polynomials. The highest accuracy and uniformity of approximation are ensured.

If a finite Markov chain (discrete time, discrete states) has a number of absorbing states, one of these will eventually be reached. In this paper are given theoretical formulae for the probability distribution, its generating function and moments of the time taken to first reach an absorbing state, and these formulae are applied to an example taken from genetics. While first passage time problems and their solutions are known for a wide variety of Markov chain processes (e.g., [2], [7], [4]), the theory seems not to have been used in population genetics. Suppose a genetic population consists of a constant number of individuals and the state of the population is defined by the numbers of the various genotypes existing at a given time. Then if mutation is absent, all individuals will eventually become of the same genotype because of random influences such as births, deaths, mating, selection, chromosome breakages and recombinations. The population behavior may in some circumstances be approximated by a Markov chain with absorbing states. In Section 2, two alternative approaches are given for the theoretical determination of absorption time properties, using well known techniques. In Section 3, the consequences of the theoretical results are investigated for a particular population model introduced by Moran [9], [10], and explicit expressions for the distribution of the gene fixation time are obtained in terms of Chebyshev's orthogonal polynomials. The derivation requires finding the pre- and post-eigenvectors of the matrix of transition probabilities, and an incidental by-product is the proof of certain identities for the orthogonal polynomials. The material presented in Section 2 and Section 3 is obtained by exact methods. In Section 4, the Fokker-Planck diffusion equation is used to obtain approximate results, and these are compared with those of the exact theory to ascertain the accuracy of the diffusion approximation.

Clutter suppression is a challenging task in synthetic aperture radar-ground moving target indication (SAR-GMTI). In general, sufficient secondary samples are not easily acquired due to the nonstationary and nonhomogeneous characteristics of bistatic SAR (BiSAR) clutter, resulting in worse clutter suppression results. Recently, space–time adaptive processing based on sparse recovery (SR-STAP) has been developed since its better clutter suppression performance with less samples. However, since the off-grid problem in space–time domain caused by BiSAR’s separate configuration, existing SR-STAP would suffer from severe performance degradation. To address this problem, a clutter-ridge matched STAP (CRM-STAP) method for BiSAR nonstationary clutter suppression is proposed. First, clutter distribution modeling with arbitrary BiSAR configuration is applied to accurately obtain the clutter ridge in space–time domain. Then, keystone transform and time-division processing are applied to correct range cell migration and eliminate Doppler frequency migration, respectively. Next, to solve the off-grid problem, the CRM dictionary is reconstructed via adaptive gradient method, which is established along the direction of clutter ridge and its orthogonal direction. Then, with the constructed CRM dictionary, the clutter covariance matrix (CCM) estimation process is transformed to a multimeasured vector optimization problem, and it can be directly solved by the sparse Bayesian learning algorithm. Finally, based on the estimated CCM, the CRM-STAP filter is built to suppress the nonstationary clutter effectively. Compared with the existing STAP and SR-STAP methods, this method can avoid the performance degradation in clutter suppression caused by the off-grid problem and overcomes the strong nonstationary problem of BiSAR clutter in heterogeneous environments. In October 2020, we have successfully carried out the world’s first airborne BiSAR-GMTI experiment, and the experimental results are given to verify the effectiveness of this method.

The Strong Chebyshev Distribution and Orthogonal Laurent Polynomials

Chebyshev collocation method for static intrinsic equations of geometrically exact beams

Abstract. Buckling of nonuniform carbon nanotubes are studied with the axial load taken as a combination of concentrated and axially distributed loads. Constitutive modelling of the nanotubes is implemented via nonlocal continuum mechanics. Problem solutions are obtained by employing a weak formulation of the problem and the Rayleigh-Ritz method which is implemented by using orthogonal Chebyshev polynomials. The accuracy of the method of solution is verified against available results. Solutions are obtained for the cases of uniformly distributed and triangularly distributed axial loads. Contour plots are given to assess the effect of nonuniform cross-sections and the small-scale parameter on the buckling load for a combination of simply supported, clamped and free boundary conditions.

Via simulating the contribution of spin-orbit interaction to nuclear masses by orthogonal Chebyshev polynomials, the mass excesses are calculated for a group of atomic nuclei characterized by the isospins of Tz = 51/2, 26, 53/2, 55/2, 28, and 57/2 and by the presence of restored Wigner’s spin-isospin SU(4) symmetry. The root-mean-square deviation of the results of these calculations from their experimental counterparts is σ = 140 keV. The potential of the proposed method is discussed.

Orthogonal Chebyshev Polynomials

Chebyshev collocation method for the free vibration analysis of geometrically exact beams with fully intrinsic formulation

{101̄1} semipolar GaN-based light-emitting diodes (LEDs) grown on 1° miscut m-plane sapphires substrates via metal organic chemical vapor deposition showed undulated surface morphology with ridges and valleys. On the ridge regions, two dominant emission peaks, one at a shorter wavelength (∼438 nm) and one at a longer wavelength (∼490 nm), were observed using electroluminescence and micro-photoluminescence. In the valley regions, the longer peak was observed to be significantly quenched due to the grain boundary. The origin of the longer peak is believed to be not only inhomogeneous distribution of In composition in multiple quantum wells (MQWs) but also strong localization around the ridge region. Moreover, thickness variation of faceted MQWs could be associated with the peak broadening in 101̄1 semipolar LEDs. The results were also confirmed by cathodoluminescence and cross-sectional transmission electron microscopy.

This paper introduces a new technique for the formulation of parametric surfaces. Applying translation operations to tangent vectors $${n_{\circ} {\bf \upsilon}}$$ results in null point pairs $${\tau}$$ . We treat these null point pairs as surface and mesh curvature control points which can be interpolated and exponentiated to construct continuous topological transformations $${\mathcal{K}}$$ of the form $${e^{{-}\frac{\tau}{2}}}$$ 2. Some basic algorithms are proposed, including the boost which bends a line to a circle of curvature $${\kappa}$$ , and the twisted boost which generates the Hopf fibration. We investigate methods to control curvature in two orthogonal directions u and v and examine a few distance-based and linear weighting techniques for synthesizing surface patches using multiple curvature control points. We consider the expressivity of the technique in manipulating meshes, and find that applying these rotors to mesh points provides a novel and computationally efficient method for creating boosted forms.

Recent advances in deep learning based image segmentation methods have enabled real-time performance with human-level accuracy. However, occasionally even the best method fails due to low image quality, artifacts or unexpected behaviour of black box algorithms. Being able to predict segmentation quality in the absence of ground truth is of paramount importance in clinical practice, but also in large-scale studies to avoid the inclusion of invalid data in subsequent analysis. In this work, we propose two approaches of real-time automated quality control for cardiovascular MR segmentations using deep learning. First, we train a neural network on 12,880 samples to predict Dice Similarity Coefficients (DSC) on a per-case basis. We report a mean average error (MAE) of 0.03 on 1,610 test samples and 97% binary classification accuracy for separating low and high quality segmentations. Secondly, in the scenario where no manually annotated data is available, we train a network to predict DSC scores from estimated quality obtained via a reverse testing strategy. We report an MAE=0.14 and 91% binary classification accuracy for this case. Predictions are obtained in real-time which, when combined with real-time segmentation methods, enables instant feedback on whether an acquired scan is analysable while the patient is still in the scanner. This further enables new applications of optimising image acquisition towards best possible analysis results.

This article describes the computational method for segmenting smoothed objects images on digital images is developed. To reduce computational costs the segmentation is carried out only in areas extracted by the computational method of single objects images segmentation on digital images.Segmentation of smoothed images is carried out sequentially in each selected segment. To reduce computational costs only segments that contain more than one peak are analyzed. Such segments may contain either fragments of smoothed image, or a statistically dependent image of a compact group of objects. In this regard, the decision about the segmented image type is made based by the difference between the segmentation results of both types of object images: smoothed image and an image of a compact group. As a sign of distinguishing between smoothed image and an image of a compact group the ratio between the number of pixels assigned to the image of a compact group and the smoothed image segmented with the start pixel in one peak is used.Images of objects with non-zero visible motion during the exposure time become smoothed with their own motion and have an image whose shape is stretched along the direction of its apparent movement. At the same time, single objects as well as compact groups of objects are immovable during the exposure time. The form of such images of compact groups of objects is often close to circular. To decide the extent of the segmented image it is proposed to use the degree of elongation of its image on a digital frame. As an indication of the degree of elongation of the object image the estimate of the eccentricity value is used in the paper.A study of the developed method of smoothed images segmentation on digital astronomical images was carried out on digital frames obtained using telescopes from 8 astronomical observatories. The developed computational method allowed making a preliminary decision about the type of segmented image (smoothed image or image of a compact group) directly at the segmentation stage.The developed method of segmentation of smoothed images is applied in the software package for automated detection of asteroids and comets CoLiTec. With the use of the developed method, the segmentation of images of comets, asteroids, NEOs, artificial earth satellites is carried out. When processing digital frames obtained without using the daily reference mechanism, the developed method is used to select all objects in the digital image.

The objective of this paper is to reduce the computational effort in reservoir flooding optimization problems by a combination of different optimization parametrization methods and model order reduction techniques. We compare three different parametrization methods that reduce the cardinality of the original infinite set of control-decision variables to a finite set. The three methods include a traditional piece-wise constant (PWC) approximation, a polynomial approximation by Chebyshev orthogonal polynomials and a piece-wise polynomial approximation by cubic Spline interpolation. The Proper Orthogonal Decomposition with Discrete Empirical Interpolation Method (POD-DEIM) accomplishes the reduced order modeling (ROM).. We compare a gradient-free global stochastic search approach and a gradient-based local search approach. We used Particle Swarm Optimization (PSO) as a gradient-free algorithm and Interior-Point Optimization (IPOPT) with L-BFGS method as a gradient-based algorithm. First, we compare the performances of the three parametrization methods solved by each optimizer, using fine scale simulations for an increasing level of parametrization refinement. Then, in the second part of this paper, we combine the parametrization methods with the reduced modeling workflow. For a given level of parametrization refinement, we compare the performance of each parametrization method coupled with POD-DEIM, and solved by each optimizer. In this part, we introduce an online training procedure, where the first optimization iteration is used to construct the snapshot matrix. The results demonstrate how refining the control approximation with more decision variables per well lead to better NPV values, but with a higher computational cost. The best NPV was achieved using the highest refining level with Chebyshev polynomial approximation. Both polynomial and piece-wise polynomial approximations served as better training sets for POD-DEIM leading to a more accurate and fast reduced model. With the strategy proposed, POD-DEIM showed the best optimization accuracy for Chebyshev polynomial with the gradient-free optimizer, thus permitting the use of the model reduction methodology for global-stochastic search methods. However, the gradient-based approach seems to consistently outperform the gradient-free approach in terms of NPV and number of iterations for the cases shown.

In a Banach space E, we consider the Neumann problem for a second-order homogeneous equation with a constant operator coefficient densely defined in E. Under a weakened strong positivity condition on the operator coefficient (we use the approach due to V.I. Gorbachuk and A.I. Knyazyuk to the study of a-positive operators), we present a criterion for the well-posed solvability of the problem. We obtain a representation of the solution via Chebyshev operator polynomials of the first and second kind.