Local Pointwise Research Articles

Grouping Boundary Proposals for Fast Interactive Image Segmentation.

Geodesic models are known as an efficient tool for solving various image segmentation problems. Most of existing approaches only exploit local pointwise image features to track geodesic paths for delineating the objective boundaries. However, such a segmentation strategy cannot take into account the connectivity of the image edge features, increasing the risk of shortcut problem, especially in the case of complicated scenario. In this work, we introduce a new image segmentation model based on the minimal geodesic framework in conjunction with an adaptive cut-based circular optimal path computation scheme and a graph-based boundary proposals grouping scheme. Specifically, the adaptive cut can disconnect the image domain such that the target contours are imposed to pass through this cut only once. The boundary proposals are comprised of precomputed image edge segments, providing the connectivity information for our segmentation model. These boundary proposals are then incorporated into the proposed image segmentation model, such that the target segmentation contours are made up of a set of selected boundary proposals and the corresponding geodesic paths linking them. Experimental results show that the proposed model indeed outperforms state-of-the-art minimal paths-based image segmentation approaches.

Augmented Hessian equations on Riemannian manifolds: from integral to pointwise local second derivative estimates

We obtain a priori local pointwise second derivative estimates for solutions u to a class of augmented Hessian equations on Riemannian manifolds, in terms of the C1 norm and certain W2,p norms of u. We consider the case that no structural assumptions are imposed on either the augmenting term or the right hand side of the equation, and the case where these terms are convex in the gradient variable. In the latter case, under an additional ellipticity condition we prove that the dependence on any W2,p norm can be dropped. Our results are derived using integral estimates.

Spreading speeds for time heterogeneous prey–predator systems with diffusion

We investigate the large time behavior for two components reaction–diffusion systems of prey–predator type in a time varying environment. Here we assume that these variations in time exhibit an averaging property, which will be called mean value in this work. This framework includes in particular time periodicity, almost periodicity and unique ergodicity. We describe the spreading behavior of the prey and the predator, wherein the two populations are able to co-invade the empty space. Our analysis is based the parabolic strong maximum principle for scalar equation and on the derivation of local pointwise estimates that are used to compare the solutions of the prey–predator problem with those of a KPP scalar equation on suitable spatio-temporal domains.

Localized pointwise error estimates for hybrid finite element methods

We present localized pointwise error estimates for a numerical method designed for accurate and efficient approximations for the flux variables. The method can be considered as a reduced version of the mixed finite element method. The method uses much less degrees of freedom compared to the mixed finite element methods while produces approximation solutions for the flux variable of the same accuracy. In this paper, we present optimal pointwise error estimates for the method, and they show local dependence of the error at a point and weaker dependence on global norms.

Local pointwise convergence of the 3D finite element

Local pointwise convergence of the 3D finite element

A local pointwise inequality for a biharmonic equation with negative exponents

In this paper, we are inspired by Ngô, Nguyen and Phan’s (2018 Nonlinearity 31 5484–99) study of the pointwise inequality for positive C 4-solutions of biharmonic equations with negative exponent by using the growth condition of solutions. They propose an open question of whether the growth condition is necessary to obtain the pointwise inequality. We give a positive answer to this open question. We establish the following local pointwise inequality −Δuu+α|∇u|2u2+βu−q+12⩽CR2 for positive C 4-solutions of the biharmonic equations with negative exponent −Δ2u=u−qinBR where B R denotes the ball centered at x 0 with radius R, n ⩾ 3, q > 1, and some constants α ⩾ 0, β ⩾ 0, C > 0.

VR helicity density and its application in turbomachinery tip leakage flows

Helicity is an important quantity that represents the topological interpretation of vortices; however, helicity is not a Galilean invariant. In this study, VR helicity density (HVR) is derived via taking the dot product of vorticity with the unit real eigen vector of the velocity gradient tensor when the complex eigenvalues exist. The analytical solution of HVR is derived to resolve it in a local pointwise manner, and the Galilean invariance of HVR is proved. Tip leakage flow structures in a direct numerical simulation of a tip leakage flow model and a delayed detached eddy simulation of a low-speed large-scale axial compressor rotor are extracted using helicity, eigen helicity density and HVR methods. Results show that the utilization of HVR permits the identification and accentuation of concentrated vortices. Vortices identified by HVR appear in more connective states. As in the case of helicity, the sign of HVR distinguishes between primary and secondary vortices, while eigen helicity density fails. The normalized HVR is superior to the normalized helicity density in locating the vortex axis, especially for the induced vortex structures. Hence, HVR is a strong candidate to replace the helicity density, especially when Galilean invariance is required.

Pavement distress detection using terrestrial laser scanning point clouds – Accuracy evaluation and algorithm comparison

In this paper, we compared five crack detection algorithms using terrestrial laser scanner (TLS) point clouds. The methods are developed based on common point cloud processing knowledge in along- and across-track profiles, surface fitting or local pointwise features, with or without machine learning. The crack area and volume were calculated from the crack points detected by the algorithms. The completeness, correctness, and F1 score of each algorithm were computed against manually collected references. Ten 1-m-by-3.5-m plots containing 75 distresses of six distress types (depression, disintegration, pothole, longitudinal, transverse, and alligator cracks) were selected to explain variability of distresses from a 3-km-long-road. For crack detection at plot level, the best algorithm achieved a completeness of up to 0.844, a correctness of up to 0.853, and an F1 score of up to 0.849. The best algorithm’s overall (ten plots combined) completeness, correctness, and F1 score were 0.642, 0.735, and 0.685 respectively. For the crack area estimation, the overall mean absolute percentage errors (MAPE) of the two best algorithms were 19.8% and 20.3%. In the crack volume estimation, the two best algorithms resulted in 19.3% and 14.5% MAPE. When the plots were grouped based on crack detection complexity, in the ‘easy’ category, the best algorithm reached a crack area estimation MAPE of 8.9%, while for crack volume estimation, the MAPE obtained from the best algorithm was 0.7%.

Discriminative deep semi-nonnegative matrix factorization network with similarity maximization for unsupervised feature learning

• We propose a DSNnet optimization model with non-convex equality constraints for unsupervised representation learning. • We design a neural network based algorithm to solve the proposed DSNnet model. • We introduce a novel similarity measurement between input data and learned features as a regularization term of DSNnet. Deep Semi-NMF (DSN), which learns hierarchical representations by stacking multiple layers Semi-NMF, shows competitive performance in unsupervised data analysis. However, the features learned from DSN always lack of representativity and discriminativity. In this paper, we build a novel Deep Semi-NMF network (DSNnet) to address the issues of DSN. Specifically, DSNnet contains multiple fully-connected layers, in which the activation function of each layer adopts Smoothly Clipped Absolute Deviation (SCAD). The non-negative hidden features are computed forwardly, while the network parameters are updated by the stochastic gradient descent method. Moreover, to enhance the discriminativity of features, we suggest simultaneously minimizing the reconstruction error of input and output, and maximizing the similarity between input and learned features. The proposed similarity measurement, which consists of global geometric similarity and local pointwise similarity, encourages the compactness between similar points and separateness between dissimilar points in the feature space, and is beneficial to preserve intrinsic information of original data. Extensive experiments conducted on several datasets illustrate the superiority of the proposed approach in comparison with state-of-the-art methods.

Local pointwise second derivative estimates for strong solutions to the sigma _k-Yamabe equation on Euclidean domains

We prove local pointwise second derivative estimates for positive W^{2,p} solutions to the sigma _k-Yamabe equation on Euclidean domains, addressing both the positive and negative cases. Generalisations for augmented Hessian equations are also considered.

Multiplication-invariant operators and the classification of LCA group frames

In this paper we study the properties of multiplication invariant (MI) operators acting on subspaces of the vector-valued space L2(X;H). We characterize such operators in terms of range functions by showing that there is an isomorphism between the category of MI spaces (with MI operators as morphisms) and the category of measurable range functions whose morphisms are measurable range operators. We investigate how global properties of an MI operator are reflected by local pointwise properties of its corresponding range operator. We also establish several results about frames generated by multiplications in L2(X;H). This includes the classification of frames of multiplications with respect to unitary equivalence by measurable fields of Gramians. Finally, we show applications of our results in the study of abelian group frames and translation-invariant (TI) operators acting on subspaces of L2(G), where G is a locally compact group.

WIDEBAND SATCOM MODEL: EVALUATION OF NUMERICAL ACCURACY AND EFFICIENCY

Abstract. The spectral method is typically applied as a simple and efficient method to solve the parabolic wave equation in phase screen scintillation models. The critical factors that can greatly affect the spectral method accuracy is the uniformity and smoothness of the input function. This paper observes these effects on the accuracy of the finite difference and the spectral methods applied to a wideband SATCOM signal propagation model simulated in the ultra-high frequency (UHF) band. The finite difference method uses local pointwise approximations to calculate a derivative. The spectral method uses global trigonometric interpolants that achieve remarkable accuracy for continuously differentiable functions. The differences in accuracy are presented for a Gaussian lens and Kolmogorov phase screen. The results demonstrate loss of accuracy in each method when a phase screen is applied, despite the spectral method's computational efficiency over the finite difference method. These results provide meaningful insights when discretizing an interior domain and solving the parabolic wave equation to obtain amplitude and phase of a signal perturbation.

On the thresholds of vortex visualisation methods

Since the discovery of vortex structures in turbulence, research in the area of vortex visualisation methods has been of interest. The prevalent Galilean invariant visualisation methods, like Q, Lambda2, and Omega methods, are based on the local pointwise analysis of invariants of the velocity gradient tensor. When plotting the vortex iso-surfaces, different methods will introduce different thresholds for visualisation purpose. Varying the thresholds can greatly change the appearance of the results and the interpretation can be significantly different for the same flow phenomenon. Using our direct numerical simulation data on late stage laminar turbulent boundary layer transition, we will investigate the similarities and differences among several prevailing vortex visualisation methods caused by the selection of thresholds. The sensitivity of thresholds are further explored analytically in a few flow examples. In addition, we propose an appropriate usage of the threshold which will result in remarkably similar looking vortex structures.

Global and Local Pointwise Error Estimates for Finite Element Approximations to the Stokes Problem on Convex Polyhedra

The main goal of the paper is to show new stability and localization results for the finite element solution of the Stokes system in $W^{1,\infty}$ and $L^\infty$ norms under standard assumptions o...

Local asymptotics for orthonormal polynomials in the interior of the support via universality

We establish local pointwise asymptotics for orthonormal polynomials inside the support of the measure using universality limits. For example, if a measure μ \mu has compact support, is regular in the sense of Stahl, Totik, and Ullmann, and in some subinterval I I , μ \mu is absolutely continuous and μ ′ \mu ^{\prime } is positive and continuous, we prove that for y j n y_{jn} in a compact subset of I o I^{o} with p n ′ ( y j n ) = 0 p_{n}^{\prime }\left ( y_{jn}\right ) =0 , we have lim n → ∞ p n ( y j n + z n ω ( y j n ) ) p n ( y j n ) = cos ⁡ π z \begin{equation*} \lim _{n\rightarrow \infty }\frac {p_{n}\left ( y_{jn}+\frac {z}{n\omega \left ( y_{jn}\right ) }\right ) }{p_{n}\left ( y_{jn}\right ) }=\cos \pi z \end{equation*} uniformly in y j n y_{jn} and for z z in compact subsets of the plane. Here ω \omega is the equilibrium density for the support of μ \mu .

An adjoint network approach to design stabilizable switching signals of switched Boolean networks

In this paper, two kinds of stabilizability of switched Boolean networks (SBNs), consistent stabilizability and stabilizability under time-varying output feedback (TVOF), are investigated on the basis of adjoint logical networks (ALNs), which are constructed via switching signals. Firstly, globally consistent stabilizability of SBNs is equivalently converted into local (one state) pointwise stabilizability of ALNs, under which all suitable finite-time switching signals can be designed. Then the method is generalized to design stabilizable TVOF switching signals. Finally, to show the effectiveness of obtained results, two types of stabilizability of a shift register are discussed.

A volume integral implementation of the Goldstein generalised acoustic analogy for unsteady flow simulations

A new volume integral method based on the Goldstein generalised acoustic analogy is developed and directly applied with large-eddy simulation (LES). In comparison with the existing Goldstein generalised acoustic analogy implementations, the current method does not require the computation and recording of the expensive fluctuating stress autocovariance function in the seven-dimensional space–time. Until now, the multidimensional complexity of the generalised acoustic analogy source term has been the main barrier to using it in routine engineering calculations. The new method only requires local pointwise stresses as an input that can be routinely computed during the flow simulation. On the other hand, the new method is mathematically equivalent to the original Goldstein acoustic analogy formulation, and, thus, allows for a direct correspondence between different effective noise sources in the jet and the far-field noise spectra. The implementation is performed for conditions of a high-speed subsonic isothermal jet corresponding to the Rolls-Royce SILOET experiment and uses the LES solution based on the CABARET solver. The flow and noise solutions are validated by comparison with experiment. The accuracy and robustness of the integral volume implementation of the generalised acoustic analogy are compared with those based on the standard Ffowcs Williams–Hawkings surface integral method and the conventional Lighthill acoustic analogy. As a demonstration of its capabilities to investigate jet noise mechanisms, the new integral volume method is applied to analyse the relative importance of various noise generation and propagation components within the Goldstein generalised acoustic analogy model.

Rotational properties of homeomorphisms with integrable distortion

We establish a modulus inequality, with weak assumptions on the Sobolev regularity, for homeomorphisms with integrable distortion. As an application, we find upper bounds for the pointwise rotation of planar homeomorphisms with p p -integrable distortion. When the mapping is entire we bound the local pointwise rotation and when the mapping is restricted to a bounded convex domain Ω ⊂ C \Omega \subset \mathbb {C} we concentrate on the rotation along the boundary. Furthermore, we show that these bounds are sharp in a very strong sense. Our examples will also prove that the modulus of continuity result, due to Koskela and Takkinen, for the homeomorphisms with p p -integrable distortion is sharp in this strong sense.

Dynamic wake development of a floating wind turbine in free pitch motion subjected to turbulent inflow generated with an active grid

Development of wake turbulence of a floating wind turbine model under low and high turbulence inflow was investigated in comparison to the wake of a bottom fixed turbine. In wind tunnel experiments, two inflow conditions were generated using an active grid and the wakes of the model wind turbines were measured using a rake of 16 hot-wires, at downstream positions from one to seven rotor diameters. The flow was analyzed using statistical, spectral and spatial analysis. Under low turbulence inflow, the turbine type has highest impact on the wake, where structures created at the blade tips define substantially characteristics of the wake. Formation of a correlated tip and root vortices, that is found for the fixed turbine, is inhibited by the floating turbine. Under high turbulence inflow, the turbine type plays a subordinated role. Tip vortices are destabilized by large structures created with the active grid, that persist in the wake. Further analysis using proper orthogonal decomposition reveals more complex pattern under high turbulent inflow, that contain high percentage of turbulent kinetic energy, when compared to the low turbulent inflow, where the wake is composed by local point-wise contributions to the turbulent kinetic energy.

Investigation of Tank Pressurization and Pressure Control—Part I: Experimental Study

Self-pressurization and pressure control of cryogenic storage tanks have important design consequences for propellant and life support systems currently being planned for long duration space missions. During self-pressurization, the tank's liquid fill level and the heat load from the surroundings can have significant effects on the tank's thermal stratification and pressurization rate. When controlling pressure with a mixing jet, the velocity and temperature of the jet are important design parameters affecting the thermal destratification and pressure reduction time constants. In this work, a small-scale ground-based experiment was performed, as a precursor to a microgravity experiment, to investigate the effects of these variables on the pressurization and pressure control time constants in the tank and to assess the feasibility of using a forced jet mixer for reduced boil-off pressure control. Local pointwise temperature and pressure measurements, together with qualitative contours of the thermal field in the liquid, vapor, and wall region, were made to identify and characterize important self-pressurization and pressure control trends in 1 g.