Boundary Tracing Research Articles

Droplet cell investigation of intergranular corrosion on AA2024

An original method combining a droplet cell with direct optical interrogation of the reverse side of a 50μm thick foil AA2024 has been tested to evaluate the possible analysis of the current during intergranular corrosion tests. The foil microstructure and the selected orientation were suitable for recording the current generated during the propagation in volume of a well-defined grain boundary trace. Even if it is impossible to reach a charge and mass balance from these preliminary attempts, it was demonstrated that it is possible, despite hydrogen evolution, to record a current transient resulting from the full penetration of an intergranular path.

On the accuracy of grain boundary character determination by pseudo-3D EBSD

Pseudo-3D orientation microscopy based on electron backscatter diffraction (EBSD) is a simple way to characterize all the 5 rotational parameters of grain boundaries. It is based on the observation of grain boundaries across a sharp edge of a sample using EBSD to determine the crystal orientation and orientation contrast from backscattered electrons to observe the grain boundary traces on the surface. In this paper we discuss the possible errors and the accuracy of these kind of measurements. It is found that the boundary misorientation can be measured better than 0.5°, while the boundary plane can be determined to better than 1°. A coherent twin grain boundary with well-known crystallographic parameters in an austenitic stainless steel with fcc crystal structure was taken as reference.

Boundary Hilbert spaces and trace operators

We discuss the introduction of boundary Hilbert spaces for a class of physical systems for which it is not possible to factor their state spaces as tensor products of Hilbert spaces naturally associated to their boundaries and bulks, respectively. In order to do this we make use of the so called trace operators that play a relevant role in the analysis of PDEs in bounded regions. By taking advantage of these operators and some functorial aspects of the construction of Fock spaces, we will show how to obtain quantum dynamics at the boundaries defined in appropriate Hilbert spaces associated with them.

On the p-Laplacian with Robin boundary conditions and boundary trace theorems

Let $\Omega\subset\mathbb{R}^\nu$, $\nu\ge 2$, be a $C^{1,1}$ domain whose boundary $\partial\Omega$ is either compact or behaves suitably at infinity. For $p\in(1,\infty)$ and $\alpha>0$, define \[ \Lambda(\Omega,p,\alpha):=\inf_{\substack{u\in W^{1,p}(\Omega)\\ u\not\equiv 0}}\dfrac{\displaystyle \int_\Omega |\nabla u|^p \mathrm{d} x - \alpha\displaystyle\int_{\partial\Omega} |u|^p\mathrm{d}\sigma}{\displaystyle\int_\Omega |u|^p\mathrm{d} x}, \] where $\mathrm{d}\sigma$ is the surface measure on $\partial\Omega$. We show the asymptotics \[ \Lambda(\Omega,p,\alpha)=-(p-1)\alpha^{\frac{p}{p-1}} - (\nu-1)H_\mathrm{max}\, \alpha + o(\alpha), \quad \alpha\to+\infty, \] where $H_\mathrm{max}$ is the maximum mean curvature of $\partial\Omega$. The asymptotic behavior of the associated minimizers is discussed as well. The estimate is then applied to the study of the best constant in a boundary trace theorem for expanding domains, to the norm estimate for extension operators and to related isoperimetric inequalities.

Semilinear elliptic equations with Hardy potential and subcritical source term

Let \(\Omega \) be a smooth bounded domain in \({\mathbb {R}}^N\) (\(N>2\)) and \(\delta (x):=\text {dist}\,(x,\partial \Omega )\). Assume \(\mu \in {\mathbb {R}}_+, \nu \) is a nonnegative finite measure on \(\partial \Omega \) and \(g \in C(\Omega \times {\mathbb {R}}_+)\). We study positive solutions of $$\begin{aligned} -\Delta u - \frac{\mu }{\delta ^2} u = g(x,u) \text { in } \Omega , \qquad \text {tr}^*(u)=\nu . \end{aligned}$$ (P) Here \(\text {tr}^*(u)\) denotes the normalized boundary trace of u which was recently introduced by Marcus and Nguyen (Ann Inst H Poincare Anal Non Lineaire, 34, 69–88, 2017). We focus on the case \(0 0\), we prove that there is a critical value \(q^*\) (depending only on \(N, \mu \)) for (P) in the sense that if \(q<q^*\) then (P) possesses a solution under a smallness assumption on \(\nu \), but if \(q \ge q^*\) this problem admits no solution with isolated boundary singularity. Existence result is then extended to a more general setting where g is subcritical [see (1.28)]. We also investigate the case where g is linear or sublinear and give an existence result for (P).

Investigation of the radiation properties of magnetospheric ELF waves induced by modulated ionospheric heating

Electromagnetic extremely low frequency (ELF) waves play an important role in modulating the Earth’s radiation belt electron dynamics. High-frequency (HF) modulated heating of the ionosphere acts as a viable means to generate artificial ELF waves. The artificial ELF waves can reside in two different plasma regions in geo-space by propagating in the ionosphere and penetrating into the magnetosphere. As a consequence, the entire trajectory of ELF wave propagation should be considered to carefully analyze the wave radiation properties resulting from modulated ionospheric heating. We adopt a model of full wave solution to evaluate the Poynting vector of the ELF radiation field in the ionosphere, which can reflect the propagation characteristics of the radiated ELF waves along the background magnetic field and provide the initial condition of waves for ray tracing in the magnetosphere. The results indicate that the induced ELF wave energy forms a collimated beam and the center of the ELF radiation shifts obviously with respect to the ambient magnetic field with the radiation power inversely proportional to the wave frequency. The intensity of ELF wave radiation also shows a weak correlation with the size of the radiation source or its geographical location. Furthermore, the combination of ELF propagation in the ionosphere and magnetosphere is proposed on basis of the characteristics of the ELF radiation field from the upper ionospheric boundary and ray tracing simulations are implemented to reasonably calculate magnetospheric ray paths of ELF waves induced by modulated ionospheric heating.

An efficient feature extraction technique for palm-print recognition system

Palm-print recognition has been investigated over many decades. Palm-print recognition has many phases in which region mapping and feature extraction play an important role. In this paper, we propose a region mapping model using Gradient Bidirectional Boundary Tracing (GBBT) method. We also propose a novel scheme of palm-print recognition using skeleton morphological (SM) operations to extract the combined shape, texture and colour features of the gray-scale palm-print image. To this extent we explore the idea of GBBT and SM that comprises of 11 features whose responses on the given palm-print image are processed independently and classified using Multi-SVM (MSVM). The proposed model is compared with KNN and SVM to demonstrate its efficiency. Extensive experiments are carried out on different large-scale publicly available palm-print databases in terms of its sensitivity specificity and accuracy. The experimental results indicate that our approach produces 2.509% and 2.6342% more efficacy than SVM and KNN methods, respectively.

An efficient feature extraction technique for palm-print recognition system

Palm-print recognition has been investigated over many decades. Palm-print recognition has many phases in which region mapping and feature extraction play an important role. In this paper, we propose a region mapping model using Gradient Bidirectional Boundary Tracing (GBBT) method. We also propose a novel scheme of palm-print recognition using skeleton morphological (SM) operations to extract the combined shape, texture and colour features of the gray-scale palm-print image. To this extent we explore the idea of GBBT and SM that comprises of 11 features whose responses on the given palm-print image are processed independently and classified using Multi-SVM (MSVM). The proposed model is compared with KNN and SVM to demonstrate its efficiency. Extensive experiments are carried out on different large-scale publicly available palm-print databases in terms of its sensitivity specificity and accuracy. The experimental results indicate that our approach produces 2.509% and 2.6342% more efficacy than SVM and KNN methods, respectively.

Probabilistic interpretation of the Calderón problem

In this paper, we use the theory of symmetric Dirichlet forms to give a probabilistic interpretation of Calderon's inverse conductivity problem in terms of reflecting diffusion processes and their corresponding boundary trace processes. This probabilistic interpretation comes in three equivalent formulations which open up novel perspectives on the classical question of unique determinability of conductivities from boundary data. We aim to make this work accessible to both readers with a background in stochastic process theory as well as researchers working on deterministic methods in inverse problems.

Measuring Leaf Area using Otsu Segmentation Method (LAMOS)

Objective: This paper aims to measure the leaf area using image processing techniques that automate the grid counting method. Methods: For measurement of leaf area, firstly segmentation by Otsu method is required. Subsequently, denoising by median filter and followed by object recognition, boundary tracing and region filling techniques. The tool that is used in this study is Visual C++ 2010 Express using C++ and .Net languages. Findings: Three types of leaves have been tested and the results show that this new method could be used in determining the leaf area with a small relative error. Application/Improvement: Leaf area is an important data to agronomist in conducting their research on plant growth, plant photosynthesis, plant physiological behavior and any other research that requires leaf area data.

The Dirichlet problem for elliptic systems with data in Köthe function spaces

We show that the boundedness of the Hardy–Littlewood maximal operator on a Köthe function space \mathbb X and on its Köthe dual \mathbb X ' is equivalent to the well-posedness of the \mathbb X -Dirichlet and \mathbb X '-Dirichlet problems in \mathbb R^n_+ in the class of all second-order, homogeneous, elliptic systems, with constant complex coefficients. As a consequence, we obtain that the Dirichlet problem for such systems is well-posed for boundary data in Lebesgue spaces, variable exponent Lebesgue spaces, Lorentz spaces, Zygmund spaces, as well as their weighted versions. We also discuss a version of the aforementioned result which contains, as a particular case, the Dirichlet problem for elliptic systems with data in the classical Hardy space H^1 , and the Beurling-Hardy space HA ^p for p \in (1,\infty) . Based on the well-posedness of the L^p -Dirichlet problem we then prove the uniqueness of the Poisson kernel associated with such systems, as well as the fact that they generate a strongly continuous semigroup in natural settings. Finally, we establish a general Fatou type theorem guaranteeing the existence of the pointwise nontangential boundary trace for null-solutions of such systems.

BOUNDARY DETECTION ALGORITHM BASED ON SEMI-SUBCOMPLEXES

In this paper, the concept of semi-open subcomplexes in abstract cellular complex is introduced and some of their properties are investigated by describing the notions of semi- frontier, semi-interior and semi-closure. An efficient algorithm for tracing the semi-frontier of an image is introduced and is implemented through MATLAB. Finally, the semi-frontier algorithm is compared with the boundary tracing algorithm (G. Sai Sundara Krishnan, 2012).

Symmetry breaking for a problem in optimal insulation

We consider the problem of optimally insulating a given domain Ω of Rd; this amounts to solve a nonlinear variational problem, where the optimal thickness of the insulator is obtained as the boundary trace of the solution. We deal with two different criteria of optimization: the first one consists in the minimization of the total energy of the system, while the second one involves the first eigenvalue of the related differential operator. Surprisingly, the second optimization problem presents a symmetry breaking in the sense that for a ball the optimal thickness is nonsymmetric when the total amount of insulator is small enough. In the last section we discuss the shape optimization problem in which Ω is allowed to vary too.

Indian Sign Language Numeral Recognition - An Image Processing Approach

In recent years, Sign language is an important research problem for communicating with hearing impaired people without the help of interpreter. Hand gesture is one of the methods used in sign language which is most commonly used by deaf and dumb people to communicate with each other or with normal people. The proposed algorithm aims at developing real time image processing based system for hand gesture recognition on personal computer with an USB web cam. This paper proposes a method to detect and recognize the static image of Indian Sign Language numbering system from zero to nine. The method is based on counting the open fingers in the static images. The proposed algorithm for gesture recognition is based on boundary tracing and finger tip detection and also deals with images of bare hands, which allows the signer to interact with the system in a natural way. The proposed algorithm is first detect and segments the hand region from the real time captured images. Then using the proposed methodology, it locate the fingers and classifies the gesture. Further the system convert Indian signs into text and then speech using an audio file stored on PC. The algorithm is size invariant but it is orientation dependent. The proposed system is implemented using OpenCV. General Terms Gesture Recognition, Active finger counting.

Corrosion and Deformity Recognition for Current Coin

Current coins often get damaged in the current environment, such as smudginess, discoloration, corrosion, mutilation and attrition. When the damage comes to a certain degree, the continuous use of coins will be impacted. In this paper, relevant identification technologies to mutilation and corrosion which are two common defects in circulation are investigated. At first, an auto identification and quantization algorithm about mutilation area of coin surface, based on Freeman boundary tracing is designed. On the basis of binarization, the algorithm accomplishes boundary tracing and extraction and area calculation automatically after the seed point is determined which is an arbitrary point in extracting mutilation area. Secondly, a clustering method based on HIS color model is developed for auto identification of corrosion area and calculation of corrosion area and average corrosion degree. At last, the validity and practicability of the algorithms are proved by a large number of experimental results.

PLASTIC AND GLASS GREENHOUSES DETECTION AND DELINEATION FROM WORLDVIEW-2 SATELLITE IMAGERY

Greenhouse detection using remote sensing technologies is an important research area for yield estimation, sustainable development, urban and rural planning and management. An approach was developed in this study for the detection and delineation of greenhouse areas from high resolution satellite imagery. Initially, the candidate greenhouse patches were detected using supervised classification techniques. For this purpose, Maximum Likelihood (ML), Random Forest (RF), and Support Vector Machines (SVM) classification techniques were applied and compared. Then, sieve filter and morphological operations were performed for improving the classification results. Finally, the obtained candidate plastic and glass greenhouse areas were delineated using boundary tracing and Douglas Peucker line simplification algorithms. The proposed approach was implemented in the Kumluca district of Antalya, Turkey utilizing pan-sharpened WorldView-2 satellite imageries. Kumluca is the prominent district of Antalya with greenhouse cultivation and includes both plastic and glass greenhouses intensively. When the greenhouse classification results were analysed, it can be stated that the SVM classification provides most accurate results and RF classification follows this. The SVM classification overall accuracy was obtained as 90.28%. When the greenhouse boundary delineation results were considered, the plastic greenhouses were delineated with 92.11% accuracy, while glass greenhouses were delineated with 80.67% accuracy. The obtained results indicate that, generally plastic and glass greenhouses can be detected and delineated successfully from WorldView-2 satellite imagery.

PLASTIC AND GLASS GREENHOUSES DETECTION AND DELINEATION FROM WORLDVIEW-2 SATELLITE IMAGERY

Abstract. Greenhouse detection using remote sensing technologies is an important research area for yield estimation, sustainable development, urban and rural planning and management. An approach was developed in this study for the detection and delineation of greenhouse areas from high resolution satellite imagery. Initially, the candidate greenhouse patches were detected using supervised classification techniques. For this purpose, Maximum Likelihood (ML), Random Forest (RF), and Support Vector Machines (SVM) classification techniques were applied and compared. Then, sieve filter and morphological operations were performed for improving the classification results. Finally, the obtained candidate plastic and glass greenhouse areas were delineated using boundary tracing and Douglas Peucker line simplification algorithms. The proposed approach was implemented in the Kumluca district of Antalya, Turkey utilizing pan-sharpened WorldView-2 satellite imageries. Kumluca is the prominent district of Antalya with greenhouse cultivation and includes both plastic and glass greenhouses intensively. When the greenhouse classification results were analysed, it can be stated that the SVM classification provides most accurate results and RF classification follows this. The SVM classification overall accuracy was obtained as 90.28%. When the greenhouse boundary delineation results were considered, the plastic greenhouses were delineated with 92.11% accuracy, while glass greenhouses were delineated with 80.67% accuracy. The obtained results indicate that, generally plastic and glass greenhouses can be detected and delineated successfully from WorldView-2 satellite imagery.

Well-posed boundary integral equation formulations and Nyström discretizations for the solution of Helmholtz transmission problems in two-dimensional Lipschitz domains

We present a comparison among the performance of solvers based on Nystr\om discretizations of several well-posed boundary integral equation formulations of Helmholtz transmission problems in two-dimensional Lipschitz domains. Specifically, we focus on the following four classes of boundary integral formulations of Helmholtz transmission problems: (1)~the classical first kind integral equations for transmission problems~\cite {costabel-stephan}, (2)~the classical second kind integral equations for transmission problems~\cite {KressRoach}, (3)~the single integral equation formulations~\cite {KleinmanMartin}, and (4)~certain direct counterparts of recently introduced generalized combined source integral equations \cite {turc2, turc3}. The former two formulations were the only formulations whose well-posedness in Lipschitz domains was rigorously established \cite {costabel-stephan, ToWe:1993}. We establish the well-posedness of the latter two formulations in appropriate functional spaces of boundary traces of solutions of transmission Helmholtz problems in Lipschitz domains. We give ample numerical evidence that Nystr\om solvers based on formulations (3) and (4) are computationally more advantageous than solvers based on the classical formulations (1) and (2), especially in the case of high-contrast transmission problems at high frequencies.

Fast and accurate algorithm for eye localisation for gaze tracking in low‐resolution images

Iris centre (IC) localisation in low‐resolution visible images is a challenging problem in computer vision community due to noise, shadows, occlusions, pose variations, eye blinks etc. This study proposes an efficient method for determining IC in low‐resolution images in the visible spectrum. Even low‐cost consumer‐grade webcams can be used for gaze tracking without any additional hardware. A two‐stage algorithm is proposed for IC localisation. The proposed method uses geometrical characteristics of the eye. In the first stage, a fast convolution‐based approach is used for obtaining the coarse location of IC). The IC location is further refined in the second stage using boundary tracing and ellipse fitting. The algorithm has been evaluated in public databases such as BioID, Gi4E and is found to outperform the state‐of‐the‐art methods.

Boundary Trace Operator in a Domain of Hilbert Space and the Characteristic Property of its Kernel

We prove an infinite-dimensional analog of the classical theorem on density of the set C 0 1 (G) of finite smooth functions in the kernel of the boundary trace operator γ: H 1(G) → L 2(∂G).