Image Segmentation Based on Poisson Equation

2013 ◽  
Vol 284-287 ◽  
pp. 3131-3134
Author(s):  
Zhi Heng Zhou ◽  
Hui Qiang Zhong
Keyword(s):  
Boundary Condition ◽  
Image Segmentation ◽  
Poisson Equation ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Segmentation Method ◽  
Snake Model ◽  
The Poisson Equation ◽  
Binary Segmentation ◽  
Edge Based

Image segmentation is an important part of the image processing. Currently, image segmentation methods are mainly the threshold-based segmentation method, the region-based segmentation method, the edge-based segmentation method and the Snake model based on energy function etc. This paper presents a novel image segmentation method based on the Poisson equation. The goal of the segmentation method is to divide the image into two homogeneous parts, the boundary portion and the non-boundary portion, which have similar gray values in homogeneous part. The key of the method is to build a Poisson equation with Dirichlet boundary condition. It sets a gradient threshold as the Dirichlet boundary condition of the Poisson equation, and gets a binary image by retaining the image boundary and smoothing the non-image boundary. Then simple binary segmentation will be able to get the image boundary. The experimental results show that this segmentation method can get accurate image boundaries for non-noise images and the weak noise images.

REINFORCEMENT OF THE POISSON EQUATION BY A THIN LAYER

2011 ◽  
Vol 21 (05) ◽  
pp. 1153-1192 ◽  
Author(s):  
JINGYU LI ◽  
KAIJUN ZHANG
Keyword(s):  
Boundary Condition ◽  
Shear Modulus ◽  
Poisson Equation ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Neumann Boundary ◽  
Robin Boundary Condition ◽  
Oscillation Period ◽  
The Poisson Equation ◽  
Robin Boundary

We consider the problem of reinforcing an elastic medium by a strong, rough, thin external layer. This model is governed by the Poisson equation with homogeneous Dirichlet boundary condition. We characterize the asymptotic behavior of the solution as the shear modulus of the layer goes to infinity. We find that there are four types of behaviors: the limiting solution satisfies Poisson equation with Dirichlet boundary condition, Robin boundary condition or Neumann boundary condition, or the limiting solution does not exist. The specific type depends on the integral of the load on the medium, the curvature of the interface and the scaling relations among the shear modulus, the thickness and the oscillation period of the layer.

scholarly journals Solving Poisson Equation by Distributional HK-Integral: Prospects and Limitations

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Amila J. Maldeniya ◽  
Naleen C. Ganegoda ◽  
Kaushika De Silva ◽  
Sanath K. Boralugoda
Keyword(s):  
Boundary Condition ◽  
Half Space ◽  
Poisson Equation ◽  
Dirichlet Boundary Condition ◽  
Linear Functional ◽  
Dirichlet Boundary ◽  
Two Dimensional ◽  
Continuous Linear ◽  
Continuous Linear Functional ◽  
Test Function

In this paper, we present some properties of integrable distributions which are continuous linear functional on the space of test function D ℝ 2 . Here, it uses two-dimensional Henstock–Kurzweil integral. We discuss integrable distributional solution for Poisson’s equation in the upper half space ℝ + 3 with Dirichlet boundary condition.

scholarly journals On some classes of generalized Schrödinger equations

2020 ◽  
Vol 10 (1) ◽  
pp. 522-533
Author(s):  
Amanda S. S. Correa Leão ◽  
Joelma Morbach ◽  
Andrelino V. Santos ◽  
João R. Santos Júnior
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Laplacian Operator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Stationary Problems

Abstract Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + $\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.

On the Dispersive Estimate for the Dirichlet Schrödinger Propagator and Applications to Energy Critical NLS

2014 ◽  
Vol 66 (5) ◽  
pp. 1110-1142
Author(s):  
Dong Li ◽  
Guixiang Xu ◽  
Xiaoyi Zhang
Keyword(s):  
Boundary Condition ◽  
Fundamental Solution ◽  
Unit Ball ◽  
Dirichlet Boundary Condition ◽  
Obstacle Problem ◽  
Dirichlet Boundary ◽  
Radial Symmetry ◽  
Well Posedness ◽  
Robust Algorithm ◽  
Dispersive Estimate

AbstractWe consider the obstacle problem for the Schrödinger evolution in the exterior of the unit ball with Dirichlet boundary condition. Under radial symmetry we compute explicitly the fundamental solution for the linear Dirichlet Schrödinger propagator and give a robust algorithm to prove sharp L1 → L∞ dispersive estimates. We showcase the analysis in dimensions n = 5, 7. As an application, we obtain global well–posedness and scattering for defocusing energy-critical NLS on with Dirichlet boundary condition and radial data in these dimensions.

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