Image segmentation and smoothing via partial differential equations

Download

index.pdf

Date

2009

Author

Özmen, Neslihan

Metadata

Show full item record

Item Usage Stats

280
views

94
downloads

In image processing, partial differential equation (PDE) based approaches have been extensively used in segmentation and smoothing applications. The Perona-Malik nonlinear diffusion model is the first PDE based method used in the image smoothing tasks. Afterwards the classical Mumford-Shah model was developed to solve both image segmentation and smoothing problems and it is based on the minimization of an energy functional. It has numerous application areas such as edge detection, motion analysis, medical imagery, object tracking etc. The model is a way of finding a partition of an image by using a piecewise smooth representation of the image. Unfortunately numerical procedures for minimizing the Mumford-Shah functional have some difficulties because the problem is non convex and it has numerous local minima, so approximate approaches have been proposed. Two such methods are the Ambrosio-Tortorelli approximation and the Chan-Vese active contour method. Ambrosio and Tortorelli have developed a practical numerical implementation of the Mumford-Shah model which based on an elliptic approximation of the original functional. The Chan-Vese model is a piecewise constant generalization of the Mumford-Shah functional and it is based on level set formulation. Another widely used image segmentation technique is the “Active Contours (Snakes)” model and it is correlated with the Chan-Vese model. In this study, all these approaches have been examined in detail. Mathematical and numerical analysis of these models are studied and some experiments are performed to compare their performance.

Subject Keywords

Mathematics.

URI

http://etd.lib.metu.edu.tr/upload/12610395/index.pdf
https://hdl.handle.net/11511/18435

Collections

Graduate School of Applied Mathematics, Thesis

Suggestions

OpenMETU
Core

Least-squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of diffusive-convective problems Bozkaya, Canan (Elsevier BV, 2007-01-01) Least-squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in diffusive-convective type problems with variable coefficients. The DRBEM enables us to use the fundamental solution of Laplace equation, which is easy to implement computation ally. The terms except the Laplacian are considered as the nonhomogeneity in the equation, which ar...
Application of the boundary element method to parabolic type equations Bozkaya, Nuray; Tezer-Sezgin, Münevver; Department of Mathematics (2010) In this thesis, the two-dimensional initial and boundary value problems governed by unsteady partial differential equations are solved by making use of boundary element techniques. The boundary element method (BEM) with time-dependent fundamental solution is presented as an efficient procedure for the solution of diffusion, wave and convection-diffusion equations. It interpenetrates the equations in such a way that the boundary solution is advanced to all time levels, simultaneously. The solution at a requi...
Oscillation of even order nonlinear delay dynamic equations on time scales Erbe, Lynn; Mert, Raziye; Peterson, Allan; Zafer, Ağacık (Institute of Mathematics, Czech Academy of Sciences, 2013-03-01) One of the important methods for studying the oscillation of higher order differential equations is to make a comparison with second order differential equations. The method involves using Taylor's Formula. In this paper we show how such a method can be used for a class of even order delay dynamic equations on time scales via comparison with second order dynamic inequalities. In particular, it is shown that nonexistence of an eventually positive solution of a certain second order delay dynamic inequality is...
Derivative free multilevel optimization methods Pekmen, Bengisen; Karasözen, Bülent; Department of Scientific Computing (2009) Derivative free optimization algorithms are implementations of trust region based derivative-free methods using multivariate polynomial interpolation. These are designed to minimize smooth functions whose derivatives are not available or costly to compute. The trust region based multilevel optimization algorithms for solving large scale unconstrained optimization problems resulting by discretization of partial differential equations (PDEs), make use of different discretization levels to reduce the computati...
CLUSTER ALGEBRAS AND SYMMETRIZABLE MATRICES Seven, Ahmet İrfan (American Mathematical Society (AMS), 2019-07-01) In the structure theory of cluster algebras, principal coefficients are parametrized by a family of integer vectors, called c-vectors. Each c-vector with respect to an acyclic initial seed is a real root of the corresponding root system, and the c-vectors associated with any seed defines a symmetrizable quasi-Cartan companion for the corresponding exchange matrix. We establish basic combinatorial properties of these companions. In particular, we show that c-vectors define an admissible cut of edges in the a...

Citation Formats

N. Özmen, “Image segmentation and smoothing via partial differential equations,” M.S. - Master of Science, Middle East Technical University, 2009.