scholarly journals Topological gradient for a fourth order operator used in image analysis

2015 ◽  
Vol 21 (4) ◽  
pp. 1120-1149 ◽  
Author(s):  
Gilles Aubert ◽  
Audric Drogoul
Keyword(s):  
Image Analysis ◽  
Fourth Order ◽  
Order Operator ◽  
Topological Gradient

scholarly journals An Overview of the Topological Gradient Approach in Image Processing: Advantages and Inconveniences

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Lamia Jaafar Belaid
Keyword(s):  
Image Processing ◽  
Image Analysis ◽  
Numerical Experiments ◽  
Grey Level ◽  
Major Drawback ◽  
Topological Gradient ◽  
Boundary Measurements ◽  
Topological Asymptotic Expansion ◽  
Gradient Approach ◽  
Segmentation Problem

Image analysis by topological gradient approach is a technique based upon the historic application of the topological asymptotic expansion to crack localization problem from boundary measurements. This paper aims at reviewing this methodology through various applications in image processing; in particular image restoration with edge detection, classification and segmentation problems for both grey level and color images is presented in this work. The numerical experiments show the efficiency of the topological gradient approach for modelling and solving different image analysis problems. However, the topological gradient approach presents a major drawback: the identified edges are not connected and then the results obtained particularly for the segmentation problem can be degraded. To overcome this inconvenience, we propose an alternative solution by combining the topological gradient approach with the watershed technique. The numerical results obtained using the coupled method are very interesting.

Eigenfunctions of a fourth order operator pencil

2014 ◽  
Author(s):  
Abdizhahan Sarsenbi ◽  
Makhmud Sadybekov
Keyword(s):  
Fourth Order ◽  
Operator Pencil ◽  
Order Operator

The Oscillation of Fourth Order Linear Differential Operators

1975 ◽  
Vol 27 (1) ◽  
pp. 138-145 ◽  
Author(s):  
Roger T. Lewis
Keyword(s):  
Fourth Order ◽  
Differential Operators ◽  
Adjoint Operator ◽  
Oscillatory Behavior ◽  
The Self ◽  
Order Operator ◽  
Order Linear ◽  
Linear Differential Operators ◽  
Even Order ◽  
Linear Differential

Define the self-adjoint operatorwhere r(x) > 0 on (0, ∞) and q and p are real-valued. The coefficient q is assumed to be differentiate on (0, ∞) and r is assumed to be twice differentia t e on (0, ∞).The oscillatory behavior of L4 as well as the general even order operator has been considered by Leigh ton and Nehari [5], Glazman [2], Reid [7], Hinton [3], Barrett [1], Hunt and Namb∞diri [4], Schneider [8], and Lewis [6].

scholarly journals The fourth order strongly noncanonical operators

2018 ◽  
Vol 16 (1) ◽  
pp. 1667-1674 ◽  
Author(s):  
Blanka Baculikova ◽  
Jozef Dzurina
Keyword(s):  
Canonical Form ◽  
Fourth Order ◽  
Canonical Representation ◽  
Order Operator

AbstractIt is shown that the strongly noncanonical fourth order operator$$\begin{array}{} \displaystyle \mathcal {L}\,y=\left(r_3(t)\left(r_2(t)\left(r_1(t)y'(t)\right)'\right)'\right)' \end{array}$$can be written in essentially unique canonical form as$$\begin{array}{} \displaystyle \mathcal {L}\,y = q_4(t)\left(q_3(t)\left(q_2(t)\left(q_1(t)\left(q_0(t)y(t)\right)'\right)'\right)'\right)'. \end{array}$$The canonical representation essentially simplifies examination of the fourth order strongly noncanonical equations$$\begin{array}{} \displaystyle \left(r_3(t)\left(r_2(t)\left(r_1(t)y'(t)\right)'\right)'\right)'+p(t)y(\tau(t))=0. \end{array}$$

Sign in / Sign up

Export Citation Format

Share Document