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Iterative methods for obtaining energy-minimizing parametric snakes with applications to medical imaging.

Mitrea AI, Badea R, Mitrea D, Nedevschi S, Mitrea P, Ivan DM, Gurzău OM - Comput Math Methods Med (2012)

Bottom Line: After a brief survey on the parametric deformable models, we develop an iterative method based on the finite difference schemes in order to obtain energy-minimizing snakes.We estimate the approximation error, the residue, and the truncature error related to the corresponding algorithm, then we discuss its convergence, consistency, and stability.Some aspects regarding the prosthetic sugical methods that implement the above numerical methods are also pointed out.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Technical University of Cluj-Napoca, George Baritiu Street, No. 25, 400020 Cluj-Napoca, Romania.

ABSTRACT
After a brief survey on the parametric deformable models, we develop an iterative method based on the finite difference schemes in order to obtain energy-minimizing snakes. We estimate the approximation error, the residue, and the truncature error related to the corresponding algorithm, then we discuss its convergence, consistency, and stability. Some aspects regarding the prosthetic sugical methods that implement the above numerical methods are also pointed out.

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Mentions: If we choose in (12) w1 = 1, w2 = 0.05, and the boundary conditions v(0) = v(1) = (0,5)T, v′(0) = v′(1) = (0.5,0.5)T we obtain the general solution of the (ELP) equation:(15)x(s)=C1e3.8042s+C2e−3.8042s+C3e2.3511s+C4e−2.3511s,y(s)=C5e3.8042s+C6e−3.8042s+C7e2.3511s+C8e−2.3511s.Using boundary conditions, we obtain the graph of the curve (γ) in Figure 1.


Iterative methods for obtaining energy-minimizing parametric snakes with applications to medical imaging.

Mitrea AI, Badea R, Mitrea D, Nedevschi S, Mitrea P, Ivan DM, Gurzău OM - Comput Math Methods Med (2012)

© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3303766&req=5

Mentions: If we choose in (12) w1 = 1, w2 = 0.05, and the boundary conditions v(0) = v(1) = (0,5)T, v′(0) = v′(1) = (0.5,0.5)T we obtain the general solution of the (ELP) equation:(15)x(s)=C1e3.8042s+C2e−3.8042s+C3e2.3511s+C4e−2.3511s,y(s)=C5e3.8042s+C6e−3.8042s+C7e2.3511s+C8e−2.3511s.Using boundary conditions, we obtain the graph of the curve (γ) in Figure 1.

Bottom Line: After a brief survey on the parametric deformable models, we develop an iterative method based on the finite difference schemes in order to obtain energy-minimizing snakes.We estimate the approximation error, the residue, and the truncature error related to the corresponding algorithm, then we discuss its convergence, consistency, and stability.Some aspects regarding the prosthetic sugical methods that implement the above numerical methods are also pointed out.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Technical University of Cluj-Napoca, George Baritiu Street, No. 25, 400020 Cluj-Napoca, Romania.

ABSTRACT
After a brief survey on the parametric deformable models, we develop an iterative method based on the finite difference schemes in order to obtain energy-minimizing snakes. We estimate the approximation error, the residue, and the truncature error related to the corresponding algorithm, then we discuss its convergence, consistency, and stability. Some aspects regarding the prosthetic sugical methods that implement the above numerical methods are also pointed out.

Show MeSH