Applying multiquadric quasi-interpolation for boundary detection

In this paper, we propose a novel scheme for simulating geometric active contours (geometric flow) of one kind, applying multiquadric (MQ) quasi-interpolation. We first represent the geometric flow in its parametric form. Then we obtain the numerical scheme by using the derivatives of the quasi-inte...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2011-12, Vol.62 (12), p.4356-4361
Main Authors: Gao, Qinjiao, Wu, Zongmin, Zhang, Shenggang
Format: Article
Language:English
Subjects:
Approximation
Boundaries
Boundary detection
Computer simulation
Curve evolution
Dependent variables
Derivatives
Geodesic active contour
Mathematical models
Multiquadric quasi-interpolation
Partial differential equation
Radial basis function
Temporal logic
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Summary:In this paper, we propose a novel scheme for simulating geometric active contours (geometric flow) of one kind, applying multiquadric (MQ) quasi-interpolation. We first represent the geometric flow in its parametric form. Then we obtain the numerical scheme by using the derivatives of the quasi-interpolation to approximate the spatial derivative of each dependent variable and a forward difference to approximate the temporal derivative of each dependent variable. The resulting scheme is simple, efficient and easy to implement. Also images with complex boundaries can be more easily proposed on the basis of the good properties of the MQ quasi-interpolation. Several biomedical and astronomical examples of applications are shown in the paper. Comparisons with other methods are included to illustrate the validity of the method.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2011.09.069