Applying multiquadric quasi-interpolation for boundary detection

Authors:
Qinjiao Gao;Zongmin Wu;Shenggang Zhang
Affiliations:
Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai, 200433, PR China;Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai, 200433, PR China;Department of Health Statistics, Dalian Medical University, Dalian, 116044, PR China
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

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.