Abstract: This paper proposes an adaptive method for simulating one kind of geometric active contours
(GAC) applying multiquadric (MQ) quasi-interpolation. The geometric flow is presented in its
parametric form. Then the numerical scheme is obtained: Firstly the spatial derivatives of each variable
are approximated applying the MQ quasi-interpolation; secondly the knots are moved according to the
moving knots equation to pull the knots to concentrate in regions with large variations. Thirdly the
forward difference methods are applied to approximate the temporal derivative of each variable. The
resulting scheme is simple, efficient and easy to implement. Also images with complex boundaries can
be simulated more efficiently on the basis of the good properties of the adaptive MQ method. Several
examples of applications are shown in the paper.

Key words: boundary detection, adaptive method, geometric active contours, MQ quasi-interpolation