The extraction of crack images is an important process in the area of structural health monitoring for determining the severity of the damage induced by cracks. In this paper, a radial basis functions (RBFs) based level set interpolation technique is proposed to extract the images of cracks in structures. In the proposed method, the level set in the form of radial basis functions with an ellipse constraint can represent accurately various shapes without requiring building interior and exterior layers for the sparse mesh grid of RBFs centers or using information on contour/surface normal. The initial distance function embedded in the ellipse-constrained RBFs can be interpolated on a much coarser grid. Its deformation is considered as an updating of the RBFs coefficients by solving an ordinary differential equation (ODE) and a non-convex quadratically constrained quadratic programming (QCQP). The use of a semi-definite relaxation technique in solving the non-convex QCQP problem has shown that initialization and re-initialisation are no longer necessary. The images of a number of cracks have been extracted using the proposed method. It has been shown that the proposed method can extract crack images efficiently with coarse grid of RBFs centers and is also less sensitive to the distribution of the crack images in the domain.