In this paper, we propose a variational method to segment image objects, which have a given parametric shape based on a level-set formulation of the Mumford-Shah functional, and the shape parameters. We define an energy functional composed by two complementary terms. The first one detects object boundaries using a Chan-Vese-like method. The second term constrains the contour to find a shape compatible with the parametric shape. The segmentation of the object of interest is given by the minimum of our energy functional. This minimum is computed with the calculus of variation and the gradient descent method that provide a system of evolution equations solved with the well-known level set method. We focus in this paper on the parametric category of image linear objects. Applications of the proposed model are presented on synthetic and real images.