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An algorithm, based on the Mumford-Shah (M-S) functional, for image contour segmentation and object smoothing in the presence of noise is proposed. However, in the proposed algorithm, contour length minimisation is not required and it is demonstrated that the M-S functional without contour length minimisation becomes an edge detector. Optimisation of this nonlinear functional is based on the method of calculus of variations, which is implemented by using the level set method. Fourier and Legendre's series are also employed to improve the segmentation performance of the proposed algorithm. The segmentation results clearly demonstrate the effectiveness of the proposed approach for images with low signal-to-noise ratios.