We propose a Modified Fourier Descriptor and a new distance metric for describing and comparing closed planar curves. Our method accounts for the effects of spatial discretization of shapes, an issue seldom mentioned, much less addressed in the literature. The motivating application is shape matching in a content based image retrieval system. The application requires a compact and reliable shape representation, and a feature distance measure which can be computed in real time. Experimental results suggest that our method is a feasible solution for on-line shape comparisons in such a system.