Different shape representation and classification methods for complex medical lesions were compared using oral lesions as a case study. The problem studied was the discrimination between potentially cancerous lesions, called leukoplakia, and other usually harmless lesions, called lichenoid reactions, which can appear in human oral cavities. The classification problem is difficult because these lesions vary in shape within classes and there are no easily recognizable characteristics. The representations evaluated were the centroidal profile function, the curvature function, and polar and complex coordinate functions. From these representations, translation, scale and rotation independent features were derived using Fourier transformations, auto-regressive modeling, and Zernike moments. A nonparametric kNN classifier with the leave-one-out cross-validation method was used as a classifier. An overall classification accuracy of about 84% was achieved using only the shape properties of the lesions, compared with a human visual classification rate of 65%. The best results were obtained using complex representation and Fourier/Zernike methods. In clinical practice, the preliminary diagnosis is based mainly on the visual inspection of the oral cavity, using both color, shape and texture as differentiating parameters. This study showed that machine analysis of shape could also play an important part in diagnosis and decisions regarding future treatment.