Existing polyp detection methods rely heavily on curvature-based characteristics to differentiate between lesions. These assume that the discrete triangulated surface mesh or volume closely approximates a smooth continuous surface. However, this is often not the case and because curvature is computed as a local feature and a second-order differential quantity, the presence of noise significantly affects its estimation. For this reason, a more global feature is required to provide an accurate description of the surface at hand. In this paper, a novel method incorporating a local neighborhood around the centroid of a surface patch is proposed. This is done using geodesic rings which accumulate curvature information in a neighborhood around this centroid. This geodesic-ring neighborhood approximates a single smooth, continuous surface upon which curvature and orientation estimation methods can be applied. A new global shape index, S is also introduced and computed. These curvature and orientation values will be used to classify the surface as either a bulbous polyp, ridge-like fold or semiplanar structure. Experimental results show that this method is promising (100% sensitivity, 100% specificity for lesions >;10 mm) for distinguishing between bulbous polyps, folds and planar-like structures in the colon.