Automatic¯ngerprint identi¯cation systems (AFIS) have been studied extensively and are widely used for biometric identi¯cation. Given its importance, many well-engineered methods have been developed for the di®erent stages that encompass those systems. The¯rst stage of any such system is the segmentation of the actual¯ngerprint region from the background. This is typically achieved by classifying pixels, or blocks of pixels, based on a set of features. In this paper, we describe novel features for¯ngerprint segmentation that express the underlying manifold topology associated with image patches in a local neighborhood. It is shown that ngerprint patches seen in a high-dimensional space form a simple and highly regular circular manifold. The characterization of the manifold topology suggests a set of optimal features that characterize the local properties of the¯ngerprint. Thus,¯ngerprint segmentation can be formulated as a classi¯cation problem based on the deviation from the expected topology. This leads to features that are more robust to changes in contrast than mean, variance and coherence. The superior performance of the proposed features for¯ngerprint segmentation is shown in the eight datasets from the 2002 and 2004 Fingerprint Veri¯cation Competitions.