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We propose a new affine-covariant feature, the stable affine frame (SAF). SAFs lie on the boundary of extremal regions, i.e. on isophotes. Instead of requiring the whole isophote to be stable with respect to intensity perturbation as in maximally stable extremal regions (MSERs), stability is required only locally, for the primitives constituting the three-point frames. The primitives are extracted by an affine invariant process that exploits properties of bitangents and algebraic moments. Thus, instead of using closed stable isophotes, i.e. MSERs, and detecting affine frames on them, SAFs are sought even on some unstable extremal regions. We show experimentally on standard datasets that SAFs have repeatability comparable to the best affine covariant detectors tested in the state-of-the-art report (Mikolajczyk et al., 2005) and consistently produce a significantly higher number of features per image. Moreover, the features cover images more evenly than MSERs, which facilitates robustness to occlusion.