Abstract A perennial problem in structure from motion (SfM) is visual ambiguity posed by repetitive structures. Recent disambiguating algorithms infer ambiguities mainly via explicit background context, thus face limitations in highly ambiguous scenes which are visually indistinguishable. Instead of analyzing local visual information, we propose a novel algorithm for SfM disambiguation that explores the global topology as encoded in photo collections. An important adaptation of this work is to approximate the available imagery using a manifold of viewpoints. We note that, while ambiguous images appear deceptively similar in appearance, they are actually located far apart on geodesics. We establish the manifold by adaptively identifying cameras with adjacent viewpoint, and detect ambiguities via a new measure, geodesic consistency. We demonstrate the accuracy and efficiency of the proposed approach on a range of complex ambiguity datasets, even including the challenging scenes without background conflicts.