With the aim to improve the performance of feature matching, we present an unsupervised approach to fuse various local descriptors in the space of homographies. Inspired by the observation that the homographies of correct feature correspondences vary smoothly along the spatial domain, our approach stands on the unsupervised nature of feature matching, and can select a good descriptor for matching each feature point. Specifically, the homography space serves as the common domain, in which a correspondence obtained by any descriptor is considered as a point, for integrating various heterogeneous descriptors. Both geometric coherence and spatial continuity among correspondences are considered via computing their geodesic distances in the space. In this way, mutual verification across different descriptors is allowed, and correct correspondences will be highlighted with a high degree of consistency (i.e., short geodesic distances here). It follows that one-class SVM can be applied to identifying these correct correspondences, and boosts the performance of feature matching. The proposed approach is comprehensively compared with the state-of-the-art approaches, and evaluated on four benchmarks of image matching. The promising results manifest its effectiveness.