TY - CONF T1 - Nearest-neighbor search algorithms on non-Euclidean manifolds for computer vision applications T2 - Proceedings of the Seventh Indian Conference on Computer Vision, Graphics and Image Processing Y1 - 2010 A1 - Turaga,Pavan A1 - Chellapa, Rama KW - Grassmann manifold KW - hashing KW - manifold KW - nearest-neighbor KW - region covariance KW - shapes AB - Nearest-neighbor searching is a crucial component in many computer vision applications such as face recognition, object recognition, texture classification, and activity recognition. When large databases are involved in these applications, it is also important to perform these searches in a fast manner. Depending on the problem at hand, nearest neighbor strategies need to be devised over feature and model spaces which in many cases are not Euclidean in nature. Thus, metrics that are tuned to the geometry of this space are required which are also known as geodesics. In this paper, we address the problem of fast nearest neighbor searching in non-Euclidean spaces, where in addition to dealing with the large size of the dataset, the significant computational load involves geodesic computations. We study the applicability of the various classes of nearest neighbor algorithms toward this end. Exact nearest neighbor methods that rely solely on the existence of a metric can be extended, albeit with a huge computational cost. We derive an approximate method of searching via approximate embeddings using the logarithmic map. We study the error incurred in such an embedding and show that it performs well in real experiments. JA - Proceedings of the Seventh Indian Conference on Computer Vision, Graphics and Image Processing T3 - ICVGIP '10 PB - ACM CY - New York, NY, USA SN - 978-1-4503-0060-5 UR - http://doi.acm.org/10.1145/1924559.1924597 M3 - 10.1145/1924559.1924597 ER -