Nearest-neighbor search algorithms on non-euclidean manifolds for computer vision applications

Pavan Turaga, Rama Chellappa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Scopus citations

Abstract

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.

Original languageEnglish (US)
Title of host publicationProceedings - 7th Indian Conference on Computer Vision, Graphics and Image Processing, ICVGIP 2010
Pages282-289
Number of pages8
DOIs
StatePublished - Dec 1 2010
Externally publishedYes
Event7th Indian Conference on Computer Vision, Graphics and Image Processing, ICVGIP 2010 - Chennai, India
Duration: Dec 12 2010Dec 15 2010

Publication series

NameACM International Conference Proceeding Series

Other

Other7th Indian Conference on Computer Vision, Graphics and Image Processing, ICVGIP 2010
CountryIndia
CityChennai
Period12/12/1012/15/10

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Keywords

  • Grassmann manifold
  • Hashing
  • Manifold
  • Nearest-neighbor
  • Region covariance
  • Shapes

ASJC Scopus subject areas

  • Software
  • Human-Computer Interaction
  • Computer Vision and Pattern Recognition
  • Computer Networks and Communications

Cite this

Turaga, P., & Chellappa, R. (2010). Nearest-neighbor search algorithms on non-euclidean manifolds for computer vision applications. In Proceedings - 7th Indian Conference on Computer Vision, Graphics and Image Processing, ICVGIP 2010 (pp. 282-289). (ACM International Conference Proceeding Series). https://doi.org/10.1145/1924559.1924597