Many-to-many feature matching using spherical coding of directed graphs


Fatili Demirci M. F. , Shokoufandeh A., Dickinson S., Keselman Y., Bretzner L.

8th European Conference on Computer Vision, ECCV 2004, Prague, Czech Republic, 11 - 14 May 2004, vol.3021, pp.325-332 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 3021
  • City: Prague
  • Country: Czech Republic
  • Page Numbers: pp.325-332

Abstract

© Springer-Verlag Berlin Heidelberg 2004.Abstract. In recent work, we presented a framework for many-to-many matching of multi-scale feature hierarchies, in which features and their relations were captured in a vertex-labeled, edge-weighted directed graph. The algorithm was based on a metric-tree representation of labeled graphs and their metric embedding into normed vector spaces, using the embedding algorithm of Matousek [13]. However, the method was limited by the fact that two graphs to be matched were typically embedded into vector spaces with different dimensionality. Before the embeddings could be matched, a dimensionality reduction technique (PCA) was required, which was both costly and prone to error. In this paper, we introduce a more efficient embedding procedure based on a spherical coding of directed graphs. The advantage of this novel embedding technique is that it prescribes a single vector space into which both graphs are embedded. This reduces the problem of directed graph matching to the problem of geometric point matching, for which efficient many-to-many matching algorithms exist, such as the Earth Mover's Distance. We apply the approach to the problem of multi-scale, view-based object recognition, in which an image is decomposed into a set of blobs and ridges with automatic scale selection.