A scale-space Reeb-graph of topological invariants of images and its applications to content identification

Authors:
Jinhui Chao;Shintaro Suzuki
Affiliations:
Department of Information and System Engineering, Chuo University, Tokyo, Japan;Department of Information and System Engineering, Chuo University, Tokyo, Japan
Venue:
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Year:
2007

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Abstract

In this paper, a new method of content identification using topological invariants is proposed. First, we show a Reeb-graph of topological invariants of images in a scale-space. Different from well-known scale-space trees of salient or critical points based on catastrophe or singularity theory, we use topologically stable blobs or primary sketches with nonzero lifetimes in scale and nonzero areas at each scale. The continuum of such blobs as a 3D manifold is featured by trees of topological invariants of the image called a Reeb graph. We show that this Reeb-graph representation is more robust against deformation attacks and perturbation such as numerical errors than traditional scale-space trees. A fast matching algorithm for the graphs is also presented.