International Symposium on Nonlinear Theory and its Applications
A scale-space Reeb-graph of topological invariants of images and its applications to copyright protection
Jinhui Chaof, Shintaro Suzuki,
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In this paper, 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, used in image retrieving/processing and pattern recognition, we use topologically stable blobs or primary sketchs with nonzero life times in scale and nonzero areas at each scale. The continuum of such blobs as a 3D manifold is featured by tree of topological invariants called 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 graph is also presented. This scale-space Reeb-graph can be applied to passive watermark, copyright tracing/monitoring and protection.