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Edition within a graph kernel framework for shape recognition

F. -X. Dupe &
L. Brun.
The medial axis being an homotopic transformation, the
skeleton of a 2D shape corresponds to a planar graph having one face
for each hole of the shape and one node for each junction or
extremity of the branches. This graph is non simple since it can be
composed of loops and multiple-edges. Within the shape comparison
framework, such a graph is usually transformed into a simpler
structure such as a tree or a simple graph hereby loosing major
information about the shape. In this paper, we propose a graph
kernel combining a kernel between bags of trails and a kernel
between faces. The trails are defined within the original complex
graph and the kernel between trails is enforced by an edition
process. The kernel between bags of faces allows to put an emphasis
on the holes of the shapes and hence on their genre. The resulting
graph kernel is positive semi-definite on the graph domain.