author = {Dup'e, F. -X. and Brun, L.}, title = {Tree covering within a graph kernel framework for shape classification.}, booktitle = {ICIAP 2009}, year = {2009}, theme={shape,pattern}, series = {Lecture Notes in Computer Science}, volume = 5716, publisher = {Springer}, editor = {Pasquale Foggia and Carlo Sansone and Mario Vento}, pages = {278-287}, url ={paper(pdf):=https://brunl01.users.greyc.fr/ARTICLES/ICIAP2009DupeBrun.pdf}, abstract={ 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.}