author = {Dup'e, F. -X. and Brun, L.}, title = {Shape classification using a flexible graph kernel}, booktitle = {Proceedings of CAIP 2009}, year = 2009, editor = {Xiaoyi Jiang}, month = {September}, publisher = {LNCS}, theme={shape,pattern}, url={paper(pdf):=https://brunl01.users.greyc.fr/ARTICLES/caip2009.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 o ne 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, s uch a graph is usually transformed into a simpler structure such as a tree or a simp le 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. T he 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 empha sis on the holes of the shapes and hence on their genre. The resulting graph kernel is po sitive semi-definite on the graph domain.}