Discrete Representation of Top Points via Scale Space Tessellation B. Platel 1 , M. Fatih Demirci 2 , A. Shokoufandeh 2 , L.M.J. Florack 1 , F.M.W. Kanters 1 , B.M. ter Haar Romeny 1 , and S.J. Dickinson 3 1 Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands 2 Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, United States of America 3 University of Toronto, 6 King’s College Rd., Toronto, Ontario, Canada M5S 3G4 b.platel@tue.nl, {mdemirci, ashokouf}@cs.drexel.edu {l.m.j.florack, f.m.w.kanters, b.m.terhaarromeny}@tue.nl sven@cs.toronto.edu Abstract. In previous work, singular points (or top points) in the scale space representation of generic images have proven valuable for image matching. In this paper, we propose a construction that encodes the scale space description of top points in the form of a directed acyclic graph. This representation allows us to utilize graph matching algorithms for comparing images represented in terms of top point configurations in- stead of using solely the top points and their features in a point match- ing algorithm, as was done previously. The nodes of the graph represent the critical paths together with their top points. The edge set will cap- ture the neighborhood distribution of vertices in scale space, and is con- structed through a Delaunay triangulation scheme. We also will present a many-to-many matching algorithm for comparing such graph-based representations. This algorithm is based on a metric-tree representation of labelled graphs and their low-distortion embeddings into normed vec- tor spaces via spherical encoding. This is a two-step transformation that reduces the matching problem to that of computing a distribution-based distance measure between two such embeddings. To evaluate the quality of our representation, two sets of experiments are considered. First, the stability of this representation under Gaussian noise of increasing magni- tude is examined. In the second set of experiments, a series of recognition experiments is run on a small face database. 1 Introduction Previous research has shown that top points (singular points in the scale space representation of generic images) have proven to be valuable sparse image de- scriptors that can be used for image reconstruction [6, 12] and image matching [7, 14]. In our previous work, images were compared using a point matching R. Kimmel, N. Sochen, J. Weickert (Eds.): Scale-Space 2005, LNCS 3459, pp. 73–84, 2005. c  Springer-Verlag Berlin Heidelberg 2005