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 novel construction that encodes the scale space description of top points in the form of a directed acyclic graph. This representation allows us to utilize coarse-to-fine graph matching algorithms for comparing images represented in terms of top point configurations instead of using solely the top points and their features in a point matching algorithm, as was done previously. The nodes of the graph represent the critical paths together with their top points. The edge set captures the neighborhood distribution of vertices in scale space, and is constructed through a hierarchical tessellation of scale space using a Delaunay triangulation of the top points. We present a coarse-to-fine many-to-many matching algorithm for comparing such graph-based representations. The algorithm is based on a metric-tree representation of labeled graphs and their low-distortion embeddings into normed vector 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, four sets of experiments are performed. First, the stability of this representation under Gaussian noise of increasing magnitude is examined. Second, a series of recognition experiments is run on a face database. Third, a set of clutter and occlusion experiments is performed to measure the robustness of the algorithm. Fourth, the algorithm is compared to a leading interest point-based framework in an object recognition experiment.

# The Representation and Matching of Images Using Top Points

M. Demirci, B. Platel, A. Shokoufandeh, L. Florack and S. Dickinson

Journal of Mathematical Imaging and Vision 2009;35(2):103-116.