Matching delaunay graphs

Abstract

Abstract--This paper describes a Bayesian framework for matching Delaunay triangulations. Relational structures of this sort are ubiquitous in intermediate level computer vision, being used to represent both Voronoi tessellations of the image plane and volumetric surface data. Our matching process is realised in terms of probabilistic relaxation. The novelty of our method stems from its use of a support function specified in terms of face-units of the graphs under match. In this way, we draw on more expressive constraints than is possible at the level of edge-units alone. In order to apply this new relaxation process to the matching of realistic imagery requires a model of the compatibility between faces of the data and model graphs. We present a particularly simple compatibility model that is entirely devoid of free parameters. It requires only knowledge of the numbers of nodes, edges and faces in the model graph. The resulting matching scheme is evaluated on radar images and compared with its edge-based counterpart. We establish the operational limits and noise sensitivity on the matching of random-dot patterns. Copyright © 1996 Pattern Recognition Society. Published by Elsevier Science Ltd. Graph matchingRelaxation labelling Delaunay triangulation t. INTRODUCTIONDelaunay triangulations pervade computer vision. They not only provide a convenient and robust neighbourhood representation for Voronoi tessellations of the image plane, (1-3) but also provide a powerful geometric representation for volumetric information. (4-7) Ahuja (1-3) has promoted their use as a device for representing the early perceptual structure of dot patternsJ 8) Some of the computational advantages have been demonstrated by Tuceryan and Chorzempa (9) who show that the Delaunay graph has optimal stability to noise when compared with a number of alternative 2D neighbourhood graphs. Boissonnat (4) has established their effectiveness as a convenient volumetric surface representation in computational geometry. In the context of 3D vision, Faugeras et alJ 5) have identified the discontinuity preserving properties of Delaunay graphs and exploited them as a surface reconstruction device. More recently, triangulations have been exploited in the construction of deformable shape models. (7'6) Despite their widespread use and attractive computational features, little effort has been devoted to devising effective means for matching Delaunay graphs. This is surprising since the inexact graph matching problem has been the focus of sustained activity in a number of distinct methodological areas for over three decades. ~1°-17) One of the earliest practical matching techniques was the association graph idea of Barrow et alJ 18) In essence, this allowed subgraph isomorphisms to be located by transforming the matching process into one of searching for maximal cliques in an association graph. This idea was later exploited by Horaud and Skordas °1) for stereo matching. Symbolic scene descriptions have also been matched using consistent labelling techniques (14...

Low frame rate cell tracking: A Delaunay graph matching approach

“…Delaunay triangulation graph [3] has been widely used in finger print matching, face recognition, etc. The Delaunay triangulation for a set of points P in a plane is a triangulation DT (P ) in which no point in P is inside the circumcircle of any triangle in DT (P ).…”

“…The classical joint probabilistic data association filter can be applied in such tracking, but it relies on a motion model of the target which is usually unknown in root growth. Motivated by the fact that root meristem is a largely invariant structure made up of few tissue types that undergo predictable divisions and woody cells [2], we propose a novel method for low frame rate multi-cell tracking by Delaunay triangulation graph [3] matching.…”

A graph matching method and a graph matching distance based on subgraph assignments

“…However, since the similarity function which they minimize can converge in a local minimum, they may not find the optimal solution. Perhaps, the most successful of the optimization methods for graph matching use some form of probabilistic relaxation (Christmas and Kittler, 1995;Finch and Wilson, 1997;Wilson and Hancock, 1996). The idea is similar to the discrete relaxation methods; however, the compatibility constraints between vertexto-vertex assignments do not have a binary formulation, but are defined in terms of a probability function that is iteratively updated by the relaxation procedure.…”

A general shape context framework for object identification

“…Their performances were found inferior to the 6NN and ALSBIR since they did not make full use of the structural information recorded in the hyper cube. The 6NN was proposed by Huet and Hancock to compare with other graph structures, such as the Delaunay graph [31]. 6NN was found to perform the best.…”