TY - GEN
T1 - Point pattern matching via spectral geometry
AU - Robles-Kelly, Antonio
AU - Hancock, Edwin R.
PY - 2006
Y1 - 2006
N2 - In this paper, we describe the use of Riemannian geometry, and in particular the relationship between the Laplace-Beltrami operator and the graph Laplacian, for the purposes of embedding a graph onto a Riemannian manifold. Using the properties of Jacobi fields, we show how to compute an edge-weight matrix in which the elements reflect the sectional curvatures associated with the geodesic paths between nodes on the manifold. We use the resulting edge-weight matrix to embed the nodes of the graph onto a Riemannian manifold of constant sectional curvature. With the set of embedding coordinates at hand, the graph matching problem is cast as that of aligning pairs of manifolds subject to a geometric transformation. We illustrate the utility of the method on image matching using the COIL database.
AB - In this paper, we describe the use of Riemannian geometry, and in particular the relationship between the Laplace-Beltrami operator and the graph Laplacian, for the purposes of embedding a graph onto a Riemannian manifold. Using the properties of Jacobi fields, we show how to compute an edge-weight matrix in which the elements reflect the sectional curvatures associated with the geodesic paths between nodes on the manifold. We use the resulting edge-weight matrix to embed the nodes of the graph onto a Riemannian manifold of constant sectional curvature. With the set of embedding coordinates at hand, the graph matching problem is cast as that of aligning pairs of manifolds subject to a geometric transformation. We illustrate the utility of the method on image matching using the COIL database.
UR - http://www.scopus.com/inward/record.url?scp=33749618145&partnerID=8YFLogxK
U2 - 10.1007/11815921_50
DO - 10.1007/11815921_50
M3 - Conference contribution
SN - 3540372369
SN - 9783540372363
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 459
EP - 467
BT - Structural, Syntactic, and Statistical Pattern Recognition - Joint IAPR International Workshops, SSPR 2006 and SPR 2006, Proceedings
PB - Springer Verlag
T2 - Joint IAPR International Workshops on Structural, Syntactic, and Statistical Pattern Recognition, SSPR 2006 and SPR 2006
Y2 - 17 August 2006 through 19 August 2006
ER -