1. A Global Geometric Framework for Nonlinear Dimensionality Reduction
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5. For a surface represented as a polyhedral mesh exact geodesics can be computed in exponential time (2). However geodesics between all pairs of vertices on the mesh can be approximated in O ( N log N ) time using Dijkstra's algorithm to compute the shortest path along the edges of the polygons in the mesh (4). For meshes with O (10 3 ) vertices exact geodesics can be computed in about 10 min on a 500-MHz Pentium III PC; for much larger meshes faster approximation schemes are desirable.