Metrics Spaces for the Infinite Dimensional Diffeomorphisms
Metrics Spaces for the Infinite Dimensional Diffeomorphisms
In this chapter the metric space structure of shape is developed by studying the action of the infinite dimensional diffeomorphisms on the coordinate systems of shape. Riemannian manifolds allow us to developmetric distances between the groupelements. We examine the natural analog of the finite dimensional matrix groups corresponding to the infinite dimensional diffeomorphisms which are generated as flows of ordinary differential equations.We explore the construction of the metric structure of these diffeomorphisms and develop many of the properties which hold for the finite dimensional matrix groups in this infinite dimensional setting.
Keywords: affine motions, elastic matching, facial expressions, geodesic shooting, inexact matching, left invariance, photometric variability, scaling, viscous matching
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