Metrics Spaces for the Matrix Groups
Metrics Spaces for the Matrix Groups
In this chapter the metric space structure of shape is developed. We do this by first studying the action of the matrix groups on the coordinate systems of shape. We begin by reviewing the well-known properties of the finite-dimensional matrix groups, including their properties as smooth Riemannian manifolds, allowing us to develop metric distances between the groupelements. 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 and subsequently in the infinite dimensional setting as well.
Keywords: Burger’s equation, N-shapes, differential operators, landmark mapping
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