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- Alice Barbara Tumpach, Hassen Drira, Mohamed Daoudi, Anuj Srivastava
- IEEE Transactions on Pattern Analysis and Machine…
- 2016

This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) space, rather than inheriting it from pre-shape space, and using it to formulate a path energy that measures only the normal… (More)

In this paper, we construct a hyperkähler structure on the complexification OC of any Hermitian symmetric affine coadjoint orbit O of a semi-simple L∗-group of compact type, which is compatible with the complex symplectic form of Kirillov-Kostant-Souriau and restricts to the Kähler structure of O. By the identification of the complex orbit OC with the… (More)

In this paper, we describe an example of a hyperkähler quotient of a Banach manifold by a Banach Lie group. Although the initial manifold is not diffeomorphic to a Hilbert manifold (not even to a manifold modelled on a reflexive Banach space), the quotient space obtained is a Hilbert manifold, which can be furthermore identified either with the cotangent… (More)

In the finite-dimensional setting, every Hermitian-symmetric space of compact type is a coadjoint orbit of a finite-dimensional Lie group. It is natural to ask whether every infinite-dimensional Hermitiansymmetric space of compact type, which is a particular example of an Hilbert manifold, is transitively acted upon by a Hilbert Lie group of isometries. In… (More)

Mostow’s Decomposition Theorem is a refinement of the polar decomposition. It states the following. Let G be a compact connected semi-simple Lie group with Lie algebra g. Given a subspace h of g such that [X, [X,Y ]] ∈ h for all X , Y in h, the complexified group G is homeomorphic to the product G · exp im · exp ih, where m is the orthogonal of h in g with… (More)

In this paper, we describe an example of a hyperkähler quotient of a Banach manifold by a Banach Lie group. Although the initial manifold is not diffeomorphic to a Hilbert manifold (not even to a manifold modelled on a reflexive Banach space), the quotient space obtained is a Hilbert manifold, which can furthermore be identified either with the cotangent… (More)

Introduction Having applications to Form recognition in mind, we want to be able to compare shapes of surfaces in R3 in a way that does not depend on parameterizations. To accomplish such so-called gauge invariance, we defined a metric on the space of parameterized surfaces that is degenerate in the direction of reparameterization. 1 What are the surfaces… (More)

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