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S. Kh. Aranson V. Z. Grines V. A. Kaimanovich 《Journal of Dynamical and Control Systems》2003,9(4):455-468
We obtain a complete classification of supertransitive 2-webs on a closed oriented surface of genus p 1 in terms of asymptotic directions of leaves on the universal covering surface and represent all topological classes of 2-webs by means of compatible pairs of transversal perfect geodesic laminations. 相似文献
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In this paper, motivated by the restrictive conditions required to obtain an exact chained form, we propose a quadratic normal
form around a one-dimensional equilibrium submanifold for systems which are in a chained form in their first approximation.
In the case considered here, in contrast to the case of approximated feedback linearization, not all the state and input components
have the same approximation meaning. Because of this, we use a very simplified version of dilation, which is a useful way
to design a homogeneous control law for driftless systems.
Date received: December 2, 1999. Date revised: October 24, 2001. 相似文献
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We will consider a convex subset of a metric linear space and a certain group of actions G on this set, that allow us to define the notion of Haar zero measure on sets that have zero Haar measure for the translation (by adding) invariant HSY prevalence theory. In this way, we will be able to define the meaning of G-prevalent set according to the pioneering work of Christensen. Our setting considers problems which take into account the convex structure and this is quite different from the previous results on prevalence which consider basically the linear additive structure. In this setting, we will show a kind of quantitative Kupka–Smale theorem, and also we generalize a result about rotation numbers which was first considered by J.-C. Yoccoz (and, also by M. Tsujii). Among other things we present an estimation of the amount of hyperbolicity in a setting that we believe was not considered before. 相似文献
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In a previous paper, it was proposed to see the deformations of a common pattern as the action of an infinite dimensional group. We show in this paper that this approac h can be applied numerically for pattern matching in image analysis of digital images. Using Lie group ideas, we construct a distance between deformations defined through a metric given the cost of infinitesimal deformations. Then we propose a numerical scheme to solve a variational problem involving this distance and leading to a sub-optimal gradient pattern matching. Its links with fluid models are established. 相似文献
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Transport of Relational Structures in Groups of Diffeomorphisms 总被引:1,自引:0,他引:1
Laurent Younes Anqi Qiu Raimond L. Winslow Michael I. Miller 《Journal of Mathematical Imaging and Vision》2008,32(1):41-56
This paper focuses on the issue of translating the relative variation of one shape with respect to another in a template centered
representation. The context is the theory of Diffeomorphic Pattern Matching which provides a representation of the space of
shapes of objects, including images and point sets, as an infinite dimensional Riemannian manifold which is acted upon by
groups of diffeomorphisms. We discuss two main options for achieving our goal; the first one is the parallel translation,
based on the Riemannian metric; the second one, based on the group action, is the coadjoint transport. These methods are illustrated
with 3D experiments.
相似文献
Laurent YounesEmail: |
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We show how knots in
appear in a natural way as complete invariants of topological conjugacy for the simplest gradient-like diffeomorphisms on 3-manifolds. 相似文献
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2D-Shape Analysis Using Conformal Mapping 总被引:1,自引:0,他引:1
The study of 2D shapes and their similarities is a central problem in the field of vision. It arises in particular from the task of classifying and recognizing objects from their observed silhouette. Defining natural distances between 2D shapes creates a metric space of shapes, whose mathematical structure is inherently relevant to the classification task. One intriguing metric space comes from using conformal mappings of 2D shapes into each other, via the theory of Teichmüller spaces. In this space every simple closed curve in the plane (a “shape”) is represented by a ‘fingerprint’ which is a diffeomorphism of the unit circle to itself (a differentiable and invertible, periodic function). More precisely, every shape defines to a unique equivalence class of such diffeomorphisms up to right multiplication by a Möbius map. The fingerprint does not change if the shape is varied by translations and scaling and any such equivalence class comes from some shape. This coset space, equipped with the infinitesimal Weil-Petersson (WP) Riemannian norm is a metric space. In this space, the shortest path between each two shapes is unique, and is given by a geodesic connecting them. Their distance from each other is given by integrating the WP-norm along that geodesic. In this paper we concentrate on solving the “welding” problem of “sewing” together conformally the interior and exterior of the unit circle, glued on the unit circle by a given diffeomorphism, to obtain the unique 2D shape associated with this diffeomorphism. This will allow us to go back and forth between 2D shapes and their representing diffeomorphisms in this “space of shapes”. We then present an efficient method for computing the unique shortest path, the geodesic of shape morphing between each two end-point shapes. The group of diffeomorphisms of S1 acts as a group of isometries on the space of shapes and we show how this can be used to define shape transformations, like for instance ‘adding a protruding limb’ to any shape. 相似文献
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