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Minicursos

Las actividadesdel curso avanzado Técnicas de Singularidades y Geometría en Análisis de Imagen se llevarán a cabo desde el martes 3 al viernes 6 de julio de 2012 en el siguiente horario:

Basic ideas of singularity theory and their applications to geometrical problems on imagery

 

 

Curso impartido por Peter Giblin y James Damon

 

Peter Giblin (3 sesiones de 1 hora)

  • Functionss, right-equivalence, unfolding, discriminats, initial geometrical examples involving curves and surfaces
  • Infinitesimal conditions for unfoldings, applications to geometry such as focal sets, symmetry sets and medial axes of curves and surfaces
  • Mappings right-left equivalence, some beginning classifications for example projections of surfaces to the plane and projections fo surfaces with boundary. Indication of how these and related classifications apply to views of surfaces

 

James Damon (2 sesiones de 2 horas)

  • Natural images: divergent diagrams, equivalence preserving stratifications of the source of a mapping, geometric features. Method of classifications
  •  From medial to skeletal structures: computing geometry form skeletal structures, leading to multi-object structures

Techniques in shape classification

Curso impartido por  Ximo Gual y Joan Monterde

 

We shall review two different geometric techniques used in the theory of shape classification for plane or 3D objects.

The first one is based on integral geometry and it uses the support function associated to the object to obtain shape descriptors.

  • Integral Geometry
  • Generalized support function
  • Rotational formulas
  • Stereology
  • Applications

The second one uses techniques of differential geometry to compute distances and geodesics between shapes of curves.

  • Distances between shapes
  • The basic mapping in 2D
  • Jordan angles in Grasmannian manifolds
  • Construction of explicit geodesics in the shape space of plane curves
  • Generalization to shapes of 3D curves
  • Applications




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