2D-Shape Analysis Using Conformal Mapping

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 Teichm?uller 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 M?obius 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 s...

• Type: Conference
• Year: 2004
• Where: CVPR
• Authors: Eitan Sharon, David Mumford
• Keywords: Computer Vision, CVPR 2004, Intriguing Metric Space, Metric Space, Unique 2D Shape, Unique Equivalence Class, Unit Circle