Geodesic Curves for Analysis of Continuous Implicit Shapes

A method is proposed for performing shape analysis of m-surfaces, e.g. planar curves and surfaces, with a geometric interpretation. The analysis uses an implicit surface representation and connects the popular level set approach with shape analysis. The representation is continuous and completely landmark-free. Shapes are represented as points on an infinite-dimensional manifold and the distance between two surfaces is given by the length of a path on this manifold. The analysis is valid in any dimension and examples of applications such as interpolation and clustering are given.

[1]  Niels Chr. Overgaard,et al.  A Geometric Formulation of Gradient Descent for Variational Problems with Moving Surfaces , 2005, Scale-Space.

[2]  Nikos Paragios,et al.  Shape Priors for Level Set Representations , 2002, ECCV.

[3]  Daniel Cremers,et al.  Variational Segmentation with Shape Priors , 2006, Handbook of Mathematical Models in Computer Vision.

[4]  Timothy F. Cootes,et al.  Active Shape Models-Their Training and Application , 1995, Comput. Vis. Image Underst..

[5]  Stefano Soatto,et al.  A Pseudo-distance for Shape Priors in Level Set Segmentation , 2003 .

[6]  Olivier D. Faugeras,et al.  Statistical shape influence in geodesic active contours , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[7]  Anuj Srivastava,et al.  Statistical shape analysis: clustering, learning, and testing , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Olivier Faugeras,et al.  Knowledge-Based Segmentation of Medical Images , 2003 .

[9]  Anuj Srivastava,et al.  Analysis of planar shapes using geodesic paths on shape spaces , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  D. Mumford,et al.  Riemannian Geometries on Spaces of Plane Curves , 2003, math/0312384.

[11]  Ronen Basri,et al.  Determining the similarity of deformable shapes , 1998, Vision Research.

[12]  Nikos Paragios,et al.  Shape Analysis towards Model-based Segmentation , 2003 .