Shape Segmentation and Shape Matching





   For computational purpose, a concrete mathematical definition of features is required. We use a topological approach to define features of shapes.

   The input of the algorithm is the set of points sampled from the shape and the output of the algorithm is the decomposition of the area(2D) or the volume(3D) enclosed by the shape into segments respecting its features. Feature extraction has several applications in Computer Vision, Artificial Intelligence, CAD and many other areas. 


  T. K. Dey, J. Giesen and S. Goswami, Shape Segmentation and Matching with Flow Discretization, Workshop on Algorithms and Data Structures(WADS), (2003), 25--36.

 Software for 3D segmentation and matching available.

./circle23_blue.gif Segmentation


   We consider the distance function induced by a shape in its embedding dimension. Features of the shape are defined as the stable manifolds of the maxima of this distance function using generalized critical point theory.  These definitions are translated to the discrete setting which allow extracting  features from a  point sample derived from the  shape. Delaunay triangulation and its dual Voronoi diagram are used in the discrete setting to compute the critical points and approximating their stable manifolds. 


    <2D Examples>



     <3D Examples> 


 ./circle23_blue.gif Shape Matching


     We use the segmentation algorithm to match two shapes with respect to their features.


     <2D Examples>


     <3D Examples>