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