Figure 4

Illustrating variation of inner distances for shape deformation with topological changes. The red dashed lines denote the shortest paths within the shape boundary surface that connect two landmark points x and y. The object B is the deformation to the one A, and the relative changes of the inner distances between the corresponding pair of points (e.g. x and y) during the shape deformation are small. In contrast, although the object C is also a shape deformation of the object A, the topological change leads to a significant change for inner distance.