Deformations can be interpreted as resulting from a force applied to the shape. Mathematically, a deformation is defined as a mapping from a shape x to a shape y by a transformation function , i.e., . Given a notion of size of deformations, the distance between two shapes can be defined as the size of the smallest deformation between these shapes.
Shape changes can be seen as resulting from external forces acting upon them. Mathematically, a shape change is described as a transformation that maps one shape to another through a specific function , i.e., . The distance between two shapes can be quantified by considering the minimum amount of change required to transform one into the other.