Flexible Shape Matching

Some objects, e.g., fruits, show considerable intra-class variations of their shape. Whereas algorithms which are based on a rigid object model run into difficulties for deformable objects, specific approaches exist for such types of objects. These methods use parametric curves, which should approximate the object contour as good as possible. The parameters of the curve should offer enough degrees of freedom for accurate approximations. Two types of algorithms are presented in this chapter. Schemes belonging to the first class, like snakes or the contracting curve density algorithm, perform an optimization of the parameter vector of the curve in order to minimize the differences between the curve and the object contour. Second, there exist object classification schemes making use of parametric curves approximating an object. These methods typically calculate a similarity measure or distance metric between arbitrarily shaped curves. Turning functions or the so-called curvature scale space are examples of such measures. The metrics often follow the paradigm of perceptual similarity, i.e., they intend to behave similar to the human vision system.