Topological complexities of finite digital images

Digital topological methods are often used in computing the topological complexity of digital images. We give new results on the relation between reducibility and digital contractibility in order to determine the topological complexity of a digitally connected finite digital image. We present all possible cases of the topological complexity TC of a finite digital image in Z and Z^2. Finally, we determine the higher topological complexity TCn of finite irreducible digital images independently of the number of points for n 1.