The simplicial structures in digital images and its applications

Digital images become one of the basic tools in order to communicate visual information. The pictures in this paper, the pictures in a digital camera, a graphic on the calculator screen are the examples which are digitally constructed or presented. The construction of digital image processing, the storage, the manuplation are deal with representation of digital images.On the other hand digital images have certain topological and algebraic properties and a discrete structure exist in digital images.In this thesis, the structure of simplicial set and simplicial group are constructed by using the definition of simplex and simplicial complex in digital images, studied by İ. Karaca et all. Since there is additive group structure in digital images, the commutator operation redefined and the operator , which is from the Moore complex to the simplicial group was reconstructed. 2- and 3- dimensional Moore complexes are considered due to these operations and investigated how they have a commutator subgroup structure.