8connected

8connected is a term used in discrete mathematics and digital imaging to describe a particular model of neighborhood connectivity on a two-dimensional grid. In an 8connected framework, a grid cell or pixel is considered adjacent to all of its eight surrounding cells: the four orthogonal neighbors (north, east, south, west) and the four diagonal neighbors (northeast, southeast, southwest, northwest). This contrasts with 4-connected connectivity, which includes only the orthogonal neighbors. The choice between 4- and 8-connectedness influences how regions are defined and how paths are traced on the grid.

In image processing, 8connectedness is used for tasks such as connected component labeling and region growing. Using 8connectedness allows diagonal pixels to belong to the same region, which can yield different segmentation results compared with 4-connectedness. In binary images, standard labeling algorithms may be implemented with 8-connectivity, often via two-pass passes and a union-find structure to resolve equivalence classes.

In graph-theory terms, an 8connected grid describes a grid graph where each vertex connects to up to eight neighbors. The model is also relevant in cellular automata and pathfinding algorithms, where the neighborhood definition affects allowed moves and reachability.

History and terminology: The notions of 4- and 8-connectivity emerged from early digital imaging research to formalize pixel adjacency. While "8connected" is less common than "8-connected" in formal writing, it appears in informal and project-specific naming.

See also: 4-connectedness; 8-connectedness; 8-neighborhood; connected components; cellular automata.