eightneighborhood

Eightneighborhood is a term used in the study of two-dimensional grids, image processing, and related computational fields to describe the set of eight cells surrounding a central cell. In a square lattice, the eight neighbors are the cells located to the north, northeast, east, southeast, south, southwest, west, and northwest of the central position, excluding the central cell itself. This concept is often contrasted with the four-neighborhood, which includes only the orthogonally adjacent cells.

The eightneighborhood is fundamental for defining adjacency and connectivity in discrete spaces. It underpins 8-connectivity schemes in digital images and grids, influencing how algorithms determine whether separate regions are considered connected. It also affects operations that rely on neighborhood influence, such as flood-fill, morphological filtering (dilation and erosion), and various filters that aggregate neighbor values. In cellular automata and graph representations, eightneighborhood governs state updates and edge connections, respectively, shaping the evolution of patterns or the structure of the underlying network.

In practice, choosing between four- and eight-neighborhoods reflects different topology assumptions. Eightneighborhood allows diagonal connections between neighboring cells, which can lead to different segmentation outcomes or pattern dynamics compared with four-neighborhood configurations. The choice is typically guided by the desired balance between connectivity and susceptibility to diagonal artifacts, as well as the specific requirements of the application.

See also: four-neighborhood; 4-connectivity; 8-connectivity.