4-connected neighborhood

In image processing and image recognition, pixel connectivity is the way in which pixels in 2-dimensional (or voxels in 3-dimensional) images relate to their neighbors.

4-connected pixels are neighbors to every pixel that touches one of their edges. These pixels are connected horizontally and vertically. In terms of pixel coordinates, every pixel that has the coordinates

is connected to the pixel at ${\displaystyle \textstyle (x,y)}$.

6-connected pixels are neighbors to every pixel that touches one of their corners (which includes pixels that touch one of their edges) in a hexagonal grid or stretcher bond rectangular grid.

There are several ways to map hexagonal tiles to integer pixel coordinates. With one method, in addition to the 4-connected pixels, the two pixels at coordinates ${\displaystyle \textstyle (x+1,y+1)}$ and ${\displaystyle \textstyle (x-1,y-1)}$ are connected to the pixel at ${\displaystyle \textstyle (x,y)}$.

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