Connected-Components Labeling on a Raster

A raster is a regular 2D grid of cells. In airspace data, each cell encodes whether a hazard (storm, restricted zone, no-fly area) occupies that grid square — typically $1$ for foreground (hazard present) and $0$ for background (clear).

A connected component is a maximal set of foreground cells in which every cell can be reached from every other through a chain of neighbor-to-neighbor steps. The result depends on what we count as a neighbor:

• 4-connectivity: each cell's neighbors are the 4 cells sharing an edge — N, S, E, W.
• 8-connectivity: those 4 plus the 4 diagonal cells — NE, NW, SE, SW.

Consider the raster

$$R = \begin{bmatrix} 1 & 0 & 1 \\ 1 & 1 & 0 \\ 0 & 1 & 1 \end{bmatrix}.$$

Under 4-connectivity, the cell at row $0$, column $2$ has only background edge-neighbors, so it is its own component. The other five foreground cells form one connected chain through shared edges. This gives 2 components.

Under 8-connectivity, the cell at $(0,2)$ is diagonally adjacent to $(1,1)$, which links it into the main chain. All six foreground cells now form a single component. This gives 1 component.

The choice of connectivity is a modeling decision: 4-connectivity treats diagonal-only contacts as not connected, which is often appropriate for hazard rasters where corner-touching cells should be split into separate features.