Lehrveranstaltungsinhalt aus - Institute for Computer Graphics and ...

1.6. OPERATIONS ON BINARY RASTER IMAGES 43
analogous chess movements of the springer etc.
from the “Dame” game.
Another diagonal neighborhood would derive
We have neighborhoods of the first order, which are the neighbors of a pixel-x. The neighbors of
the neighbors are “neighbors of second order” with respect to a pixel at x. We could increase the
order by having neighbors of the neighbors of the neighbors.
Definition 2 Connectivity
2 Pixel haengen zusammen, wenn sie einanders Nachbarn sind und dieselbe Zusammenhangseigenschaft
V besitzen.
4-Zusammenhang:
1: if q N4-Nachbar von p then {Def. 5}
2: Pixel p und q haengen zusammen
3: else
4: Pixel p und q haengen nicht zusammen
5: end if
m-Zusammenhang:
1: if (N4 (p) geschnitten N4 (q)) = 0 then {N4( x): Menge der x-N4-Nachbarn}
2: if (q ist N4 -Nachbar von p)||(q ist ND-Nachbar von p) then {Def. 5}
3: Pixel p und q haengen zusammen
4: else
5: Pixel p und q haengen nicht zusammen
6: end if
7: else
8: Pixel p und q haengen nicht zusammen
9: end if
Connectivity is defined by two pixels belonging together: They are “connected” if they are one
another’s neighbors. So we need to have a neighbor-relationship to define connectivity. Depending
on a 4-neighborhood, an 8-neighborhood, a springer-neighborhood we can define various types of
connectivities. We therefore say that two pixels p and q are one another’s neighbors if they are
connected, if they are neighbors under a neighborhood-relationship.
This becomes pretty interesting and useful once we start to do character-recognition and we need
to figure out which pixels belong together and create certain shapes. We may have an example
of three-by-three pixels of which four pixels are black and five pixels are white. We now can
have connections established between those four black pixels under various connectivity rules. A
connectivity with eight neighbors creates a more complex shape than a connectivity via so-called m-
neighbors, where m-neighbors have been defined previously in Slide “Zusammenhaengende Pixel”.
Definition 3 Distance
Gegeben: Punkte p(x,y) und q(s,t)
1: De(p,q) = 2√ (x − s) 2 + (y − t) 2 (Euklidische Distanz)
2: D4-Distanz (City Block Distance)
3: D8-Distanz (Schachbrett-Distanz)
The neighborhood- and connectivity-relationships can be used to established distances between
pixels, to define edges, lines and region in images, to define contours of objects, to find a path
between any two locations in an image and to perhaps eliminate pixels as noise if they are not
connected to any other pixels. A quick example of a distance addresses two pixels P and Q with