COMPONENTS LABELING

In this process elements that belongs to different connected component are given different labels

CONNECTIVITY AND CONNECTED COMPONENTS

given a connectivity neighborhood defined as follows

$$\left[\begin{array}{ccc}& n& \\ n& p& n\\ & n& \end{array}\right]\to n_4(p)$$ $$\left[\begin{array}{ccc}n& n& n\\ n& p& n\\ n& n& n\end{array}\right]\to n_8(p)$$

A path from pixel $p$ to pixel $q$ is a sequence of pixels $p=p_1,p_2,\dots ,p_n=q$ such that $p_i$ and $p_{i+1}$ are neighbors according to the chosen connectivity.

A set $R$ of pixel is a connected region if all pixels are connected

A connected region is a connected (foreground/background) region if all pixels in the region are (foreground/background)

A connected component of a binary image is a maximal connected foreground region

LABELING BY FLOOD-FILL

A new label is propagated throughout a connected component starting from a “seed” pixel. Propagation is typically carried out by a iterative procedure which requires scanning the image multiple times.this solution is not efficient

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