Question: Segmentation techniques: Region growing and split and merge

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- The objective of segmentation is to partition an image into regions. In this section, segmentation is done by finding the regions directly.
Let R represent the entire image region segmentation as a process that partitions R into n sub-regions R_1,R_2,…,R_N such that,

$R_1∪R_2∪…∪R_(N=) R$

$R_i$ is connected region where i=1,2,…,N

$R_i∩R_j=∅ for i≠j$

Predicate $(R_i )$ =True for all i=1,2,..,N

There are two different approaches for region oriented segmentation.

**Region Growing by Pixel Aggregation:**- Region growing is a procedure that groups pixels or sub-regions into larger regions.
Pixel aggregation procedure starts with a set of seed point and from these grows region by appending for each seed point those neighboring pixels that have similar proportion.

**Region Splitting & Merging:**- In this method an image is first subdivided into a set of arbitrary disjointed region and then merges and/or splits the regions.
- Let R represent the entire image region and then select a predicate P.
- For image one approach for segmenting R is to subdivide it successively into smaller and smaller quadrant region so that for any region Ri, Predicate(Ri) = True.
- If Predicate(Region) = False then divide the image into quadrants.
- If Predicate(Region) = False for any quadrant then subdivide that quadrant into sub-quadrants and so on.

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