The basic idea of region splitting is to break the image into a set of disjoint regions which are coherent within themselves:

- Initially take the image as a
whole to be the area of interest.
- Look at the area of
interest and decide if all pixels contained in the region satisfy
some similarity constraint.
- If
**TRUE**then the area of interest corresponds to a region in the image. - If
**FALSE**split the area of interest (usually into four equal sub-areas) and consider each of the sub-areas as the area of interest in turn.

- This process continues until no further splitting occurs. In the
worst case this happens when the areas are just one pixel in size.
- This is a
*divide and conquer*or*top down*method.

If only a splitting schedule is used then the final segmentation would probably contain many neighbouring regions that have identical or similar properties.

Thus, a *
merging* process is used after each split which
compares adjacent regions and merges them if necessary. Algorithms of
this nature are called *split and merge* algorithms.

To illustrate the basic principle of these methods let us consider an imaginary image.

- Let denote the whole image shown in
Fig 35(a).
- Not all the pixels in
are similar so the region is split as in
Fig 35(b).
- Assume that all pixels within
regions , and respectively
are similar but those in are not.
- Therefore is split next as in Fig 35(c).
- Now
assume that all pixels within each region are similar with respect to
that region, and that after comparing the split regions, regions
and are found to be identical.
- These are thus merged together as in Fig 35(d).

**Fig. 35 Example of region splitting and merging**

We can describe the splitting of the image using a tree structure,
using a modified *quadtree*. Each non-terminal
node in the tree has at most four descendants, although it may have
less due to merging. See Fig. 36.

**Fig. 36 Region splitting and merging tree**