Region Growing-stopping rule

Descriptors alone can yield misleading results if connectivity properties are not used in the region growing process. 

For example: Visualize a random arrangement of pixels that have three distinct intensity values.

Grouping pixels with the same intensity values to form a region, without paying attention to connectivity, would yield a segmentation fault that is meaning less in the context of this discussion.

Another problem in region growing is the formulation of a stopping rule: 

Region growing has to stop when no more pixels satisfy the criteria for inclusion in that region.

Criteria such as intensity value, texture and color are local in nature and do not take into account the history of region growth.
Additional criteria that can increase the power of a region-growing algorithm utilize the concept of size, likeness between a candidate pixel and the pixels grown so far(such as comparison of the intensity of a candidate and the average intensity of the grown region) and the shape of the region being grown.

Let f(x,y) denote an input image; S(x,y) denote a seed array containing 1's at the locations of seed points and 0's elsewhere; Q denote a predicate to be applied at each location(x,y). Arrays f and S are assumed to be of the same size.

1. Find all connected components in $S(x,y)$ and reduce each connected component to one pixel; label all such pixels found as 1. All other pixels in $S$ are labeled 0.

2. Form an image $f_Q$ such that, at each point $(x,y)$, $f_Q(x,y)=1$ if the input image satisfies a given predicate, $Q$, at those coordinates, and $f_Q(x,y)=0$otherwise.

3. Let $g$ be an image formed by appending to each seed point in $S$ all the 1-valued points in $f_Q$ that are 8-connected to that seed point.

4. Label each connected component in $g$ with a different region label (e.g., integers or letters). This is the segmented image obtained by region growing.

Segmentation by region growing