Because there is no information described in the paper for the region merging, so we considered the methods by ourself as the following, these methods should be used after finish Boundary Connection step:

Step 1:  Region Labeling

We treat each closing region as a component. If an image have n regions, then after component labeling, we will get from 1 to n components. All the pixels in the image will be labeled with the their region number.
Algorithm:

1. Scan the image from left to right, top to bottom.
2. If the pixel is 1(belongs to some regio), then
• If only one of its upper and upper-left and upper-right and left neighbors has a label, then copy the label.
• If more than one of these four neighbors have a label, and their labels are same, then copy the label.
• If more than one of these four neighbors have different labels, then copy one of the labels. If there is a upper-left neighbor, then copy its label; else if there is a upper neighbor, then copy its label; else copy upper-right neighbor's label. Then, enter all these different labels in the equivalence table as equivalent labels.
• Otherwise assign a new label to this pixel and enter this label in the equivalence table.
3. If there an more pixels to consider, then go to step2.
4. Find the lowest label for each equivalent set in equivalence table.
5. Scan the picture, replace each label by the lowest label in tis equivalent set.

After the component labeling, we will find a region adjacency graph(RAG). RAG is used to represent regions and relationships among them in an image. So, after building a RAG, we can easily know which two region are adjacent.

Algorithm:

Scan the components labeled image. For each pixel, assume this pixel belongs to component i. Then for its 8 neighbors, if the neighbor is labeled with a different label with the this pixel, for example, j, then add an arc between component i and component j.

After we get RAG, we can begin to merge statisticlly similar regions. We compare their mean intensities. If the mean intensities don't differ by more than some predetermined value, the regions are considered similar and should be candidates for merging.

(Due to the time restriction, we didn't finish all these part of work)