How to do detect and join convex portions in a bw image with some criteria?

Hi, I have a binary image in which there are roughly convex portions which would finally make closed shapes. I have attached the image here. This is what I want to do: 1) The joint convex parts which face in opposite directions are to be separated. 2) The disjoint convex parts that face each other and are also close to each other(by image co-ordinate values) are to be fused together. 3) There are similar objects in the image so the algorithm must work for all.

Basically I need to close all convex regions. Please tell me how to proceed. I am stuck here since last two days. I have knowledge about convexhull. But that was not working fine because there are many convex portions of different sizes and facing in different directions.

Answer 1

[Image Analyst]

You'll probably have to manually split those apart since where you split it doesn't seem to follow any normal splitting method, like watershed for example. Same for connecting them. You have a very special description for how things should be joined that does not match up with any usual joining methods, like morphological closing, so you're stuck writing your own if you can, but you may have to end up manually painting regions together.