I don't know what the second part of your question means. What does "according to their connectivity mean"? Let's say you had a dumbbell shape What are the two shapes you'd like if it was split according to 4-connectivity, and what would the pair of shapes look like if you did it according to 8-connectivity?
If you have a single image, you must have a decrease in the number of pixels because the interface line/curve will be removed.
What's wrong with watershed?
You forgot to attach the image, which would help illustrate your question better. Usually when people ask for image processing advice they attach an image, or they are asked to.
