How to make better connectivity between these edges in matlab ?

[Image Analyst]

Why do you need to? What are you ultimately after? You may not need to connect the edges if you can find another metric that delivers what you need to know. Have you looked at ridge-finding filters like Hessians, Frangi, COSFIRE-B, etc.? Try the File Exchange.

[Jabbar moosavi]

I need the sharper edge with better connectivity because I want to apply some edge detection method on it ,but for example when i apply canny edge detection the output is a dual edge .