How to link this blob sequential?

Above the image is my task. In this task yellow rectangle is starting point and cofee color rectangle is end point. So i have to connect the each blob from yellow rectangle and reach the coffee rectangle through white path.

In this task now i have the centroids of the each blob. And i don't know after? how to connect the each blob from yellow reactangle.

My idea is drawing horizontal and vertical line from yellow reactangle centroid through white pixels and if these lines touches another boundry. Then we will connect these blobs centroid.

My doubt is how to draw horizontal and vertical line form one pixel(centroid) and check the color of each pixel in that line?

Answer 1

[Image Analyst]

My answers were already given in your duplicate question http://www.mathworks.com/matlabcentral/answers/111680#comment_188935

[saravanakumar D]

I read that answer. But i think This is not have two walls. So this is not perfect maze. I just want to store the blob name in one array which are in path to reach end. Ouput i want is [Rectange,circle,hexagone,triangle,circle,rectangle]

 Now i have centroid of all the blobs. But i don't know how connnect the blob continuously