convert labelmap to set of polygon lines

I have a labelmap e.g.

A=[0 0 0 1
   0 1 1 2
   0 1 1 2
   1 2 2 1]

I want to get a set of polygon lines that describes this labelmap. For example

label 0: (1,3),(1,1),(3,1),(1,3) %label 0 is the polygon region connecting these points

and so on. Is there any efficient way of doing so?

[em]

Just to make it more clear. I have a labelmap matrix describing an image. As shown in the image, it is visualized in Matlab by

imshow(im,[])

How can I extract polygon boundaries describing each label region? For all labels, I would have a set of polygon boundaries. What is the most efficient way of extract all these polygon boundaries?

Answer 1

[Image Analyst]

You're talking about the convex hull, convhull(). It's sort of like this

A=[0 0 0 1
   0 1 1 2
   0 1 1 2
   1 2 2 1]
[rows, columns] = find(A==0)
xy = [rows,columns]
indexes = convhull(xy)
r = rows(indexes)
c = columns(indexes)

but I don't have time now to do exactly what you want. convhull gives all points on the outer edges, like the 2,2 element, which you don't want for some reason. Maybe it'll be okay though if you just describe why you want the data in this form.

[Image Analyst]

Regarding your clarification (wish you had posted that originally) -- you don't want what you originally asked for at all . You don't want lines. You want the boundary pixel locations. So simply use bwboundaries():

labelNumber = 3; % Whatever label you want
boundary = bwboundary(labeledImage == labelNumber);
x = boundary{1}(:, 2);
y = boundary{1}(:, 1);