Matlab: find inner boundary of set of vertices - matlab

Question

I have a set of (x,y) points defined in the following way:
map=[0,0;66,0;66,44;44,44;44,66;110,66;110,110;0,110];
There is then a function that connects these points (which are vertices, i.e. corner points) together to form a closed shape. The example vertices I have given form a shape something like this:
________________________________________
| |
| |
| |
| ____________________|
| |
| |_______
| |
| |
| |
| |
|___________________________|
I would like to now automatically generate a second set of vertices that form a boundary inside the shape, offset by some amount. I.e. this:
inner_boundary=[5,5;61,5;61,39;39,39;39,71;105,71;105,105;5,105];
________________________________________
| ___________________________________ |
| | | |
| | _____________________| |
| | | ____________________|
| | | |
| | | |_______
| | |________ |
| | | |
| | | |
| |______________________| |
|___________________________|
Any ideas on how to do this? I've been racking my brains but can't think of a robust way to do this. I need it to automatically do this for any input set of vertices. Also, to clarify - I am just interested in how to specify the set of vertices, not the drawing part.
Many thanks!

Answer 1

Here is a solution based on Image Processing Toolbox functions. The basic idea is as follows:
Use "poly2mask" to create a BW (0-1) image from the polygon
coordinates
Use "imerode" to erode the mask by 1 pixel
Use "bwboundaries" to trace the new, eroded, boundary
Code example:
x = [4 10 10 4 4];
y = [4 4 10 10 4];
mask = poly2mask(x,y,12,12);
mask_eroded = imerode(mask, 1);
newBnds = bwboundaries(mask_eroded);
newBnds = newBnds{1};
Note that the newBnds will probably contain more points than you want because it traces every single pixel on the boundary. You can write a simple iterative routine to discard non-endpoints.