Yes. Use bwdist() to get the Euclidean Distance Transform, which is the number of pixels away from the edge. Then take the max of that. That will be the longest stretch you can go from the center of a shape to an edge and will be the distance of a shape from the center to the vertex. So locate the location of the max of the EDT with find(). Then draw a shape with its center at that location, making sure that your vertex touches the edge. Sorry, I don't already have code to do that algorithm.
For outside the shape, you might want this: http://www.mathworks.com/matlabcentral/fileexchange/34767-a-suite-of-minimal-bounding-objects
