Eccentricity measures the shortest length of the paths from a given vertex v to reach any other vertex w of a connected graph Computed for every vertex v it transforms the connectivity structure of the graph into a set of values For a connected region of a digital image it is defined through its neighbourhood graph and the given metric This transform assigns to each element of a region a value that depends on it's location inside the region and the region's shape The definition and several properties are given Presented experimental results verify its robustness against noise, and its increased stability compared to the distance transform Future work will include using it for shape decomposition, representation, and matching.