Exact Euclidean Medial Axis in Higher Resolution

The notion of skeleton plays a major role in shape analysis. Some usually desirable characteristics of a skeleton are: sufficient for the reconstruction of the original object, centered, thin and homotopic. The Euclidean Medial Axis presents all these characteristics in a continuous framework. In the discrete case, the Exact Euclidean Medial Axis (MA) is also sufficient for reconstruction and centered. It no longer preserves homotopy but it can be combined with a homotopic thinning to generate homotopic skeletons. The thinness of the MA, however, may be discussed. In this paper we present the definition of the Exact Euclidean Medial Axis on Higher Resolution which has the same properties as the MA but with a better thinness characteristic, against the price of rising resolution. We provide and prove an efficient algorithm to compute it.