Euclidean Eccentricity Transform by Discrete Arc Paving

The eccentricity transform associates to each point of a shape the geodesic distance to the point farthest away from it. The transform is defined in any dimension, for simply and non simply connected sets. It is robust to Salt & Pepper noise and is quasi-invariant to articulated motion. Discrete analytical concentric circles with constant thickness and increasing radius pave the 2D plane. An ordering between pixels belonging to circles with different radius is created that enables the tracking of a wavefront moving away from the circle center. This is used to efficiently compute the single source shape bounded distance transform which in turn is used to compute the eccentricity transform. Experimental results for three algorithms are given: a novel one, an existing one, and a refined version of the existing one. They show a good speed/error compromise.