An Elastic Energy Minimization Framework for Mean Contour Calculation

Abstract: In this paper we propose a contour mean calculation and interpolation method designed for averaging manual delineations of objects performed by experts and interpolate 3D layer stack images. The proposed method retains all visible information of the input contour set: the relative positions, orientations and size, but allows invisible quantities - parameterization and the centroid - to be changed. The chosen representation space - the position vector rescaled by square root velocity - is a real valued vector space on which the imposed L2 metric is used to define the distance function. With respect to this representation the re-parameterization group acts by isometries and the distance has well defined meaning: the sum of the central second moments of the coordinate functions. To identify the optimal re-parameterization system and proper centroid we use double energy minimization realized in a variational framework.