An Elastic Energy Minimization Framework for Mean Contour Calculation

TL;DR

This paper introduces an elastic energy minimization framework for calculating mean contours that preserves all visible features of input contours while allowing flexible re-parameterization and interpolation, improving the analysis of 3D image stacks.

Contribution

It presents a novel contour mean calculation method based on elastic energy minimization in a real-valued vector space, enabling better averaging and interpolation of expert delineations.

Findings

Retains all visible information of input contours.

Allows flexible re-parameterization and centroid adjustment.

Provides a mathematically rigorous framework for contour averaging.

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.