The Euler-Lagrange equation for interpolating sequence of landmark datasets

Abstract

Non-rigid registration of landmarked datasets is an important problem that finds many applications in medical image analysis. In this paper, we present a method for interpolating a sequence of landmarks. The sequence of landmarks may be a model of growth, where anatomical object boundaries are parametrized by landmarks and the growth processes generate a landmarked sequence in time. In a variational optimization framework, the matching diffeomorphism for this problem is generated from a gradient algorithm based on the Euler-Lagrange equation of a cost framed in the inexact matching setting.