Metamorphosis of Images in Reproducing Kernel Hilbert Spaces

TL;DR

This paper introduces a shooting method for morphing images within reproducing kernel Hilbert spaces, enabling statistical analysis and template estimation in computational anatomy.

Contribution

It develops a novel shooting approach for metamorphosis in RKHS, deriving equations and demonstrating the method's effectiveness for image morphing.

Findings

Derived shooting equations from a Lagrangian perspective.

Presented a numerical implementation for image morphing.

Illustrated the method with simple image examples.

Abstract

Metamorphosis is a method for diffeomorphic matching of shapes, with many potential applications for anatomical shape comparison in medical imagery, a problem which is central to the field of computational anatomy. An important tool for the practical application of metamorphosis is a numerical method based on shooting from the initial momentum, as this would enable the use of statistical methods based on this momentum, as well as the estimation of templates from hyper-templates using morphing. In this paper we introduce a shooting method, in the particular case of morphing images that lie in a reproducing kernel Hilbert space (RKHS). We derive the relevant shooting equations from a Lagrangian frame of reference, present the details of the numerical approach, and illustrate the method through morphing of some simple images.