Methods based on Radon transform for non-affine deformable image registration of noisy images

TL;DR

This paper introduces two Radon transform-based deformable image registration methods capable of capturing non-affine deformations in noisy images, with theoretical guarantees and validation on synthetic and lung images.

Contribution

The study presents novel Radon transform-based DIR methods with proven existence and uniqueness, and demonstrates their effectiveness in noisy and non-affine deformation scenarios.

Findings

Methods successfully capture non-affine deformations.

Effective in noisy image registration.

Validated on synthetic and lung images.

Abstract

Deformable image registration is a standard engineering problem used to determine the distortion experienced by a body by comparing two images of it in different states. This study introduces two new DIR methods designed to capture non-affine deformations using Radon transform-based similarity measures and a classical regularizer based on linear elastic deformation energy. It establishes conditions for the existence and uniqueness of solutions for both methods and presents synthetic experimental results comparing them with a standard method based on the sum of squared differences similarity measure. These methods have been tested to capture various non-affine deformations in images, both with and without noise, and their convergence rates have been analyzed. Furthermore, the effectiveness of these methods was also evaluated in a lung image registration scenario.