A Tournament of Transformation Models: B-Spline-based vs. Mesh-based Multi-Objective Deformable Image Registration

TL;DR

This study directly compares B-spline and dual-dynamic mesh transformation models for deformable image registration (DIR) by optimizing both with the same multi-objective evolutionary method, MO-RV-GOMEA, and includes a gradient-descent baseline for context. It integrates a novel B-spline DIR approach into Elastix and leverages MOREA for mesh optimization, evaluating two objectives: $f_{\text{similarity}}$ and $f_{\text{def. magnitude}}$, on pelvic CT registrations from three cervical cancer patients with large deformations. The results show that the optimization method markedly affects the quality and diversity of registrations, with mesh models producing more localized deformations and closer target matches, while B-spline models offer broader diversity but less locality. The findings highlight the critical impact of transformation-model choice in DIR and underscore the value of multi-objective optimization for obtaining a representative range of high-quality registrations across problems.

Abstract

The transformation model is an essential component of any deformable image registration approach. It provides a representation of physical deformations between images, thereby defining the range and realism of registrations that can be found. Two types of transformation models have emerged as popular choices: B-spline models and mesh models. Although both models have been investigated in detail, a direct comparison has not yet been made, since the models are optimized using very different optimization methods in practice. B-spline models are predominantly optimized using gradient-descent methods, while mesh models are typically optimized using finite-element method solvers or evolutionary algorithms. Multi-objective optimization methods, which aim to find a diverse set of high-quality trade-off registrations, are increasingly acknowledged to be important in deformable image registration. Since these methods search for a diverse set of registrations, they can provide a more complete picture of the capabilities of different transformation models, making them suitable for a comparison of models. In this work, we conduct the first direct comparison between B-spline and mesh transformation models, by optimizing both models with the same state-of-the-art multi-objective optimization method, the Multi-Objective Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (MO-RV-GOMEA). The combination with B-spline transformation models, moreover, is novel. We experimentally compare both models on two different registration problems that are both based on pelvic CT scans of cervical cancer patients, featuring large deformations. Our results, on three cervical cancer patients, indicate that the choice of transformation model can have a profound impact on the diversity and quality of achieved registration outcomes.

Figures (6)

• Figure 1: 2D illustration of how the B-spline transformation model and the dual-dynamic mesh transformation model both decompose the image domain and allow for partial, local objective value re-evaluations. Note that (a) and (b) visualize control point grids on the source image, while (c) and (d) visualize meshes on both the source and target image.
• Figure 2: 2D illustration of the core optimization loops inside the three registration approaches which are experimentally compared in this work.
• Figure 3: Sagittal slices of the source and target images of the two registration problems of Patient 1.
• Figure 4: Comparison of the registrations found by the three compared approaches for Patient 1. Each registration represents a different trade-off of the two optimization objectives. For each highlighted registration, the same sagittal slice of the transformed source image is shown and the DVF is rendered on top of the image, with arrow colors indicating local deformation magnitude objective values. Dominated solutions in each set of solutions are indicated with a lighter color shade.
• Figure 5: Comparison of the registrations found by the three compared approaches for Patient 2. Further explanation is given in the caption of Figure \ref{['fig:fronts:p1']}.