Fitness-based Linkage Learning and Maximum-Clique Conditional Linkage Modelling for Gray-box Optimization with RV-GOMEA

For many real-world optimization problems it is possible to perform partial evaluations, meaning that the impact of changing a few variables on a solution's fitness can be computed very efficiently. It has been shown that such partial evaluations can be excellently leveraged by the Real-Valued GOMEA (RV-GOMEA) that uses a linkage model to capture dependencies between problem variables. Recently, conditional linkage models were introduced for RV-GOMEA, expanding its state-of-the-art performance even to problems with overlapping dependencies. However, that work assumed that the dependency structure is known a priori. Fitness-based linkage learning techniques have previously been used to detect dependencies during optimization, but only for non-conditional linkage models. In this work, we combine fitness-based linkage learning and conditional linkage modelling in RV-GOMEA. In addition, we propose a new way to model overlapping dependencies in conditional linkage models to maximize the joint sampling of fully interdependent groups of variables. We compare the resulting novel variant of RV-GOMEA to other variants of RV-GOMEA and VkD-CMA on 12 problems with varying degree of overlapping dependencies. We find that the new RV-GOMEA not only performs best on most problems, also the overhead of learning the conditional linkage models during optimization is often negligible.

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

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.

MOREA: a GPU-accelerated Evolutionary Algorithm for Multi-Objective Deformable Registration of 3D Medical Images

Finding a realistic deformation that transforms one image into another, in case large deformations are required, is considered a key challenge in medical image analysis. Having a proper image registration approach to achieve this could unleash a number of applications requiring information to be transferred between images. Clinical adoption is currently hampered by many existing methods requiring extensive configuration effort before each use, or not being able to (realistically) capture large deformations. A recent multi-objective approach that uses the Multi-Objective Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (MO-RV-GOMEA) and a dual-dynamic mesh transformation model has shown promise, exposing the trade-offs inherent to image registration problems and modeling large deformations in 2D. This work builds on this promise and introduces MOREA: the first evolutionary algorithm-based multi-objective approach to deformable registration of 3D images capable of tackling large deformations. MOREA includes a 3D biomechanical mesh model for physical plausibility and is fully GPU-accelerated. We compare MOREA to two state-of-the-art approaches on abdominal CT scans of 4 cervical cancer patients, with the latter two approaches configured for the best results per patient. Without requiring per-patient configuration, MOREA significantly outperforms these approaches on 3 of the 4 patients that represent the most difficult cases.

Multi-Objective Dual Simplex-Mesh Based Deformable Image Registration for 3D Medical Images -- Proof of Concept

Reliably and physically accurately transferring information between images through deformable image registration with large anatomical differences is an open challenge in medical image analysis. Most existing methods have two key shortcomings: first, they require extensive up-front parameter tuning to each specific registration problem, and second, they have difficulty capturing large deformations and content mismatches between images. There have however been developments that have laid the foundation for potential solutions to both shortcomings. Towards the first shortcoming, a multi-objective optimization approach using the Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (RV-GOMEA) has been shown to be capable of producing a diverse set of registrations for 2D images in one run of the algorithm, representing different trade-offs between conflicting objectives in the registration problem. This allows the user to select a registration afterwards and removes the need for up-front tuning. Towards the second shortcoming, a dual-dynamic grid transformation model has proven effective at capturing large differences in 2D images. These two developments have recently been accelerated through GPU parallelization, delivering large speed-ups. Based on this accelerated version, it is now possible to extend the approach to 3D images. Concordantly, this work introduces the first method for multi-objective 3D deformable image registration, using a 3D dual-dynamic grid transformation model based on simplex meshes while still supporting the incorporation of annotated guidance information and multi-resolution schemes. Our proof-of-concept prototype shows promising results on synthetic and clinical 3D registration problems, forming the foundation for a new, insightful method that can include bio-mechanical properties in the registration.