The feasibility of manual parameter tuning for deformable breast MR image registration from a multi-objective optimization perspective

Abstract

Deformable image registration is typically formulated as an optimization problem involving a linearly weighted combination of terms that correspond to objectives of interest (e.g. similarity, deformation magnitude). The weights, along with multiple other parameters, need to be manually tuned for each application, a task currently addressed mainly via trial-and-error approaches. Such approaches can only be successful if there is a sensible interplay between parameters, objectives, and desired registration outcome. This, however, is not well established. To study this interplay, we use multi-objective optimization, where multiple solutions exist that represent the optimal trade-offs between the objectives, forming a so-called Pareto front. Here, we focus on weight tuning. To study the space a user has to navigate during manual weight tuning, we randomly sample multiple linear combinations. To understand how these combinations relate to desirability of registration outcome, we associate with each outcome a mean target registration error (TRE) based on expert-defined anatomical landmarks. Further, we employ a multi-objective evolutionary algorithm that optimizes the weight combinations, yielding a Pareto front of solutions, which can be directly navigated by the user. To study how the complexity of manual weight tuning changes depending on the registration problem, we consider an easy problem, prone-to-prone breast MR image registration, and a hard problem, prone-to-supine breast MR image registration. Lastly, we investigate how guidance information as an additional objective influences the prone-to-supine registration outcome. Results show that the interplay between weights, objectives, and registration outcome makes manual weight tuning feasible for the prone-to-prone problem, but very challenging for the harder prone-to-supine problem. Here, patient-specific, multi-objective weight optimization is needed, obtaining a mean TRE of 13.6 mm without guidance information reduced to 7.3 mm with guidance information, but also providing a Pareto front that exhibits an intuitively sensible interplay between weights, objectives, and registration outcome, allowing outcome selection.

Evolutionary Machine Learning for Multi-Objective Class Solutions in Medical Deformable Image Registration

“…We subdivided our prone-supine cases as follows. Given that via patient-specific parameter optimization, potentially clinically-useful registration results (on the basis of achieved mean target registration error (TRE)) were found for four cases [10], we grouped these cases together. We call this prone-supine Group A ( Figure 2).…”

“…Having a class solution for DIR, i.e., a configuration of parameters for which DIR performs well on all instances of a DIR problem, would facilitate wide-scale clinical application. Although several approaches have been proposed [8][9][10], still, often, parameters are manually tuned for each case of the DIR problem separately via trial-and-error adaptations, followed by visual inspection of the registration outcome.…”

“…Finding a class solution may, however, be impossible for challenging DIR cases, as it was shown that preferred parameter settings can vary greatly even for different instances of the same type of registration problem [9][10][11]. Different parameter configurations lead to different DIR outcomes, due to different trade-offs between the objectives of interest in DIR, such as similarity between the images and the amount of deformation.…”

“…In cases where the Pareto front is not known (such as in the case of DIR), it can be said that a non-dominated front is obtained, i.e., a front where no solution is better in both objectives than any other solution in this front. Recently, it was shown that using a patient-specific multi-objective optimization approach can be useful for challenging DIR cases, for which manual tuning becomes far more complex [10]. This multi-objective, patient-specific approach can also be considered an online tuning approach: online in the sense that here, the tuning algorithm is run to search for the best parameter settings for the DIR algorithm for a specific patient.…”

“…In this work, we consider an alternative approach for efficient parameter tuning: an evolutionary multi-objective machine learning approach that computes, in an offline training phase, a multi-objective class solution, i.e., a set of parameter configurations, that, when used on any instance of a DIR problem, yields DIR outcomes that approximate the non-dominated front. To this end, we re-design the parameter optimization problem, and we evaluate the performance of the evolutionary machine learning approach by performing a comparison with the method presented in [10]. Since computing the multi-objective class solution needs to be performed only once, it is then sufficient for a new DIR instance to run multiple DIRs straightforwardly using the class solutions to obtain a navigable set of DIR outcomes for that instance.…”