Smart grid initialization reduces the computational complexity of multi-objective image registration based on a dual-dynamic transformation model to account for large anatomical differences

We recently demonstrated the strong potential of using dual-dynamic transformation models when tackling deformable image registration problems involving large anatomical differences. Dual-dynamic transformation models employ two moving grids instead of the common single moving grid for the target image (and single fixed grid for the source image). We previously employed powerful optimization algorithms to make use of the additional flexibility offered by a dual-dynamic transformation model with good results, directly obtaining insight into the trade-off between important registration objectives as a result of taking a multi-objective approach to optimization. However, optimization has so far been initialized using two regular grids, which still leaves a great potential of dual-dynamic transformation models untapped: a-priori grid alignment with image structures/areas that are expected to deform more. This allows (far) less grid points to be used, compared to using a sufficiently refined regular grid, leading to (far) more efficient optimization, or, equivalently, more accurate results using the same number of grid points. We study the implications of exploiting this potential by experimenting with two new smart grid initialization procedures: one manual expert-based and one automated image-feature-based. We consider a CT test case with large differences in bladder volume with and without a multi-resolution scheme and find a substantial benefit of using smart grid initialization

A novel model-based evolutionary algorithm for multi-objective deformable image registration with content mismatch and large deformations: Benchmarking efficiency and quality

Taking a multi-objective optimization approach to deformable image registration has recently gained attention, because such an approach removes the requirement of manually tuning the weights of all the involved objectives. Especially for problems that require large complex deformations, this is a non-trivial task. From the resulting Pareto set of solutions one can then much more insightfully select a registration outcome that is most suitable for the problem at hand. To serve as an internal optimization engine, currently used multi-objective algorithms are competent, but rather inefficient. In this paper we largely improve upon this by introducing a multi-objective real-valued adaptation of the recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) for discrete optimization. In this work, GOMEA is tailored specifically to the problem of deformable image registration to obtain substantially improved efficiency. This improvement is achieved by exploiting a key strength of GOMEA: iteratively improving small parts of solutions, allowing to faster exploit the impact of such updates on the objectives at hand through partial evaluations. We performed experiments on three registration problems. In particular, an artificial problem containing a disappearing structure, a pair of pre- and post-operative breast CT scans, and a pair of breast MRI scans acquired in prone and supine position were considered. Results show that compared to the previously used evolutionary algorithm, GOMEA obtains a speed-up of up to a factor of ∼1600 on the tested registration problems while achieving registration outcomes of similar quality

Getting the most out of additional guidance information in deformable image registration by leveraging multi-objective optimization

Incorporating additional guidance information, e.g., landmark/contour correspondence, in deformable image registration is often desirable and is typically done by adding constraints or cost terms to the optimization function. Commonly, deciding between a “hard” constraint and a “soft” additional cost term as well as the weighting of cost terms in the optimization function is done on a trial-and-error basis. The aim of this study is to investigate the advantages of exploiting guidance information by taking a multi-objective optimization perspective. Hereto, next to objectives related to match quality and amount of deformation, we define a third objective related to guidance information. Multi-objective optimization eliminates the need to a-priori tune a weighting of objectives in a single optimization function or the strict requirement of fulfilling hard guidance constraints. Instead, Pareto-efficient trade-offs between all objectives are found, effectively making the introduction of guidance information straightforward, independent of its type or scale. Further, since complete Pareto fronts also contain less interesting parts (i.e., solutions with near-zero deformation effort), we study how adaptive steering mechanisms can be incorporated to automatically focus more on solutions of interest. We performed experiments on artificial and real clinical data with large differences, including disappearing structures. Results show the substantial benefit of using additional guidance information. Moreover, compared to the 2-objective case, additional computational cost is negligible. Finally, with the same computational budget, use of the adaptive steering mechanism provides superior solutions in the area of interest

On explaining machine learning models by evolving crucial and compact features

Feature construction can substantially improve the accuracy of Machine Learning (ML) algorithms. Genetic Programming (GP) has been proven to be effective at this task by evolving non-linear combinations of input features. GP additionally has the potential to improve ML explainability since explicit expressions are evolved. Yet, in most GP works the complexity of evolved features is not explicitly bound or minimized though this is arguably key for explainability. In this article, we assess to what extent GP still performs favorably at feature construction when constructing features that are (1) Of small-enough number, to enable visualization of the behavior of the ML model; (2) Of small-enough size, to enable interpretability of the features themselves; (3) Of sufficient informative power, to retain or even improve the performance of the ML algorithm. We consider a simple feature construction scheme using three different GP algorithms, as well as random search, to evolve features for five ML algorithms, including support vector machines and random forest. Our results on 21 datasets pertaining to classification and regression problems show that constructing only two compact features can be sufficient to rival the use of the entire original feature set. We further find that a modern GP algorithm, GP-GOMEA, performs best overall. These results, combined with examples that we provide of readable constructed features and of 2D visualizations of ML behavior, lead us to positively conclude that GP-based feature construction still works well when explicitly searching for compact features, making it extremely helpful to explain ML models

Spatial redistribution of irregularly-spaced Pareto fronts for more intuitive navigation and solution selection

A multi-objective optimization approach is o.en followed by an a posteriori decision-making process, during which the most appropriate solution of the Pareto set is selected by a professional in the .eld. Conventional visualization methods do not correct for Pareto fronts with irregularly-spaced solutions. However, achieving a uniform spread of solutions can make the decision-making process more intuitive when decision tools such as sliders, which represent the preference for each objective, are used. We propose a method that maps anm-dimensional Pareto front to an (m-1)-simplex and spreads out points to achieve a more uniform distribution of these points in the simplex while maintaining the local neighborhood structure of the solutions as much as possible. .is set of points can then more intuitively be navigated due to the more uniform distribution. We test our approach on a set of non-uniformly spaced 3D Pareto fronts of a real-world problem: deformable image registration of medical images. The results of these experiments are visualized as points in a triangle, showing that we indeed achieve a representation of the Pareto front with a near-uniform distribution of points where these are still positioned as expected, i.e., according to their quality in each of the objectives of interest

Niching an estimation-of-distribution algorithm by hierarchical Gaussian mixture learning

Estimation-of-Distribution Algorithms (EDAs) have been applied with quite some success when solving real-valued optimization problems, especially in the case of Black Box Optimization (BBO). Generally, the performance of an EDA depends on the match between its driving probability distribution and the landscape of the problem being solved. Because most well-known EDAs, including CMA-ES, NES, and AMaLGaM, use a uni-modal search distribution, they have a high risk of getting trapped in local optima when a problem is multi-modal with a (moderate) number of relatively comparable modes. This risk could potentially be mitigated using niching methods that define multiple regions of interest where separate search distributions govern sub-populations. However, a key question is how to determine a suitable number of niches, especially in BBO. In this paper, we present a novel, adaptive niching approach that determines the niches through hierarchical clustering based on the correlation between the probability densities and fitness values of solutions. We test the performance of a combination of this niching approach with AMaLGaM on both new and well-known niching benchmark problems and ind that the new approach properly identifies multiple landscape modes, leading to much beter performance on multi-modal problems than with a non-niched, uni-modal EDA