Data visualisation is an important area of research: as the amount of data keeps increasing, we have to find ways of showcasing this data to provide an intuition for trends and patterns within it. This can be a particular challenge for high-dimensional data, since we cannot perceive it as is. A common approach is to use dimensionality-reduction techniques to bring the high-dimensional data into lower dimensions, which can then be visualised. One such technique is t-distributed Stochastic Neighbour Embedding (t-SNE), which produces good visualisations but struggles with long runtimes. This paper explores the effect of using sampled data instead of the full dataset to produce t-SNE embeddings, reducing the runtime of the algorithm and hence providing visualisations faster. We show that both visually and numerically, uniform random sampling and Poisson disk sampling can result in much faster runtimes while producing similar, or even more meaningful embeddings than the embedding of the entire dataset.

Modern data analysis often involves working with large multidimensional datasets. Visualizing this kind of data helps leverage human intuition and pattern recognition to reveal hidden relationships. t-SNE is a widely used tool for creating such visualizations. Despite its popularity, it suffers drawbacks in the form of hard-to-tune parameters with no heuristic for guaranteed best results. Due to the size of the data researchers have to work with, the algorithm can often exceed the available memory and lead to slowdowns and crashes. This paper investigates the behaviour of memory usage with respect to the tunable parameter perplexity and the size of the data. It provides a reliable way for researchers to predict the memory consumption before running the algorithm for the popular openTSNE implementation of t-SNE. In addition, a modification to reduce the peak memory usage of the implementation is presented. Together, these contributions improve the reliability and efficiency of t-SNE pipelines in memory-constrained environments.

T-SNE is widely used for visualising high-dimensional data in lower dimensions.
To reduce the costs of parameter optimisation, t-SNE is performed on a sample of the original data. After sampling the points, the distances between them need to be calculated, which is expensive due to the high dimensionality of the data. We apply Dijkstra's algorithm to approximate the distances and similarities between the sampled points. This reduces the algorithm's execution time by up to 40% without degrading the quality of the projections.

Visualizing high-dimensional data is a key challenge in modern data analysis. T-distributed Stochastic Neighbor Embedding (t-SNE) is a popular nonlinear dimensionality reduction technique that maps such data into a low-dimensional embedding while preserving local relationships. A critical hyperparameter in t-SNE is perplexity. Choosing an appropriate value of perplexity for a particular use-case is non-trivial, especially for large datasets, where repeated t-SNE computations become computationally prohibitive. To mitigate this, the sample-based approach runs t-SNE twice: first on a downsampled subset of the data and then on the full dataset. This introduces two perplexity parameters: sample perplexity for the first run and full perplexity for the second run.

In this work, we systematically investigate the impact of varying combinations of sample perplexity and full perplexity on the quality of the final t-SNE embedding. Our findings show that sample perplexity predominantly determines the global layout of the embedding, while full perplexity influences local refinement. We also compare our approach with different strategies for choosing perplexity values, and find that while some offer better preservation of structural details, they provide less flexibility.

Dimensionality reduction techniques, such as t-SNE, are widely used to visualize high-dimensional data and have a crucial role in practical tasks such as biological data exploration, anomaly detection, or clustering large datasets. However, they are highly dependent on hyperparameters or sampling strategies. This paper investigates whether the structural similarity between sampled and full embeddings can be measured using Procrustes analysis by comparing the structural similarity of the embeddings. This work provides a reproducible framework that quantifies the difference between visualizations produced by sampling t-SNE. These insights provide users a medium to create visualizations with t-SNE without exhaustive experimentation (for example, creating all visualizations), making t-SNE more accessible and reliable.

Covariance Neural Networks (VNNs) leverage the covariance matrix of user-item rating data to construct graph structures that enable effective graph convolutions for collaborative filtering. However, empirical covariance estimates often contain noisy correlations arising from limited or sparse data, which can degrade the stability and predictive accuracy of VNNs. This paper investigates how sparsification techniques applied to the covariance matrix can mitigate noise and improve model efficiency. We propose a flexible framework that performs thresholding, which removes edges with weights below a fixed cutoff, and stochastic sparsification, which randomly retains edges based on their strength, thereby adapting to both sparse and dense covariance patterns.

This thesis presents a computational framework aimed at enabling the analysis and modeling of boomerangs from example shapes. The goal is to provide a systematic and data-driven tool for boomerang design based on real-world geometries. A key challenge in this context is establishing accurate shape correspondences between handcrafted, asymmetric, and aerodynamically functional boomerangs.
To address this, the proposed pipeline integrates multiple components: landmark-based pre-alignment, boundary extraction using alpha shapes, curve parameterization, and Least Squares Conformal Mapping (LSCM) to compute surface correspondences. Building on these correspondences, the framework further incorporates principal component analysis (PCA) and Free-Form Deformation (FFD) to enable the generation of new shapes.
Experimental results show that the method achieves low Hausdorff and Chamfer distances and has been evaluated using area- and shear-based distortion metrics. Nonetheless, some localized inaccuracies - particularly near high-curvature regions - highlight areas for improvement in boundary handling and local control. Additional limitations include the reliance on manual landmark selection, the linearity of PCA, and the sensitivity of the pipeline to alpha shape parameters.
By combining elements of computational geometry with principles of aerodynamic design, this research bridges the gap between empirical craftsmanship and formal shape analysis. The resulting methodology not only enables the comparison and modeling of boomerangs but also lays the groundwork for future tools in boomerang shape exploration and design.

Radiotherapy (RT) is a widespread and effective technique to treat cancers by killing cancerous cells with rays of radiation. Building upon advances in image guidance and dose delivery technology like Proton Therapy, Adaptive RT promises more effective tumor decimation and a reduction of the incidence and severity of side effects. Unfortunately, the clinical implementation of adaptive workflows is challenging due to their resource-intensive nature. Therefore, their successful adoption lingers on overcoming several bottlenecks in the treatment planning process.

In this dissertation, we focus on methods used for the image segmentation or contouring step, which allows the localization of the anatomical structures required for dose optimization and evaluation. Until recently, clinicians had to manually delineate dozens of organs-at-risk and target volumes across hundreds of slices of the patient’s three-dimensional images. A process that is extremely time-consuming. The advent of deep learning-based artificial intelligence (AI) has changed the landscape: a modern auto-segmentation AI can produce segmentations for most of a patient’s anatomy in minutes.

Despite increasing automation in the segmentation process, it remains time and resource-intensive. Due to the segmentations’ criticality for the patient’s outcome and the errors the AI will commit, clinicians must perform a quality assessment of the AI’s outputs. Depending on the case’s complexity, the duration of the quality assessment process can negate the time gains auto-segmentation tools bring.

Deep ensemble AIs represent an advancement in medical image segmentation. Instead of providing a deterministic output, deep ensemble AIs produce a set of plausible candidates that aim to model inter-clinician annotation variability. Consensus segmentations obtained from ensembles tend to be more accurate and robust than the single-prediction deterministic counterpart. Nevertheless, by only using the consensus, a lot of potentially useful information is being discarded.

In this dissertation, we contribute to different phases of the segmentation quality assessment process. We characterize this process and introduce methods that leverage the raw outputs of deep ensemble AIs to support and speed up quality assessment tasks. The methods presented show new ways of analyzing and using ensembles in RT. Nevertheless, since these are relevant outside RT, we keep the presentation of the methods general and evaluate them in other application scenarios, such as the analysis of simulation ensembles or meteorological data.

Before fixing segmentation failures, clinicians must find them. This process can be time-consuming and fatiguing when failures are sparse and spread through the patient’s three-dimensional images. We present and evaluate a delineation error detection system, which guides clinicians to slices of three-dimensional images that contain potentially clinically relevant segmentation failures. We co-designed the DEDS with clinicians and refined it based on an observational study, which allowed us to characterize clinicians’ navigation patterns and the use of information sources like AI uncertainty and patients’ dose distributions. We evaluated the DEDS’ potential to speed up the QA process through a simulation study with a retrospective cohort of patients. Results indicate that speed-ups are the most significant when equipping the DEDS with information sources indicative of clinical priority, which prevents unnecessary edits.

Visual inspection of the segmentation ensemble permits understanding the main trends and detecting anomalies that might indicate segmentation failures. Using a spaghetti plot to visualize all ensemble members is straightforward but prone to clutter. Contour boxplots prevent clutter and extra complexity by distilling essential ensemble information, which permits more efficient ensemble inspection. Nevertheless, they are time-consuming to compute, reducing their practical value. We present Inclusion Depth for contour ensembles. Inclusion Depth yields per ensemble member centrality scores that allow characterizing the distribution of segmentation ensembles in terms of properties like the median, trimmed mean, confidence bands, and outliers. Compared to previous contour depth notions, Inclusion Depth is significantly faster, making it more applicable in practice for time-critical contexts like QA in adaptive RT. We show how Inclusion Depth permits creating contour boxplots for ensembles with hundreds of segmentations in seconds.

It is not uncommon for distinct representative shapes to co-occur within a contour ensemble. With ensembles created by clinicians, for instance, different institutions, training sessions, or experience levels can lead to distinct shapes (i.e., modes of variation) for the same structure. When trained on these data, deep ensemble AIs would yield similarly multimodal ensembles. In quality assessment, being able to extract these representatives would pave the way for new ensemble-based interactive segmentation workflows. Applying traditional contour depth notions to these multi-modal ensembles collapses the existing variation modes and can lead to uninformative centrality scores. To address this issue, we present the first framework for multi-modal contour depth, which also includes notable runtime improvements for depth computation. When used with Inclusion Depth, multi-modal contour depth permits clustering the different modes of variation and determining cluster-dependent scores that appropriately characterize the data. Variation modes can be then independently analyzed using uni-modal depth machinery like contour boxplots. xiii

The global perspective of contour depth methods, which consider the entire volume, may be insufficient when parts of the contours are noisy or when the resolution of the ensemble is too large to process within a reasonable time. Correlation clustering methods provide a solution by partitioning the spatial domain of the ensemble into highly correlated regions that can be used to localize analyses. Existing correlation clustering algorithms do not scale well as the resolution of the ensemble increases. We introduce the Local-to-Global Correlation Clustering (LoGCC) method, which partitions the ensemble’s spatial domain into coarser primitives, representing areas of consistent ensemble member behavior. Unlike previous correlation clustering methods, the proposed LoGCC achieves significantly faster runtimes by leveraging the ensemble’s spatial structure and decoupling computations into local and global steps. Like with Inclusion Depth, these speed gains enable LoGCC to analyze large datasets in time-critical fields such as adaptive radiotherapy (RT).

Throughout this dissertation, our approach focused on designing modular, flexible analysis methods applicable across different tasks and domains. We demonstrate how the delineation error detection system, multi-modal Inclusion Depth, and Local-to-Global Correlation Clustering support quality assessment in RT and extend to fields like meteorology. We also speculate on their potential as foundational elements for more complex workflows. For example, extracted modes of variation, which indicate representative shapes in the ensemble, could be repurposed as an interactive segmentation tool. Alternatively, consistent regions detected by correlation clustering could be used as building blocks to enable localized contour analysis and editing.

We hope the proposed contour ensemble visual analysis methods inspire the development of more efficient analysis workflows that harness ensembles’ power in RT and beyond.

Mesh data is widely used in engineering for instance for simulations, CAD engineering and visualizations. The accuracy and quality of the meshes influence the reliability and validity of these processes. Besides manual modelling, scanning is becoming increasingly more common due to the increase in devices that have scanning capabilities. Unwanted noise is often present in scanned models. The process of mesh denoising is removing the unwanted noise whilst keeping the features of the mesh. These features are often anisotropic, e.g. sharp edges and corners.

The DeltaConv convolution is an anisotropic convolution, Wiersma et al. [24] show the advantage of using the anisotropic DeltaConv convolution for anisotropic tasks over other isotropic convolutions. In this thesis it is investigated if state-of-the-art mesh denoising can benefit from using the DeltaConv convolution. This is done by integrating the DeltaConv convolution in the Dual-DMP [6] algorithm, and tuning this network.

In this thesis we found that state-of-the-art mesh denoising can benefit from using the DeltaConv convolution. Due to the expressiveness of the DeltaConv convolution, objects with sharp features are denoised better than the state-of-the-art algorithms and on smooth meshes, DeltaConv works comparable to state-of-the-art algorithms.

The n-body problem is the simulation of pair-wise interactions between n objects. This problem appears in many forms, with the classic example being the modeling of gravitational forces between point masses, necessary for cosmological simulations. Many approximation approaches have been devised to reduce the complexity of this problem.

t-SNE is a data visualization method that requires repeatedly solving a variant of the n-body problem. A recent paper (An Efficient Dual-Hierarchy t-SNE Minimization, van de Ruit et. al.) proposes a novel algorithm that outperforms other t-SNE minimization methods on medium-scale datasets. The report proves the viability of a dual-traversal method that uses an embedding tree to emit forces and an independent field tree to collect forces. Because the embedding tree is a Linear-BVH and the field tree is an orthtree built to a fixed depth, the overall algorithm has linear complexity.

This thesis demonstrates how the dual-tree approach can be adapted for gravitational n-body simulations. Following this, it measures the performance against similar implementations of other algorithms and shows that while the adapted Dual Hierarchy approach is faster than Barnes-Hut, it is outperformed by the Fast Multipole Method on realistic large-scale cosmological datasets.

Accurate segmentation of anatomical structures and abnormalities in medical images is crucial, but manual segmentation is time-consuming and automated approaches lack clinical accuracy. In recent years, active learning approaches that aim to combine automatic segmentation with manual input have gained attention in the field, aiming to reduce the annotation effort required for training segmentation models. Batch query retrieval is a key component of active learning as it is a technique that allows for the simultaneous selection of multiple regions/points for annotation. This study investigates the effectiveness of discrete batch query retrieval methods compared to the traditional approach using gradient descent in the context of 3D medical image segmentation. Our experiments show that the active learning paradigm with batch query retrieval provides a few advantages over the gradient descent approach. Additionally, we analyze the impact of discretizing the query retrieval strategy on system performance. Our findings suggest that discretization can lead to slight performance degradation in terms of segmentation quality but offer computational advantages and faster convergence. We also discuss open issues, such as the interpretability of active learning methods, and recommend further research on combining active learning with other segmentation techniques. Overall, our study contributes to the understanding of active learning in medical image segmentation and provides insights for developing more efficient and accurate interactive segmentation models.

Although automated segmentation of 3D medical images produce near-ideal results, they encounter limitations and occasional errors, necessitating manual intervention for error correction. Recent studies introduce an active learning pipeline as an efficient solution for this, requiring user corrections only on some of the most uncertain parts of
the automatically segmented image. It does so by combining different uncertainty fields, which are various ways to quantify possible errors. We investigate into its individual uncertainty fields and their combination scheme in attempt to validate its methods. Additionally, we replace its methods for estimating uncertainty with another common way to do so, called the ensemble method, to test possible improvements at uncertainty estimation. Results of this research validates the combination method of the active learning pipeline, and shows weak advantages but strong disadvantages of the ensemble method when compared to the combined method of the active learning pipeline.

Segmentation of 3D medical images is useful for various medical tasks. However, fully automated segmentation lacks the accuracy required for medical purposes while manual segmentation is too time-consuming. Therefore, an active learning method can be used to generate an accurate segmentation using less user input. The active learning pipeline consists of automatic 3D segmentation, generation of a 3D uncertainty field and an optimization algorithm finding the optimal plane in the uncertainty field. This plane can then be shown to a user to be labeled so that the segmentation can be improved. This process is repeated until the user is satisfied with the output. If the plane is chosen so that it contains more errors, then less user input will be needed. This paper focusses on evaluating different optimization algorithms in the context of this pipeline. The three algorithms that are evaluated are particle swarm optimization, gradient descent and L-BFGS-B. The results of the evaluation show that particle swarm optimization converges the quickest, but to lower values than gradient descent. Gradient descent converges slowly, but to high values. L-BFGS-B converges quickly to values that are as high as those from gradient descent. Therefore, using L-BFGS-B in the pipeline instead of gradient descent will decrease the runtime of the pipeline. Using particle swarm optimization will decrease the runtime even further, but at the cost of requiring more user input to obtain a segmentation of acceptable quality.

During the preoperative planning for breast-conserving surgery, the surgeon makes use of an MRI scan of the breast cancer patient in the prone position to accurately locate the tumour. However, surgery is performed with the patient in the supine position. The surgeon needs to mentally translate the location of the tumour from the prone position towards the supine position. The usage of mixed reality systems in the form of the Microsoft HoloLens could visually aid the surgeon by projecting the tumour in the supine position onto the patient. This requires us to obtain the tumour in the supine position by dealing with the prone-to-supine breast image registration problem.
We propose to maximize the overlap between the prone and supine surfaces of the breast through the use of soft constraints to guide the deformation. An initial subspace FEM simulation pulls the prone and supine surfaces towards each other at specified landmark correspondences between the surfaces. The resulting prone surface is projected onto the supine surface and these surface vertices are restricted to tangential movement across the surface of the breast. The tissues at the interior of the breast are deformed accordingly. Our experiments with synthesized data indicate the robustness of our method under various scenarios, except for the rigid misalignment between the prone and supine meshes. This problem of misalignment also affects the experiments with real-world data, which results in distances greater than 12mmbetween the centroids of the resulting deformed tumour and the ground-truth tumour.

The Hierarchical Subspace Iteration Method is a novel method used to compute eigenpairs of the Laplace-Beltrami problem. It reduces the number of iterations required for convergence by restricting the problem to a smaller space and prolonging the solution as a starting point. This method has shown great performance improvements for Laplace-Beltrami eigenproblems.
We propose an adaptation to the Hierarchical Subspace Iteration Method that allows for computing vibration modes of elastic objects. We evaluate potential optimizations that can be made, as well as the performance characteristics of the method. Our method was shown to be faster than SIM in most cases while even beating Matlab's Lanczos solver in some cases.

To design more efficient sailing boat sails and to analyze the efficiency of a sail trim on the water, it is very helpful to have the ability to obtain a digital copy of real-life sail configurations. As a step towards obtaining such digital copies, the Sailing Innovation Centre in collaboration with GeoDelta has created point cloud measurements from sails by placing physical markers on them. This paper introduces a physics-based reconstruction method that uses a known sail rest shape combined with this point cloud data to reconstruct the sail configuration at the time that the measurement was taken. By using a physics-based sail model and the knowledge that the sail is subject to gravity and wind forces together with a known sail rest shape, we can create plausible reconstructions even for areas in the sail where fewer to no markers are placed. Using measurements that were taken before this reconstruction method was proposed in combination with an approximated sail rest shape and material properties, our reconstruction method was approximated to have an average reconstruction distance below 1cm for a 2.5m by 4.5m sail. Taking new measurements following our proposed guidelines in combination with having a more correct sail rest shape and better knowing the sail material properties is very likely to yield even better results.

To protect the Netherlands better from flooding, and with an eye on sea-level rise in the rest of the world, more accurate assessments are needed for dykes. The calculation for the most occurring failure mechanism in dykes, i.e. macro-instability, is limited by not being able to calculate large deformation when sliding occurs within a dyke. The random material point method (RMPM) is able to capture the complete failure path, including the residual dyke strength, while taking the heterogeneity of the soil into account, thereby improving the assessment of failure processes. However, as the method is not (yet) used in current practice, clear communication of the results is essential for convincing a wider public of the contribution of this method. Visuals are an important tool in communication, as it increases comprehension of the subject matter if the visual is designed efficiently. This research aims to investigate the available software and which techniques are suitable to make realistic and informative visualizations for a given RMPM dataset of slope failure problems.
A method to create visualization with a certain graphical realism in three-dimensional space is developed. The technique uses a computer graphic software (Blender) combined with an add-on, i.e. an extension plugin. The add-on allows to work with VTK software to process scientific data for visualization, thereby maintaining the scientific correctness of the visualizations. Moreover, a rendering pipeline in Blender is created, which transforms the properties from scientific colors into realistic materials, making the visualizations more intuitive.
However, the dataset is too large to summarize in a straightforward illustration. Therefore, a data analysis is obtained to classify each realization into five pre-defined failure profiles, which are determined based on a literature study. Four failure profiles are classified based on the number of retrogressive failures and whether or not the realization resulted in flooding, while the fifth class describes horizontal failures. A technique has been developed to separate the horizontal failures from the other classes based on the plastic deviatoric strain attribute. Additionally, the data analysis aims to characterize the behavior of each failure profile from an early start, such that the findings could be used for current methods, which could not calculate the full failure profile.
Therefore, this thesis needs to investigate the reduction of the dataset to make it more time efficient when doing a data analysis. It is extended on the clustering algorithm, which has the function to detect failure blocks based on the displacement per dyke profile. The reduction method replaces an amount of data by one representative point per cluster. It not only reduced the size of the dataset significantly, from 3000 GB to 6 GB, it also made the comparison of attributes between realizations, and therefore the data analysis, easier.
The data analysis shows that it is hard to distinguish different failure profiles using only data of the initial failure, which shows the importance of using RMPM to account for post-failure behavior instead of using the current assessment i.e. FEM and LEM. One finding is that equilibrium of the initial failure block is often reached before a vertical crest displacement equal to 0.5 times the height of the dyke. This indicates that the crude estimation in the current assessment is highly conservative. Moreover, within the assumption, it is hypothesized that the secondary failure block will only form after the initial failure block has reached its equilibrium, which is shown otherwise within the data analysis of this thesis.
This work proposes a method for data analysis of RMPM using parallel coordinates, which can be extended to other RMPM datasets for macro-instability and can help to improve the prediction of the probability of flooding. Moreover, it proposes a method to visualize the prominent features, determined using parallel coordinates, in Blender-VTK. This work can, in future research, be extended to other geotechnical problems, such as 3-dimensional dyke slope failure.

Grid-based fluid simulations are often limited in resolution by their high memory usage and computational costs. One approach to reducing memory usage and computational costs is to vary the grid resolution over the spatial domain. We introduce DCGrid, a new data structure for fluid simulations. DCGrid is suited for instantiation in GPU memory and allows for varying resolution over the spatial domain. We developed an efficient, optimization-based method for local mesh refinement that automatically adapts the grid resolution according to user-defined parameters during simulations. Additionally, we complement our data structure with an efficient scheme for approximate handling of collisions between fluid and static solids on cells with varying resolutions. We integrate DCGrid in a cloud simulation and extend a terrain-atmosphere interaction model to work with cells of varying resolution and rapidly changing conditions. Furthermore, we demonstrate the performance of our new methods on both simple simulations of smoke flow and complex simulations of weather phenomena and compare them to similar fluid simulations on state-of-the-art adaptive grid structures.

This research provides an overview on how training Convolutional Neural Networks (CNNs) on imbalanced datasets affect the performance of the CNNs. Datasets could be imbalanced as a result of several reasons. There are for example naturally less samples of rare diseases. Since the network is trained less on those instances, this might lead to worse performance on those cases. However, it might be more crucial to identify those cases properly. Furthermore, it is non-trivial to check whether real-time generated data is balanced. The networks in this research are trained on three different types of synthetic datasets. Balanced datasets, datasets with missing targets and datasets that have normally distributed targets. The task of the network is to find the standard deviation of the pixel intensity of the input. The results show that it is best to train the network on balanced datasets, however training networks on datasets with normally distributed targets does not result in a big loss. Furthermore, in this case the CNNs were still able to learn the task with decent performance if the training set missed targets.

Despite evidence that collaborating in the supply chain can reduce inefficiency and result in mutual gain, parties do not wish to collaborate if they have to share their private proprietary information. The main reason for their privacy concern is that the party does not want to lose their competitive advantage by giving away company secrets. Collaborative optimization algorithms can be applied to problems in the supply chain, and secure multiparty computation is incorporated as part of the algorithm to preserve the privacy of the parties. This paper aims to create an overview of privacy-preserving applications in the collaborative supply chain by conducting a literary study that focuses on secure collaborative optimization research and its limitations.

Research findings showed that secure multiparty computation can be applied to the following supply chain collaboration problems: capacity sharing, price-masking, distributed scheduling, collaborative production and transport, vehicle routing, and resource allocation. These algorithms use multiparty computation that is secure under the semi-honest adversarial model, because a malicious model is generally too inefficient for practical use. This choice comes with a cost in privacy, as the semi-honest model assumes parties collaborating will not break the protocol. This is a weak assumption that results in an impractical protocol, as real life applications of semi-honest multiparty computation would not be protected against a party that benefits from cheating. Furthermore, secure multiparty computation has a limitation that it cannot prevent a party from lying in its private input.

This paper recommends for future secure collaborative optimization research to combine multiparty computation with game theory. Achieving incentive compatibility in a protocol proves that it is in the best interest for a party to not cheat, as it either leads to a loss in benefits or they are caught. This allows for the MPC protocol to keep its efficiency by being secure under just a semi-honest adversarial model, as well as offer greater protection for honest parties from a rational malicious party.