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K.A. Hildebrandt

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37 records found

Journal article (2026) - Jackson Campolattaro, Ruben Wiersma, Klaus Hildebrandt
We introduce Geometric Multigrid Neural Networks (GMNN), a novel network structure for geometric deep learning on point clouds and surfaces. Convolutional neural networks face a common challenge: how can relevant features be communicated over longer distances? Our architecture facilitates long-distance communication with Geometric Multigrid Convolution (GMC) blocks, which apply convolutions in parallel to features defined on each level of a multigrid representation of the surface, and enable communication all the way up and down the hierarchy. We observe two major structural advantages of such a network: First, because each GMC operates on all levels of the multigrid hierarchy, even early stages can make use of coarse-scale information and receptive field grows rapidly with depth. Second, networks built with this backbone have the freedom to route information between different scales, including in ways not possible for other architectures. Because of these advantages, we find that a GMNN can combine the fast convergence of a shallow network with the greater expressiveness of a deeper, larger network. We build a GMNN from the components of a state-of-the-art U-Net, and find that on real tasks it can match or exceed the accuracy of the base network while using fewer epochs and roughly half the parameter count. ...
Journal article (2025) - Jette J. Peek, Klaus Hildebrandt, Xucong Zhang, Rohit K. Kharbanda, Maurice A.P. Oudeman, Robert J.M. Klautz, Meindert Palmen, Edris A.F. Mahtab
Objective:
In mitral valve surgery, it is important to be aware of adjacent intraoperatively invisible anatomy, to avoid complications and enhance safety. In this feasibility study, we aimed to develop semi-automated intraoperative 3-dimensional (3D) augmented reality (3D-AR) overlays for robotic mitral valve repair.

Methods:
In 5 patients undergoing robot-assisted mitral valve repair, a 3D point cloud was generated, using intraoperatively recorded images from both eyes of the stereoscopic da Vinci camera (Intuitive Surgical, Sunnyvale, CA, USA). An intraoperative 3D-AR overlay was created using a scale-adaptive iterative closest point algorithm and landmarks placed on the mitral valve annulus. Finally, important anatomical structures such as the circumflex artery, Koch’s triangle, and aortic valve leaflets could be visualized as a 3D-AR overlay on top of the surgical vision. To evaluate the accuracy, these 3D point clouds were validated by calculating the 3D point cloud accuracy and landmark registration error (LRE).

Results:
The 3D point clouds and 3D-AR overlays were successfully created for all 5 patients. The 3D point clouds were accurate, with a median error of −0.92 mm, and the LRE was 5.12 mm. The time for creating the 3D-AR overlay was approximately 5 min. Besides creating the 3D-AR overlays, we could visualize the models directly within the robotic console during the surgical procedure.

Conclusions:
We present an algorithm for generating accurate semiautomatic 3D-AR overlays, visualizing essential anatomical structures during robot-assisted mitral valve repair. This may lead to automated intraoperative 3D-AR vision during robotic cardiac surgery, with the potential of increasing safety, accuracy, and efficiency. ...
Journal article (2024) - Prerak Mody, Merle Huiskes, Nicolas F. Chaves-de-Plaza, Alice Onderwater, Rense Lamsma, Klaus Hildebrandt, Nienke Hoekstra, Eleftheria Astreinidou, Marius Staring, More authors...
Background and purpose: Retrospective dose evaluation for organ-at-risk auto-contours has previously used small cohorts due to additional manual effort required for treatment planning on auto-contours. We aimed to do this at large scale, by a) proposing and assessing an automated plan optimization workflow that used existing clinical plan parameters and b) using it for head-and-neck auto-contour dose evaluation. Materials and methods: Our automated workflow emulated our clinic's treatment planning protocol and reused existing clinical plan optimization parameters. This workflow recreated the original clinical plan (POG) with manual contours (PMC) and evaluated the dose effect (POG-PMC) on 70 photon and 30 proton plans of head-and-neck patients. As a use-case, the same workflow (and parameters) created a plan using auto-contours (PAC) of eight head-and-neck organs-at-risk from a commercial tool and evaluated their dose effect (PMC-PAC). Results: For plan recreation (POG-PMC), our workflow had a median impact of 1.0% and 1.5% across dose metrics of auto-contours, for photon and proton respectively. Computer time of automated planning was 25% (photon) and 42% (proton) of manual planning time. For auto-contour evaluation (PMC-PAC), we noticed an impact of 2.0% and 2.6% for photon and proton radiotherapy. All evaluations had a median ΔNTCP (Normal Tissue Complication Probability) less than 0.3%. Conclusions: The plan replication capability of our automated program provides a blueprint for other clinics to perform auto-contour dose evaluation with large patient cohorts. Finally, despite geometric differences, auto-contours had a minimal median dose impact, hence inspiring confidence in their utility and facilitating their clinical adoption. ...
Journal article (2024) - N. F. Chaves-de-Plaza, M. Molenaar, P. Mody, M. Staring, R. van Egmond, E. Eisemann, A. Vilanova, K. Hildebrandt
The contour depth methodology enables non-parametric summarization of contour ensembles by extracting their representatives, confidence bands, and outliers for visualization (via contour boxplots) and robust downstream procedures. We address two shortcomings of these methods. Firstly, we significantly expedite the computation and recomputation of Inclusion Depth (ID), introducing a linear-time algorithm for epsilon ID, a variant used for handling ensembles with contours with multiple intersections. We also present the inclusion matrix, which contains the pairwise inclusion relationships between contours, and leverage it to accelerate the recomputation of ID. Secondly, extending beyond the single distribution assumption, we present the Relative Depth (ReD), a generalization of contour depth for ensembles with multiple modes. Building upon the linear-time eID, we introduce CDclust, a clustering algorithm that untangles ensemble modes of variation by optimizing ReD. Synthetic and real datasets from medical image segmentation and meteorological forecasting showcase the speed advantages, illustrate the use case of progressive depth computation and enable non-parametric multimodal analysis. To promote research and adoption, we offer the contour-depth Python package. ...
The need to understand the structure of hierarchical or high-dimensional data is present in a variety of fields. Hyperbolic spaces have proven to be an important tool for embedding computations and analysis tasks as their non-linear nature lends itself well to tree or graph data. Subsequently, they have also been used in the visualization of high-dimensional data, where they exhibit increased embedding performance. However, none of the existing dimensionality reduction methods for embedding into hyperbolic spaces scale well with the size of the input data. That is because the embeddings are computed via iterative optimization schemes and the computation cost of every iteration is quadratic in the size of the input. Furthermore, due to the non-linear nature of hyperbolic spaces, euclidean acceleration structures cannot directly be translated to the hyperbolic setting. This article introduces the first acceleration structure for hyperbolic embeddings, building upon a polar quadtree. We compare our approach with existing methods and demonstrate that it computes embeddings of similar quality in significantly less time. Implementation and scripts for the experiments can be found at https://graphics.tudelft.nl/accelerating-hyperbolic-tsne . ...
Journal article (2024) - Nicolas F. Chaves-de-Plaza, Prerak Mody, Marius Staring, Rene van Egmond, Anna Vilanova, Klaus Hildebrandt
Ensembles of contours arise in various applications like simulation, computer-Aided design, and semantic segmentation. Uncovering ensemble patterns and analyzing individual members is a challenging task that suffers from clutter. Ensemble statistical summarization can alleviate this issue by permitting analyzing ensembles' distributional components like the mean and median, confidence intervals, and outliers. Contour boxplots, powered by Contour Band Depth (CBD), are a popular non-parametric ensemble summarization method that benefits from CBD's generality, robustness, and theoretical properties. In this work, we introduce Inclusion Depth (ID), a new notion of contour depth with three defining characteristics. First, ID is a generalization of functional Half-Region Depth, which offers several theoretical guarantees. Second, ID relies on a simple principle: The inside/outside relationships between contours. This facilitates implementing ID and understanding its results. Third, the computational complexity of ID scales quadratically in the number of members of the ensemble, improving CBD's cubic complexity. This also in practice speeds up the computation enabling the use of ID for exploring large contour ensembles or in contexts requiring multiple depth evaluations like clustering. In a series of experiments on synthetic data and case studies with meteorological and segmentation data, we evaluate ID's performance and demonstrate its capabilities for the visual analysis of contour ensembles. ...

Do AI-supported optimization and human preferences meet?

Journal article (2024) - Nicolas F. Chaves-de-Plaza, Prerak Mody, Klaus Hildebrandt, Marius Staring, Eleftheria Astreinidou, Mischa de Ridder, Huib de Ridder, Anna Vilanova, René van Egmond
Artificial Intelligence (AI)-based auto-delineation technologies rapidly delineate multiple structures of interest like organs-at-risk and tumors in 3D medical images, reducing personnel load and facilitating time-critical therapies. Despite its accuracy, the AI may produce flawed delineations, requiring clinician attention. Quality assessment (QA) of these delineations is laborious and demanding. Delineation error detection systems (DEDS) aim to aid QA, yet questions linger about potential challenges to their adoption and time-saving potential. To address these queries, we first conducted a user study with two clinicians from Holland Proton Therapy Center, a Dutch cancer treatment center. Based on the study’s findings about the clinicians’ error detection workflows with and without DEDS assistance, we developed a simulation model of the QA process, which we used to assess different error detection workflows on a retrospective cohort of 42 head and neck cancer patients. Results suggest possible time savings, provided the per-slice analysis time stays close to the current baseline and trading-off delineation quality is acceptable. Our findings encourage the development of user-centric delineation error detection systems and provide a new way to model and evaluate these systems’ potential clinical value. ...
Journal article (2024) - J. J. Peek, X. Zhang, K. Hildebrandt, S. A. Max, A. H. Sadeghi, A. J.J.C. Bogers, E. A.F. Mahtab
Purpose: In this feasibility study, we aimed to create a dedicated pulmonary augmented reality (AR) workflow to enable a semi-automated intraoperative overlay of the pulmonary anatomy during video-assisted thoracoscopic surgery (VATS) or robot-assisted thoracoscopic surgery (RATS). Methods: Initially, the stereoscopic cameras were calibrated to obtain the intrinsic camera parameters. Intraoperatively, stereoscopic images were recorded and a 3D point cloud was generated from these images. By manually selecting the bifurcation key points, the 3D segmentation (from the diagnostic CT scan) was registered onto the intraoperative 3D point cloud. Results: Image reprojection errors were 0.34 and 0.22 pixels for the VATS and RATS cameras, respectively. We created disparity maps and point clouds for all eight patients. Time for creation of the 3D AR overlay was 5 min. Validation of the point clouds was performed, resulting in a median absolute error of 0.20 mm [IQR 0.10–0.54]. We were able to visualize the AR overlay and identify the arterial bifurcations adequately for five patients. In addition to creating AR overlays of the visible or invisible structures intraoperatively, we successfully visualized branch labels and altered the transparency of the overlays. Conclusion: An algorithm was developed transforming the operative field into a 3D point cloud surface. This allowed for an accurate registration and visualization of preoperative 3D models. Using this system, surgeons can navigate through the patient's anatomy intraoperatively, especially during crucial moments, by visualizing otherwise invisible structures. This proposed registration method lays the groundwork for automated intraoperative AR navigation during minimally invasive pulmonary resections. ...
Widely used pipelines for analyzing high-dimensional data utilize two-dimensional visualizations. These are created, for instance, via t-distributed stochastic neighbor embedding (t-SNE). A crucial element of the t-SNE embedding procedure is the perplexity hyperparameter. That is because the embedding structure varies when perplexity is changed. A suitable perplexity choice depends on the data set and the intended usage for the embedding. Therefore, perplexity is often chosen based on heuristics, intuition, and prior experience. This paper uncovers a linear relationship between perplexity and the data set size. Namely, we show that embeddings remain structurally consistent across data set samples when perplexity is adjusted accordingly. Qualitative and quantitative experimental results support these findings. This informs the visualization process, guiding the user when choosing a perplexity value. Finally, we outline several applications for the visualization of high-dimensional data via t-SNE based on this linear relationship. ...
We introduce a geometric multigrid method for solving linear systems arising from variational problems on surfaces in geometry processing, Gravo MG. Our scheme uses point clouds as a reduced representation of the levels of the multigrid hierarchy to achieve a fast hierarchy construction and to extend the applicability of the method from triangle meshes to other surface representations like point clouds, nonmanifold meshes, and polygonal meshes. To build the prolongation operators, we associate each point of the hierarchy to a triangle constructed from points in the next coarser level. We obtain well-shaped candidate triangles by computing graph Voronoi diagrams centered around the coarse points and determining neighboring Voronoi cells. Our selection of triangles ensures that the connections of each point to points at adjacent coarser and finer levels are balanced in the tangential directions. As a result, we obtain sparse prolongation matrices with three entries per row and fast convergence of the solver. Code is available at https://graphics.tudelft.nl/gravo_mg. ...
Preprint (2023) - Nicolas F. Chaves-de-Plaza, P. Mody, K.A. Hildebrandt, M. Staring, Eleftheria Astreinidou, Mischa de Ridder, H. de Ridder, A. Vilanova Bartroli, R. van Egmond
Artificial Intelligence (AI)-based auto-delineation technologies rapidly delineate multiple structures of interest like organs-at-risk and tumors in 3D medical images, reducing personnel load and facilitating time-critical therapies. Despite its accuracy, the AI may produce flawed delineations, requiring clinician attention. Quality assessment (QA) of these delineations is laborious and demanding. Delineation error detection systems aim to aid QA, yet questions linger about clinician adoption, challenges, and time-saving potential. In this study, we address these queries in two stages. First, we investigate the error detection workflow of a radiotherapy technologist and a radiation oncologist from Holland Proton Therapy Center, a Dutch cancer treatment center. The user study revealed which information sources clinicians prefer to use for the error prioritization task and elucidated clinicians' slice-based navigation workflows with and without system assistance. Based on the findings from the user study, we developed a simulation model of the QA process, which we used to assess different error detection workflows on a retrospective cohort of 42 head and neck cancer patients. The simulation study results indicate potential time savings through error and dose information, contingent on per-slice analysis time remaining near the current baseline. Our findings encourage the development of user-centric delineation error detection systems and provide a new way to model and evaluate these systems' potential clinical value. ...
Conference paper (2022) - Prerak Mody, Nicolas F. Chaves-de-Plaza, Klaus Hildebrandt, Marius Staring
Bayesian Neural Nets (BNN) are increasingly used for robust organ auto-contouring. Uncertainty heatmaps extracted from BNNs have been shown to correspond to inaccurate regions. To help speed up the mandatory quality assessment (QA) of contours in radiotherapy, these heatmaps could be used as stimuli to direct visual attention of clinicians to potential inaccuracies. In practice, this is non-trivial to achieve since many accurate regions also exhibit uncertainty. To influence the output uncertainty of a BNN, we propose a modified accuracy-versus-uncertainty (AvU) metric as an additional objective during model training that penalizes both accurate regions exhibiting uncertainty as well as inaccurate regions exhibiting certainty. For evaluation, we use an uncertainty-ROC curve that can help differentiate between Bayesian models by comparing the probability of uncertainty in inaccurate versus accurate regions. We train and evaluate a FlipOut BNN model on the MICCAI2015 Head and Neck Segmentation challenge dataset and on the DeepMind-TCIA dataset, and observed an increase in the AUC of uncertainty-ROC curves by 5.6% and 5.9%, respectively, when using the AvU objective. The AvU objective primarily reduced false positives regions (uncertain and accurate), drawing less visual attention to these regions, thereby potentially improving the speed of error detection. ...
Post-translational modifications (PTMs) affecting a protein's residues (amino acids) can disturb its function, leading to illness. Whether or not a PTM is pathogenic depends on its type and the status of neighboring residues. In this paper, we present the ProtoFold Neighborhood Inspector (PFNI), a visualization system for analyzing residues neighborhoods. The main contribution is a visualization idiom, the Residue Constellation (RC), for identifying and comparing three-dimensional neighborhoods based on per-residue features and spatial characteristics. The RC leverages two-dimensional representations of the protein's three-dimensional structure to overcome problems like occlusion, easing the analysis of neighborhoods that often have complicated spatial arrangements. Using the PFNI, we explored proteins' structural PTM data, which allowed us to identify patterns in the distribution and quantity of per-neighborhood PTMs that might be related to their pathogenic status. In the following, we define the tasks that guided the development of the PFNI and describe the data sources we derived and used. Then, we introduce the PFNI and illustrate its usage through an example of an analysis workflow. We conclude by reflecting on preliminary findings obtained while using the tool on the provided data and future directions concerning the development of the PFNI. ...
Learning from 3D point-cloud data has rapidly gained momentum, motivated by the success of deep learning on images and the increased availability of 3D~data. In this paper, we aim to construct anisotropic convolution layers that work directly on the surface derived from a point cloud. This is challenging because of the lack of a global coordinate system for tangential directions on surfaces. We introduce DeltaConv, a convolution layer that combines geometric operators from vector calculus to enable the construction of anisotropic filters on point clouds. Because these operators are defined on scalar- and vector-fields, we separate the network into a scalar- and a vector-stream, which are connected by the operators. The vector stream enables the network to explicitly represent, evaluate, and process directional information. Our convolutions are robust and simple to implement and match or improve on state-of-the-art approaches on several benchmarks, while also speeding up training and inference. ...
Preprint (2022) - Nicolas F. Chaves-de-Plaza, P. Mody, K.A. Hildebrandt, M. Staring, E. Astreinidou, M. de Ridder, H. de Ridder, R. van Egmond
Delineation of tumors and organs-at-risk permits detecting and correcting changes in the patients' anatomy throughout the treatment, making it a core step of adaptive proton therapy (APT). Although AI-based auto-contouring technologies have sped up this process, the time needed to perform the quality assessment (QA) of the generated contours remains a bottleneck, taking clinicians between several minutes up to an hour to complete. This paper introduces a fast contouring workflow suitable for time-critical APT, enabling detection of anatomical changes in shorter time frames and with a lower demand of clinical resources. The proposed AI-infused workflow follows two principles uncovered after reviewing the APT literature and conducting several interviews and an observational study in two radiotherapy centers in the Netherlands. First, enable targeted inspection of the generated contours by leveraging AI uncertainty and clinically-relevant features such as the proximity of the organs-at-risk to the tumor. Second, minimize the number of interactions needed to edit faulty delineations with redundancy-aware editing tools that provide the user a sense of predictability and control. We use a proof of concept that we validated with clinicians to demonstrate how current and upcoming AI capabilities support the workflow and how it would fit into clinical practice. ...
Journal article (2022) - A. Nasikun, K.A. Hildebrandt
Sparse eigenproblems are important for various applications in computer graphics. The spectrum and eigenfunctions of the Laplace–Beltrami operator, for example, are fundamental for methods in shape analysis and mesh processing. The Subspace Iteration Method is a robust solver for these problems. In practice, however, Lanczos schemes are often faster. In this article, we introduce the Hierarchical Subspace Iteration Method (HSIM), a novel solver for sparse eigenproblems that operates on a hierarchy of nested vector spaces. The hierarchy is constructed such that on the coarsest space all eigenpairs can be computed with a dense eigensolver. HSIM uses these eigenpairs as initialization and iterates from coarse to fine over the hierarchy. On each level, subspace iterations, initialized with the solution from the previous level, are used to approximate the eigenpairs. This approach substantially reduces the number of iterations needed on the finest grid compared to the non-hierarchical Subspace Iteration Method. Our experiments show that HSIM can solve Laplace–Beltrami eigenproblems on meshes faster than state-of-the-art methods based on Lanczos iterations, preconditioned conjugate gradients, and subspace iterations. ...
Book chapter (2022) - N.F. Chaves de Plaza, P. Mody, K.A. Hildebrandt, M. Staring, Eleftheria Astreinidou, Mischa de Ridder, H. de Ridder, R. van Egmond
Delineation of tumours and organs-at-risk permits detecting and correcting changes in the patients' anatomy throughout the treatment, making it a core step of adaptive external beam radiotherapy. Although auto-contouring technologies have sped up this process, the time needed to perform the quality assessment of the generated contours remains a bottleneck, taking clinicians between several minutes and an hour to complete. The authors of this article conducted several interviews and an observational study at two treatment centres in the Netherlands to identify challenges and opportunities for speeding up the delineation process in adaptive therapies. The study revealed three contextual variables that influence contouring performance: usable additional information, applicable domain-specific knowledge, and available editing capabilities in contouring software. In practice, clinicians leverage these variables to accelerate contouring in two ways. First, they use domain-specific knowledge and relevant clinical features such as the proximity of the organs-at-risk to the tumour to enable targeted inspection of the delineation. Second, clinicians modulate editing precision depending on the effect they anticipate the edit will have on the patient outcome. By implementing these acceleration strategies in guidelines and contouring tools, developers and workflow builders could increase contouring efficiency and consistency without affecting the patient outcome. ...

An Adaptive Grid Structure for Memory-Constrained Fluid Simulation on the GPU

Journal article (2022) - Wouter Raateland, Torsten Hädrich, Jorge Alejandro Amador Herrera, Daniel T. Banuti, Wojciech Pałubicki, Sören Pirk, Klaus Hildebrandt, Dominik L. Michels
We introduce Dynamic Constrained Grid (DCGrid), a hierarchical and adaptive grid structure for fluid simulation combined with a scheme for effectively managing the grid adaptations. DCGrid is designed to be implemented on the GPU and used in high-performance simulations. Specifically, it allows us to efficiently vary and adjust the grid resolution across the spatial domain and to rapidly evaluate local stencils and individual cells in a GPU implementation. A special feature of DCGrid is that the control of the grid adaption is modeled as an optimization under a constraint on the maximum available memory, which addresses the memory limitations in GPU-based simulation. To further advance the use of DCGrid in high-performance simulations, we complement DCGrid with an efficient scheme for approximating collisions between fluids and static solids on cells with different resolutions. We demonstrate the effectiveness of DCGrid for smoke flows and complex cloud simulations in which terrain-atmosphere interaction requires working with cells of varying resolution and rapidly changing conditions. Finally, we compare the performance of DCGrid to that of alternative adaptive grid structures. ...

Geometric priors make dataset variations vanish

Deep learning has improved vanishing point detection in images. Yet, deep networks require expensive annotated datasets trained on costly hardware and do not generalize to even slightly different domains, and minor problem variants. Here, we address these issues by injecting deep vanishing point detection networks with prior knowledge. This prior knowledge no longer needs to be learned from data, saving valuable annotation efforts and compute, unlocking realistic few-sample scenarios, and reducing the impact of domain changes. Moreover, the interpretability of the priors allows to adapt deep networks to minor problem variations such as switching between Manhattan and non-Manhattan worlds. We seamlessly incorporate two geometric priors: (i) Hough Transform -- mapping image pixels to straight lines, and (ii) Gaussian sphere -- mapping lines to great circles whose intersections denote vanishing points. Experimentally, we ablate our choices and show comparable accuracy to existing models in the large-data setting. We validate our model's improved data efficiency, robustness to domain changes, adaptability to non-Manhattan settings. ...
Journal article (2022) - Prerak Mody, Nicolas Chaves de Plaza, Klaus Hildebrandt, René van Egmond, Huib de Ridder, Marius Staring
Deep learning models for organ contouring in radiotherapy are poised for clinical usage, but currently, there exist few tools for automated quality assessment (QA) of the predicted contours. Bayesian models and their associated uncertainty, can potentially automate the process of detecting inaccurate predictions. We investigate two Bayesian models for auto-contouring, DropOut and FlipOut, using a quantitative measure – expected calibration error (ECE) and a qualitative measure – region-based accuracy-vs-uncertainty (R-AvU) graphs. It is well understood that a model should have low ECE to be considered trustworthy. However, in a QA context, a model should also have high uncertainty in inaccurate regions and low uncertainty in accurate regions. Such behaviour could direct visual attention of expert users to potentially inaccurate regions, leading to a speed-up in the QA process. Using R-AvU graphs, we qualitatively compare the behaviour of different models in accurate and inaccurate regions. Experiments are conducted on the MICCAI2015 Head and Neck Segmentation Challenge and on the DeepMindTCIA CT dataset using three models: DropOut-DICE, Dropout-CE (Cross Entropy) and FlipOut-CE. Quantitative results show that DropOut-DICE has the highest ECE, while Dropout-CE and FlipOut-CE have the lowest ECE. To better understand the difference between DropOut-CE and FlipOut-CE, we use the R-AvU graph which shows that FlipOut-CE has better uncertainty coverage in inaccurate regions than DropOut-CE. Such a combination of quantitative and qualitative metrics explores a new approach that helps to select which model can be deployed as a QA tool in clinical settings.
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