Uncertainty Visualization Research Articles

Effect of white matter uncertainty visualization in neurosurgical decision making.

Fiber tracking is a powerful technique that provides insight into the brain's white matter structure. Despite its potential, the inherent uncertainties limit its widespread clinical use. These uncertainties potentially hamper the clinical decisions neurosurgeons have to make before, during, and after the surgery. Many techniques have been developed to visualize uncertainties, however, there is limited evidence to suggest whether these uncertainty visualization influences neurosurgical decision-making. In this paper, we evaluate the hypothesis that uncertainty visualization in fiber tracking influences neurosurgeon's decisions and the confidence in their decisions. For this purpose, we designed a user study through an online interactive questionnaire and evaluate the influence of uncertainty visualization in neurosurgical decision-making. The results of this study emphasize the importance of uncertainty visualization in clinical decision making by highlighting the influence of different interval of uncertainty visualization in critical clinical decisions.

Quantifying and visualising uncertainty in deep learning-based segmentation for radiation therapy treatment planning: What do radiation oncologists and therapists want?

Background and purposeDuring the ESTRO 2023 physics workshop on “AI for the fully automated radiotherapy treatment chain”, the topic of deep learning (DL) segmentation was discussed. Despite its widespread use in radiotherapy, the time needed to evaluate and correct DL segmentations remains burdensome. While segmentation uncertainty could be beneficial for clinicians, there is a lack of understanding on what information should be presented to ease their task. This study aimed to gather insights from clinicians on uncertainty visualisation options. Materials and methodsTwo sessions of structured interviews were conducted across four institutions already using DL segmentation clinically. The first session focused on the main problems hindering the clinical use of DL. In the second session, ten visualisation options displaying uncertainty information at different levels (structure, slice, or voxel) with binary or continuous values were presented. Dosimetric information was also present in some visualisations. For each case, sixteen clinicians (radiation oncologists and radiation therapists) were asked to grade an overall score, the usability, the training required, and the expected time gain. ResultsParticipants preferred the binary voxel-level uncertainty visualisation, followed by binary structure-level uncertainty visualisation. Combining structure-level and voxel-level visualisation methods has been proposed as a promising approach. The benefits of dosimetric information were perceived diversely among participants since it complexifies the display but could be useful for the online adaptive workflow. ConclusionPreferences for uncertainty visualisation methods were assessed within a multi-institutional experienced group of clinicians. Further refinement of preferences may help in selecting the best options for clinical implementation.

Designing the Australian Cancer Atlas: visualizing geostatistical model uncertainty for multiple audiences.

The Australian Cancer Atlas (ACA) aims to provide small-area estimates of cancer incidence and survival in Australia to help identify and address geographical health disparities. We report on the 21-month user-centered design study to visualize the data, in particular, the visualization of the estimate uncertainty for multiple audiences. The preliminary phases included a scoping study, literature review, and target audience focus groups. Several methods were used to reach the wide target audience. The design and development stage included digital prototyping in parallel with Bayesian model development. Feedback was sought from multiple workshops, audience focus groups, and regular meetings throughout with an expert external advisory group. The initial scoping identified 4 target audience groups: the general public, researchers, health practitioners, and policy makers. These target groups were consulted throughout the project to ensure the developed model and uncertainty visualizations were effective for communication. In this paper, we detail ACA features and design iterations, including the 3 complementary ways in which uncertainty is communicated: the wave plot, the v-plot, and color transparency. We reflect on the methods, design iterations, decision-making process, and document lessons learned for future atlases. The ACA has been hugely successful since launching in 2018. It has received over 62000 individual users from over 100 countries and across all target audiences. It has been replicated in other countries and the second version of the ACA was launched in May 2024. This paper provides rich documentation for future projects.

Enhancing User Perception of Reliability in Computer Vision: Uncertainty Visualization for Probability Distributions

Non-expert users often find it challenging to perceive the reliability of computer vision systems accurately. In human–computer decision-making applications, users’ perceptions of system reliability may deviate from the probabilistic characteristics. Intuitive visualization of system recognition results within probability distributions can serve to enhance interpretability and support cognitive processes. Different visualization formats may impact users’ reliability perceptions and cognitive abilities. This study first compared the mapping relationship between users’ perceived values of system recognition results and the actual probabilistic characteristics of the distribution when using density strips, violin plots, and error bars to visualize normal distributions. The findings indicate that when density strips are used for visualization, users’ perceptions align most closely with the probabilistic integrals, exhibiting the shortest response times and highest cognitive arousal. However, users’ perceptions often exceed the actual probability density, with an average coefficient of 2.53 times, unaffected by the form of uncertainty visualization. Conversely, this perceptual bias did not appear in triangular distributions and remained consistent across symmetric and asymmetric distributions. The results of this study contribute to a better understanding of user reliability perception for interaction designers, helping to improve uncertainty visualization and thereby mitigate perceptual biases and potential trust risks.

Topological Characterization and Uncertainty Visualization of Atmospheric Rivers

AbstractAtmospheric rivers (ARs) are long, narrow regions of water vapor in the Earth's atmosphere that transport heat and moisture from the tropics to the mid‐latitudes. ARs are often associated with extreme weather events in North America and contribute significantly to water supply and flood risk. However, characterizing ARs has been a major challenge due to the lack of a universal definition and their structural variations. Existing AR detection tools (ARDTs) produce distinct AR boundaries for the same event, making the risk assessment of ARs a difficult task. Understanding these uncertainties is crucial to improving the predictability of AR impacts, including their landfall areas and associated precipitation, which could cause catastrophic flooding and landslides over the coastal regions. In this work, we develop an uncertainty visualization framework that captures boundary and interior uncertainties, i.e., structural variations, of an ensemble of ARs that arise from a set of ARDTs. We first provide a statistical overview of the AR boundaries using the contour boxplots of Whitaker et al. that highlight the structural variations of AR boundaries based on their nesting relationships. We then introduce the topological skeletons of ARs based on Morse complexes that characterize the interior variation of an ensemble of ARs. We propose an uncertainty visualization of these topological skeletons, inspired by MetroSets of Jacobson et al. that emphasizes the agreements and disagreements across the ensemble members. Through case studies and expert feedback, we demonstrate that the two approaches complement each other, and together they could facilitate an effective comparative analysis process and provide a more confident outlook on an AR's shape, area, and onshore impact.

Quantification and visualization of uncertainties in reconstructed penumbral images of implosions at Omega.

Penumbral imaging is a technique used in plasma diagnostics in which a radiation source shines through one or more large apertures onto a detector. To interpret a penumbral image, one must reconstruct it to recover the original source. The inferred source always has some error due to noise in the image and uncertainty in the instrument geometry. Interpreting the inferred source thus requires quantification of that inference's uncertainty. Markov chain Monte Carlo algorithms have been used to quantify uncertainty for similar problems but have never been used for the inference of the shape of an image. Because of this, there are no commonly accepted ways of visualizing uncertainty in two-dimensional data. This paper demonstrates the application of the Hamiltonian Monte Carlo algorithm to the reconstruction of penumbral images of fusion implosions and presents ways to visualize the uncertainty in the reconstructed source. This methodology enables more rigorous analysis of penumbral images than has been done in the past.

Exploring visual quality of multidimensional time series projections

Dimensionality reduction is often used to project time series data from multidimensional to two-dimensional space to generate visual representations of the temporal evolution. In this context, we address the problem of multidimensional time series visualization by presenting a new method to show and handle projection errors introduced by dimensionality reduction techniques on multidimensional temporal data. For visualization, subsequent time instances are rendered as dots that are connected by lines or curves to indicate the temporal dependencies. However, inevitable projection artifacts may lead to poor visualization quality and misinterpretation of the temporal information. Wrongly projected data points, inaccurate variations in the distances between projected time instances, and intersections of connecting lines could lead to wrong assumptions about the original data. We adapt local and global quality metrics to measure the visual quality along the projected time series, and we introduce a model to assess the projection error at intersecting lines. These serve as a basis for our new uncertainty visualization techniques that use different visual encodings and interactions to indicate, communicate, and work with the visualization uncertainty from projection errors and artifacts along the timeline of data points, their connections, and intersections. Our approach is agnostic to the projection method and works for linear and non-linear dimensionality reduction methods alike.

The influence of uncertainty visualization on cognitive load in a safety- and time-critical decision-making task

Decisions with spatial visualizations are often made under uncertainty and high time pressure. However, missing or improper representation of uncertainty can hamper the decision-making process. This paper investigates the impact of uncertainty visualization on cognitive load in the context of a safety-critical, time-sensitive decision-making task with a transportation system map. In a controlled experiment (n = 40) with a dual-task paradigm, we compared three different uncertainty visualization techniques and a baseline for different levels of time pressure. Cognitive load was measured using psycho-physiological metrics based on eye tracking and galvanic skin response, as well as self-reported. The results reveal significant differences in cognitive load among different visualization types, with line uncertainty representation techniques leading to lower cognitive load under both low and high-time pressure scenarios ( α < 0.05 ).

The Art of Brainwaves: A Survey on Event-Related Potential Visualization Practices

Electroencephalography (EEG) and event-related potentials (ERPs) have been analyzed for more than 70 years. Yet, we know little about how practitioners visualize the results of their analyses. Here, we designed an online survey (n=213) targeting M/EEG practitioners from novice to expert level. Our primary goal is to better understand the visualization tools currently in use, the challenges researchers face, and their experiences and opinions on how best to display their brain data. Finally, we explored whether researchers are aware of more general visualization issues related to visualization of uncertainty and color maps. In this paper, we provide an overview of the most popular ERP visualization tools. Additionally, we found that the community does not have a unique nomenclature to refer to some plot types, and we propose a set of recommendations to name the most popular ERP plot types. Finally, we provide an analysis of practitioner feature preferences for software developers and conclude with further recommendations for ERP practitioners.

Uncertainty quantification for structural response field with ultra-high dimensions

The structural response field is crucial for understanding mechanical behavior, especially under uncertain conditions. However, current uncertainty quantification predominantly address one-dimensional output under multi-dimensional input. For the structural full field response with ultra-high dimension, quantifying corresponding uncertainties becomes a formidable task. This paper introduces an efficient uncertainty quantification method for structural response field. Initially, the manifold learning is introduced to transform uncertainty quantification of ultra-high-dimensional responses into the quantification of low-dimensional manifold projections. Subsequently, polynomial chaos expansions facilitate uncertainty propagation, allowing for the effective evaluation of statistical moments for each projection. Leveraging the established manifold structure enables obtaining analytical solutions for statistical moments of full field responses without additional computational costs. In the absence of prior information, the derivative λ-PDF is utilized to model uncertainty of response at any position, so as to realize the visualization of uncertainty. The proposed uncertainty quantification for structural response field provides a non-intrusive analysis framework, which can conveniently deal with structural multi-field coupling problems. Finally, three engineering examples involving multi field coupling are presented to demonstrate the effectiveness and practicability of proposed uncertainty quantification of structural response field.

Multi-Feature Uncertainty Analysis for Urban-Scale Hypothetical 3D Reconstructions: Piazza delle Erbe Case Study

For the hypothetical reconstruction of architectural heritage, there are still no scientific standards of reference concerning their sharing and documentation. Recent international initiatives established the basis to address this problem; however, still, much work needs to be done in order to systematise good practices for the process of reconstruction and its dissemination. This contribution aims to take a step forward in the analysis and visualisation of uncertainty. Some authors have suggested various approaches to visualise uncertainty for single buildings; however, case studies at the urban scale are rarely investigated. This research proposes an improved source-based multi-feature approach aimed at analysing and visualising (through false-colour shading) the uncertainty of hypothetical 3D digital models of urban areas. The assessment of uncertainty is also quantified qualitatively by using newly defined formulas which calculate the average uncertainty weighted on the volume of the 3D model. This methodology aims to improve the objectiveness, unambiguity, transparency, reusability, and readability of hypothetical reconstructive 3D models, and its use is exemplified in the case study of the hypothetical reconstruction of Piazza delle Erbe in Verona, a project presented in the form of a docufilm at EXPO 2015 in Milan.

Evaluating the Impact of Uncertainty Visualization on Model Reliance.

Machine learning models have gained traction as decision support tools for tasks that require processing copious amounts of data. However, to achieve the primary benefits of automating this part of decision-making, people must be able to trust the machine learning model's outputs. In order to enhance people's trust and promote appropriate reliance on the model, visualization techniques such as interactive model steering, performance analysis, model comparison, and uncertainty visualization have been proposed. In this study, we tested the effects of two uncertainty visualization techniques in a college admissions forecasting task, under two task difficulty levels, using Amazon's Mechanical Turk platform. Results show that (1) people's reliance on the model depends on the task difficulty and level of machine uncertainty and (2) ordinal forms of expressing model uncertainty are more likely to calibrate model usage behavior. These outcomes emphasize that reliance on decision support tools can depend on the cognitive accessibility of the visualization technique and perceptions of model performance and task difficulty.

Uncertainty Visualization of Critical Points of 2D Scalar Fields for Parametric and Nonparametric Probabilistic Models.

This paper presents a novel end-to-end framework for closed-form computation and visualization of critical point uncertainty in 2D uncertain scalar fields. Critical points are fundamental topological descriptors used in the visualization and analysis of scalar fields. The uncertainty inherent in data (e.g., observational and experimental data, approximations in simulations, and compression), however, creates uncertainty regarding critical point positions. Uncertainty in critical point positions, therefore, cannot be ignored, given their impact on downstream data analysis tasks. In this work, we study uncertainty in critical points as a function of uncertainty in data modeled with probability distributions. Although Monte Carlo (MC) sampling techniques have been used in prior studies to quantify critical point uncertainty, they are often expensive and are infrequently used in production-quality visualization software. We, therefore, propose a new end-to-end framework to address these challenges that comprises a threefold contribution. First, we derive the critical point uncertainty in closed form, which is more accurate and efficient than the conventional MC sampling methods. Specifically, we provide the closed-form and semianalytical (a mix of closed-form and MC methods) solutions for parametric (e.g., uniform, Epanechnikov) and nonparametric models (e.g., histograms) with finite support. Second, we accelerate critical point probability computations using a parallel implementation with the VTK-m library, which is platform portable. Finally, we demonstrate the integration of our implementation with the ParaView software system to demonstrate near-real-time results for real datasets.

Does Interactive Conditioning Help Users Better Understand the Structure of Probabilistic Models?

Despite growing interest in probabilistic modeling approaches and availability of learning tools, people are hesitant to use them. There is a need for tools to communicate probabilistic models more intuitively and help users build, validate, use effectively or trust probabilistic models. We focus on visual representations of probabilistic models and introduce the Interactive Pair Plot (IPP) for visualization of a model's uncertainty, a scatter plot matrix of a probabilistic model allowing interactive conditioning on the model's variables. We investigate whether the use of interactive conditioning in a scatter plot matrix of a model helps users better understand variables' relations. We conducted a user study and the findings suggest that improvements in the understanding of the interaction group are the most pronounced for more exotic structures, such as hierarchical models or unfamiliar parameterizations, in comparison to the understanding of the static group. As the detail of the inferred information increases, interactive conditioning does not lead to considerably longer response times. Finally, interactive conditioning improves participants' confidence about their responses.

Illuminating the Landscape of Differential Privacy: An Interview Study on the Use of Visualization in Real-World Deployments.

As Differential Privacy (DP) transitions from theory to practice, visualization has surfaced as a catalyst in promoting acceptance and usage. Despite the potential of visualization tools to support differential privacy implementation, their development is limited by a lack of understanding of the overall deployment process, practitioner challenges, and the role of visual tools in real-world deployments. To narrow this gap, we interviewed 18 professionals from various backgrounds who regularly engage with differential privacy in their work. Our objectives were to understand the differential privacy implementation process and associated challenges; explore the actors (individuals involved in differential privacy implementation), how they use or struggle to use visualization; and identify the benefits and challenges of using visualization in the implementation process. Our results delineate the differential privacy implementation process into five distinct stages and highlight the main actors alongside the diverse visualization applications and shortcomings. We find that visualizations can be used to build foundational differential privacy knowledge, describe implementation parameters, and evaluate private outputs. However, the visualization strategies described often fail to address the diverse technical backgrounds and varied privacy and accuracy concerns of users, hindering effective communication between the different actors involved in the implementation process. From our findings, we propose three research directions: visualizations for setting and evaluating noise addition, evaluation of uncertainty visualization related to trust in differential privacy, and research focused on pedagogical visualizations for complex data science topics. A free copy of this paper and all supplemental materials are available at https://osf.io/qhyzt/?view_only=1a5c7d7553c840ab9f125d88bc13946f.

Uncertainty-Aware Seasonal-Trend Decomposition Based on Loess.

Seasonal-trend decomposition based on loess (STL) is a powerful tool to explore time series data visually. In this paper, we present an extension of STL to uncertain data, named uncertainty-aware STL (UASTL). Our method propagates multivariate Gaussian distributions mathematically exactly through the entire analysis and visualization pipeline. Thereby, stochastic quantities shared between the components of the decomposition are preserved. Moreover, we present application scenarios with uncertainty modeling based on Gaussian processes, e.g., data with uncertain areas or missing values. Besides these mathematical results and modeling aspects, we introduce visualization techniques that address the challenges of uncertainty visualization and the problem of visualizing highly correlated components of a decomposition. The global uncertainty propagation enables the time series visualization with STL-consistent samples, the exploration of correlation between and within decomposition's components, and the analysis of the impact of varying uncertainty. Finally, we show the usefulness of UASTL and the importance of uncertainty visualization with several examples. Thereby, a comparison with conventional STL isperformed.

Uncertainty-aware MR-based CT synthesis for robust proton therapy planning of brain tumour

Background and purposeDeep learning techniques excel in MR-based CT synthesis, but missing uncertainty prediction limits its clinical use in proton therapy. We developed an uncertainty-aware framework and evaluated its efficiency in robust proton planning. Materials and methodsA conditional generative-adversarial network was trained on 64 brain tumour patients with paired MR-CT images to generate synthetic CTs (sCT) from combined T1-T2 MRs of three orthogonal planes. A Bayesian neural network predicts Laplacian distributions for all voxels with parameters (μ, b). A robust proton plan was optimized using three sCTs of μ and μ±b. The dosimetric differences between the plan from sCT (sPlan) and the recalculated plan (rPlan) on planning CT (pCT) were quantified for each patient. The uncertainty-aware robust plan was compared to conventional robust (global ± 3 %) and non-robust plans. ResultsIn 8-fold cross-validation, sCT-pCT image differences (Mean-Absolute-Error) were 80.84 ± 9.84HU (body), 35.78 ± 6.07HU (soft tissues) and 221.88 ± 31.69HU (bones), with Dice scores of 90.33 ± 2.43 %, 95.13 ± 0.80 %, and 85.53 ± 4.16 %, respectively. The uncertainty distribution positively correlated with absolute prediction error (Correlation Coefficient: 0.62 ± 0.01). The uncertainty-conditioned robust optimisation improved the rPlan-sPlan agreement, e.g., D95 absolute difference (CTV) was 1.10 ± 1.24 % compared to conventional (1.64 ± 2.71 %) and non-robust (2.08 ± 2.96 %) optimisation. This trend was consistent across all target and organs-at-risk indexes. ConclusionThe enhanced framework incorporates 3D uncertainty prediction and generates high-quality sCTs from MR images. The framework also facilitates conditioned robust optimisation, bolstering proton plan robustness against network prediction errors. The innovative feature of uncertainty visualisation and robust analyses contribute to evaluating sCT clinical utility for individual patients.

A study of Bayesian deep network uncertainty and its application to synthetic CT generation for MR-only radiotherapy treatment planning.

The use of synthetic computed tomography (CT) for radiotherapy treatment planning has received considerable attention because of the absence of ionizing radiation and close spatial correspondence to source magnetic resonance (MR) images, which have excellent tissue contrast. However,in an MR-only environment, little effort has been made to examine the quality of synthetic CT images without using the original CT images. To estimate synthetic CT quality without referring to original CT images, this study established the relationship between synthetic CT uncertainty and Bayesian uncertainty, and proposed a new Bayesian deep network for generating synthetic CT images and estimating synthetic CT uncertainty for MR-only radiotherapy treatment planning. A novel deep Bayesian network was formulated using probabilistic network weights. Two mathematical expressions were proposed to quantify the Bayesian uncertainty of the network and synthetic CT uncertainty, which was closely related to the mean absolute error (MAE) in Hounsfield Unit (HU) of synthetic CT. These uncertainties were examined to demonstrate the accuracy of representing the synthetic CT uncertainty using a Bayesian counterpart. We developed a hybrid Bayesian architecture and a new data normalization scheme, enabling the Bayesian network to generate both accurate synthetic CT and reliable uncertainty information when probabilistic weights were applied. The proposed method was evaluated in 59 patients (13/12/32/2 for training/validation/testing/uncertainty visualization) diagnosed with prostate cancer, who underwent same-day pelvic CT- and MR-acquisitions. To assess the relationship between Bayesian and synthetic CT uncertainties, linear and non-linear correlation coefficients were calculated on per-voxel, per-tissue, and per-patient bases. For accessing the accuracy of the CT number and dosimetric accuracy, the proposed method was compared with a commercially available atlas-based method (MRCAT) and a U-Net conditional-generative adversarial network (UcGAN). The proposed model exhibited 44.33 MAE, outperforming UcGAN 52.51 and MRCAT 54.87. The gamma rate (2%/2mm dose difference/distance to agreement) of the proposed model was 98.68%, comparable to that of UcGAN (98.60%) and MRCAT (98.56%). The per-patient and per-tissue linear correlation coefficients between the Bayesian and synthetic CT uncertainties ranged from 0.53 to 0.83, implying a moderate to strong linear correlation. Per-voxel correlation coefficients varied from -0.13 to 0.67 depending on the regions-of-interest evaluated, indicating tissue-dependent correlation. The R2 value for estimating MAE solely using Bayesian uncertainty was 0.98, suggesting that the uncertainty of the proposed model was an ideal candidate for predicting synthetic CT error, without referring to the original CT. This study established a relationship between the Bayesian model uncertainty and synthetic CT uncertainty. A novel Bayesian deep network was proposed to generate a synthetic CT and estimate its uncertainty. Various metrics were used to thoroughly examine the relationship between the uncertainties of the proposed Bayesian model and the generated synthetic CT. Compared with existing approaches, the proposed model showed comparable CT number and dosimetric accuracies. The experiments showed that the proposed Bayesian model was capable of producing accurate synthetic CT, and was an effective indicator of the uncertainty and error associated with synthetic CT in MR-only workflows.

Visualizing Uncertainty in Sets.

Set visualization facilitates the exploration and analysis of set-type data. However, how sets should be visualized when the data is uncertain is still an open research challenge. To address the problem of depicting uncertainty in set visualization, we ask (i) which aspects of set type data can be affected by uncertainty and (ii) which characteristics of uncertainty influence the visualization design. We answer these research questions by first describing a conceptual framework that brings together (i) the information that is primarily relevant in sets (i.e., set membership, set attributes, and element attributes) and (ii) different plausible categories of (un)certainty (i.e., certainty, undefined uncertainty as a binary fact, and defined uncertainty as quantifiable measure). Following the structure of our framework, we systematically discuss basic visualization examples of integrating uncertainty in set visualizations. We draw on existing knowledge about general uncertainty visualization and previous evidence of its effectiveness.

Validating a Task Complexity Framework for Studies of Uncertainty Visualization

In this study, we validate and extend previous theoretical and empirical work on the design of visualizations to support decision makers using interfaces with high levels of information density and evolving constraints. Prior research proposed and validated a theoretical framework of task complexity to facilitate the systematic evaluation of uncertainty visualizations for these contexts. We adopted this approach to the evaluation of visualizations of uncertainty, displaying hurricane visualizations on a map rather than abstract symbols on a grid, manipulating the dispersion of visualizations, and varying an additional visuospatial element––visualization orientation––to improve the ecological validity of the experimental task. The results of this study provide evidence for the utility of a task complexity framework for research on the visualization efficacy.