Fuzzy Volume Rendering

Regularized Multi-Decoder Ensemble for an Error-Aware Scene Representation Network

Feature grid Scene Representation Networks (SRNs) have been applied to scientific data as compact functional surrogates for analysis and visualization. As SRNs are black-box lossy data representations, assessing the prediction quality is critical for scientific visualization applications to ensure that scientists can trust the information being visualized. Currently, existing architectures do not support inference time reconstruction quality assessment, as coordinate-level errors cannot be evaluated in the absence of ground truth data. By employing the uncertain neural network architecture in feature grid SRNs, we obtain prediction variances during inference time to facilitate confidence-aware data reconstruction. Specifically, we propose a parameter-efficient multi-decoder SRN (MDSRN) architecture consisting of a shared feature grid with multiple lightweight multilayer perceptron decoders. MDSRN can generate a set of plausible predictions for a given input coordinate to compute the mean as the prediction of the multi-decoder ensemble and the variance as a confidence score. The coordinate-level variance can be rendered along with the data to inform the reconstruction quality, or be integrated into uncertainty-aware volume visualization algorithms. To prevent the misalignment between the quantified variance and the prediction quality, we propose a novel variance regularization loss for ensemble learning that promotes the Regularized multi-decoder SRN (RMDSRN) to obtain a more reliable variance that correlates closely to the true model error. We comprehensively evaluate the quality of variance quantification and data reconstruction of Monte Carlo Dropout (MCD), Mean Field Variational Inference (MFVI), Deep Ensemble (DE), and Predicting Variance (PV) in comparison with our proposed MDSRN and RMDSRN applied to state-of-the-art feature grid SRNs across diverse scalar field datasets. We demonstrate that RMDSRN attains the most accurate data reconstruction and competitive variance-error correlation among uncertain SRNs under the same neural network parameter budgets. Furthermore, we present an adaptation of uncertainty-aware volume rendering and shed light on the potential of incorporating uncertain predictions in improving the quality of volume rendering for uncertain SRNs. Through ablation studies on the regularization strength and decoder count, we show that MDSRN and RMDSRN are expected to perform sufficiently well with a default configuration without requiring customized hyperparameter settings for different datasets.

Fiber Uncertainty Visualization for Bivariate Data With Parametric and Nonparametric Noise Models

Visualization and analysis of multivariate data and their uncertainty are top research challenges in data visualization. Constructing fiber surfaces is a popular technique for multivariate data visualization that generalizes the idea of level-set visualization for univariate data to multivariate data. In this paper, we present a statistical framework to quantify positional probabilities of fibers extracted from uncertain bivariate fields. Specifically, we extend the state-of-the-art Gaussian models of uncertainty for bivariate data to other parametric distributions (e.g., uniform and Epanechnikov) and more general nonparametric probability distributions (e.g., histograms and kernel density estimation) and derive corresponding spatial probabilities of fibers. In our proposed framework, we leverage Green's theorem for closed-form computation of fiber probabilities when bivariate data are assumed to have independent parametric and nonparametric noise. Additionally, we present a nonparametric approach combined with numerical integration to study the positional probability of fibers when bivariate data are assumed to have correlated noise. For uncertainty analysis, we visualize the derived probability volumes for fibers via volume rendering and extracting level sets based on probability thresholds. We present the utility of our proposed techniques via experiments on synthetic and simulation datasets.

Direct Volume Rendering with Nonparametric Models of Uncertainty

We present a nonparametric statistical framework for the quantification, analysis, and propagation of data uncertainty in direct volume rendering (DVR). The state-of-the-art statistical DVR framework allows for preserving the transfer function (TF) of the ground truth function when visualizing uncertain data; however, the existing framework is restricted to parametric models of uncertainty. In this paper, we address the limitations of the existing DVR framework by extending the DVR framework for nonparametric distributions. We exploit the quantile interpolation technique to derive probability distributions representing uncertainty in viewing-ray sample intensities in closed form, which allows for accurate and efficient computation. We evaluate our proposed nonparametric statistical models through qualitative and quantitative comparisons with the mean-field and parametric statistical models, such as uniform and Gaussian, as well as Gaussian mixtures. In addition, we present an extension of the state-of-the-art rendering parametric framework to 2D TFs for improved DVR classifications. We show the applicability of our uncertainty quantification framework to ensemble, downsampled, and bivariate versions of scalar field datasets.

A Generative Model for Volume Rendering

We present a technique to synthesize and analyze volume-rendered images using generative models. We use the Generative Adversarial Network (GAN) framework to compute a model from a large collection of volume renderings, conditioned on (1) viewpoint and (2) transfer functions for opacity and color. Our approach facilitates tasks for volume analysis that are challenging to achieve using existing rendering techniques such as ray casting or texture-based methods. We show how to guide the user in transfer function editing by quantifying expected change in the output image. Additionally, the generative model transforms transfer functions into a view-invariant latent space specifically designed to synthesize volume-rendered images. We use this space directly for rendering, enabling the user to explore the space of volume-rendered images. As our model is independent of the choice of volume rendering process, we show how to analyze volume-rendered images produced by direct and global illumination lighting, for a variety of volume datasets.

A Statistical Direct Volume Rendering Framework for Visualization of Uncertain Data

With uncertainty present in almost all modalities of data acquisition, reduction, transformation, and representation, there is a growing demand for mathematical analysis of uncertainty propagation in data processing pipelines. In this paper, we present a statistical framework for quantification of uncertainty and its propagation in the main stages of the visualization pipeline. We propose a novel generalization of Irwin-Hall distributions from the statistical viewpoint of splines and box-splines, that enables interpolation of random variables. Moreover, we introduce a probabilistic transfer function classification model that allows for incorporating probability density functions into the volume rendering integral. Our statistical framework allows for incorporating distributions from various sources of uncertainty which makes it suitable in a wide range of visualization applications. We demonstrate effectiveness of our approach in visualization of ensemble data, visualizing large datasets at reduced scale, iso-surface extraction, and visualization of noisy data.

Modality-Driven Classification and Visualization of Ensemble Variance

Advances in computational power now enable domain scientists to address conceptual and parametric uncertainty by running simulations multiple times in order to sufficiently sample the uncertain input space. While this approach helps address conceptual and parametric uncertainties, the ensemble datasets produced by this technique present a special challenge to visualization researchers as the ensemble dataset records a distribution of possible values for each location in the domain. Contemporary visualization approaches that rely solely on summary statistics (e.g., mean and variance) cannot convey the detailed information encoded in ensemble distributions that are paramount to ensemble analysis; summary statistics provide no information about modality classification and modality persistence. To address this problem, we propose a novel technique that classifies high-variance locations based on the modality of the distribution of ensemble predictions. Additionally, we develop a set of confidence metrics to inform the end-user of the quality of fit between the distribution at a given location and its assigned class. Finally, for the special application of evaluating the stability of bimodal regions, we develop local and regional metrics.

MObjects--a novel method for the visualization and interactive exploration of defects in industrial XCT data

This paper describes an advanced visualization method for the analysis of defects in industrial 3D X-Ray Computed Tomography (XCT) data. We present a novel way to explore a high number of individual objects in a dataset, e.g., pores, inclusions, particles, fibers, and cracks demonstrated on the special application area of pore extraction in carbon fiber reinforced polymers (CFRP). After calculating the individual object properties volume, dimensions and shape factors, all objects are clustered into a mean object (MObject). The resulting MObject parameter space can be explored interactively. To do so, we introduce the visualization of mean object sets (MObject Sets) in a radial and a parallel arrangement. Each MObject may be split up into sub-classes by selecting a specific property, e.g., volume or shape factor, and the desired number of classes. Applying this interactive selection iteratively leads to the intended classifications and visualizations of MObjects along the selected analysis path. Hereby the given different scaling factors of the MObjects down the analysis path are visualized through a visual linking approach. Furthermore the representative MObjects are exported as volumetric datasets to serve as input for successive calculations and simulations. In the field of porosity determination in CFRP non-destructive testing practitioners use representative MObjects to improve ultrasonic calibration curves. Representative pores also serve as input for heat conduction simulations in active thermography. For a fast overview of the pore properties in a dataset we propose a local MObjects visualization in combination with a color-coded homogeneity visualization of cells. The advantages of our novel approach are demonstrated using real world CFRP specimens. The results were evaluated through a questionnaire in order to determine the practicality of the MObjects visualization as a supportive tool for domain specialists.