arXiv subjects

Jixian Li

Publications and source records attributed to Jixian Li.

13 recordsLinked to original sources

arXiv2026

Topology-Preserving Meshing of Implicit Scalar Fields via Monotonicity Constraints

Topological analysis of scalar fields yields structures such as the Morse-Smale complex (MSC) that summarize salient features across multiple scales. Existing MSC extraction algorithms typically assume an explicit representation of the input field, such as a discretely sampled mesh. However, recent advances in visualization have popularized implicit field representations, for which these assumptions no longer hold. In this work, we address the problem of extracting an MSC from an implicitly defined 2D scalar field. We present a method for constructing a triangulated piecewise-linear (PL) mesh that aims to preserve the critical points of an underlying implicit scalar field. Our central insight is that if all edges are monotonic with respect to the underlying field, then the resulting PL approximation is topologically consistent with respect to critical points. Based on this insight, we introduce a refinement procedure that mitigates monotonicity violations. Requiring only pointwise evaluations and modest mesh refinement, the approach produces PL meshes that are correct with regards to critical points in our experiments. Finally, we demonstrate that additional targeted refinement improves the geometric fidelity of MSC separatrices.

cs.CG↗

arXiv2026

May (A)I Beautify Your Visualization? Expert Judgments of Acceptable Aesthetic Alterations

In 3D visualizations of natural phenomena, improving aesthetics can provide measurable benefits, but often involves transformations that affect how the data is perceived. As a growing range of tools - including AI-based methods - make visual design and modification more accessible, it is increasingly important to understand trade offs and concerns when making these changes. We conducted an expert survey (N=95) with visualization researchers, practitioners, and domain scientists, investigating reactions to fifteen alterations spanning presentation-level adjustments (e.g., lighting, camera position) and data-level modifications (e.g., removing errors, filling gaps), applied by both humans and AI systems. Results show differences in perceived acceptability are driven by the transformation's meaning, regardless of whether it operates at the presentation or data level. Additionally, certain modifications were consistently judged as more permissible than others regardless of human or AI authorship. While this relative ordering remains largely stable, AI-generated transformations are consistently rated as less acceptable than identical human-produced changes. These results reveal a distinction between more permissible and more sensitive alterations, and suggest the need for both designers and AI-assisted visualization tools to incorporate constraints and guardrails that reflect these differences.

cs.HC↗

arXiv2025

Uncertainty Tube Visualization of Particle Trajectories

Predicting particle trajectories with neural networks (NNs) has substantially enhanced many scientific and engineering domains. However, effectively quantifying and visualizing the inherent uncertainty in predictions remains challenging. Without an understanding of the uncertainty, the reliability of NN models in applications where trustworthiness is paramount is significantly compromised. This paper introduces the uncertainty tube, a novel, computationally efficient visualization method designed to represent this uncertainty in NN-derived particle paths. Our key innovation is the design and implementation of a superelliptical tube that accurately captures and intuitively conveys nonsymmetric uncertainty. By integrating well-established uncertainty quantification techniques, such as Deep Ensembles, Monte Carlo Dropout (MC Dropout), and Stochastic Weight Averaging-Gaussian (SWAG), we demonstrate the practical utility of the uncertainty tube, showcasing its application on both synthetic and simulation datasets.

cs.LG↗

arXiv2025

A Fast Iterative Robust Principal Component Analysis Method

Principal Component Analysis (PCA) is widely used for dimensionality reduction and data analysis. However, PCA results are adversely affected by outliers often observed in real-world data. Existing robust PCA methods are often computationally expensive or exhibit limited robustness. In this work, we introduce a Fast Iterative Robust (FIR) PCA method by efficiently estimating the inliers center location and covariance. Our approach leverages Incremental PCA (IPCA) to iteratively construct a subset of data points that ensures improved location and covariance estimation that effectively mitigates the influence of outliers on PCA projection. We demonstrate that our method achieves competitive accuracy and performance compared to existing robust location and covariance methods while offering improved robustness to outlier contamination. We utilize simulated and real-world datasets to evaluate and demonstrate the efficacy of our approach in identifying and preserving underlying data structures in the presence of contamination.

cs.CE↗

arXiv2025

Hyper-differential sensitivity analysis with respect to model discrepancy: Prior distributions

Hyper-differential sensitivity analysis with respect to model discrepancy was recently developed to enable uncertainty quantification for optimization problems. The approach consists of two primary steps: (i) Bayesian calibration of the discrepancy between high- and low-fidelity models, and (ii) propagating the model discrepancy uncertainty through the optimization problem. When high-fidelity model evaluations are limited, as is common in practice, the prior discrepancy distribution plays a crucial role in the uncertainty analysis. However, specification of this prior is challenging due to its mathematical complexity and many hyper-parameters. This article presents a novel approach to specify the prior distribution. Our approach consists of two parts: (1) an algorithmic initialization of the prior hyper-parameters that uses existing data to initialize a hyper-parameter estimate, and (2) a visualization framework to systematically explore properties of the prior and guide tuning of the hyper-parameters to ensure that the prior captures the appropriate range of uncertainty. We provide detailed mathematical analysis and a collection of numerical examples that elucidate properties of the prior that are crucial to ensure uncertainty quantification.

math.NA↗

arXiv2024

Estimation and Visualization of Isosurface Uncertainty from Linear and High-Order Interpolation Methods

Isosurface visualization is fundamental for exploring and analyzing 3D volumetric data. Marching cubes (MC) algorithms with linear interpolation are commonly used for isosurface extraction and visualization. Although linear interpolation is easy to implement, it has limitations when the underlying data is complex and high-order, which is the case for most real-world data. Linear interpolation can output vertices at the wrong location. Its inability to deal with sharp features and features smaller than grid cells can lead to an incorrect isosurface with holes and broken pieces. Despite these limitations, isosurface visualizations typically do not include insight into the spatial location and the magnitude of these errors. We utilize high-order interpolation methods with MC algorithms and interactive visualization to highlight these uncertainties. Our visualization tool helps identify the regions of high interpolation errors. It also allows users to query local areas for details and compare the differences between isosurfaces from different interpolation methods. In addition, we employ high-order methods to identify and reconstruct possible features that linear methods cannot detect. We showcase how our visualization tool helps explore and understand the extracted isosurface errors through synthetic and real-world data.

cs.GR↗

arXiv2024

Glyph-Based Uncertainty Visualization and Analysis of Time-Varying Vector Fields

Uncertainty is inherent to most data, including vector field data, yet it is often omitted in visualizations and representations. Effective uncertainty visualization can enhance the understanding and interpretability of vector field data. For instance, in the context of severe weather events such as hurricanes and wildfires, effective uncertainty visualization can provide crucial insights about fire spread or hurricane behavior and aid in resource management and risk mitigation. Glyphs are commonly used for representing vector uncertainty but are often limited to 2D. In this work, we present a glyph-based technique for accurately representing 3D vector uncertainty and a comprehensive framework for visualization, exploration, and analysis using our new glyphs. We employ hurricane and wildfire examples to demonstrate the efficacy of our glyph design and visualization tool in conveying vector field uncertainty.

cs.HC↗

arXiv2024

Text-based Transfer Function Design for Semantic Volume Rendering

Transfer function design is crucial in volume rendering, as it directly influences the visual representation and interpretation of volumetric data. However, creating effective transfer functions that align with users' visual objectives is often challenging due to the complex parameter space and the semantic gap between transfer function values and features of interest within the volume. In this work, we propose a novel approach that leverages recent advancements in language-vision models to bridge this semantic gap. By employing a fully differentiable rendering pipeline and an image-based loss function guided by language descriptions, our method generates transfer functions that yield volume-rendered images closely matching the user's intent. We demonstrate the effectiveness of our approach in creating meaningful transfer functions from simple descriptions, empowering users to intuitively express their desired visual outcomes with minimal effort. This advancement streamlines the transfer function design process and makes volume rendering more accessible to a wider range of users.

cs.GR↗

arXiv2024

Interactive Visualization of Time-Varying Flow Fields Using Particle Tracing Neural Networks

In this paper, we present a comprehensive evaluation to establish a robust and efficient framework for Lagrangian-based particle tracing using deep neural networks (DNNs). Han et al. (2021) first proposed a DNN-based approach to learn Lagrangian representations and demonstrated accurate particle tracing for an analytic 2D flow field. In this paper, we extend and build upon this prior work in significant ways. First, we evaluate the performance of DNN models to accurately trace particles in various settings, including 2D and 3D time-varying flow fields, flow fields from multiple applications, flow fields with varying complexity, as well as structured and unstructured input data. Second, we conduct an empirical study to inform best practices with respect to particle tracing model architectures, activation functions, and training data structures. Third, we conduct a comparative evaluation of prior techniques that employ flow maps as input for exploratory flow visualization. Specifically, we compare our extended model against its predecessor by Han et al. (2021), as well as the conventional approach that uses triangulation and Barycentric coordinate interpolation. Finally, we consider the integration and adaptation of our particle tracing model with different viewers. We provide an interactive web-based visualization interface by leveraging the efficiencies of our framework, and perform high-fidelity interactive visualization by integrating it with an OSPRay-based viewer. Overall, our experiments demonstrate that using a trained DNN model to predict new particle trajectories requires a low memory footprint and results in rapid inference. Following best practices for large 3D datasets, our deep learning approach using GPUs for inference is shown to require approximately 46 times less memory while being more than 400 times faster than the conventional methods.

cs.GR↗

arXiv2023

Autoencoder-Aided Visualization of Collections of Morse Complexes

Though analyzing a single scalar field using Morse complexes is well studied, there are few techniques for visualizing a collection of Morse complexes. We focus on analyses that are enabled by looking at a Morse complex as an embedded domain decomposition. Specifically, we target 2D scalar fields, and we encode the Morse complex through binary images of the boundaries of decomposition. Then we use image-based autoencoders to create a feature space for the Morse complexes. We apply additional dimensionality reduction methods to construct a scatterplot as a visual interface of the feature space. This allows us to investigate individual Morse complexes, as they relate to the collection, through interaction with the scatterplot. We demonstrate our approach using a synthetic data set, microscopy images, and time-varying vorticity magnitude fields of flow. Through these, we show that our method can produce insights about structures within the collection of Morse complexes.

cs.HC↗

arXiv2019

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.

cs.GR↗

arXiv2019

NeuralCubes: Deep Representations for Visual Data Exploration

Visual exploration of large multidimensional datasets has seen tremendous progress in recent years, allowing users to express rich data queries that produce informative visual summaries, all in real time. Techniques based on data cubes are some of the most promising approaches. However, these techniques usually require a large memory footprint for large datasets. To tackle this problem, we present NeuralCubes: neural networks that predict results for aggregate queries, similar to data cubes. NeuralCubes learns a function that takes as input a given query, for instance, a geographic region and temporal interval, and outputs the result of the query. The learned function serves as a real-time, low-memory approximator for aggregation queries. NeuralCubes models are small enough to be sent to the client side (e.g. the web browser for a web-based application) for evaluation, enabling data exploration of large datasets without database/network connection. We demonstrate the effectiveness of NeuralCubes through extensive experiments on a variety of datasets and discuss how NeuralCubes opens up opportunities for new types of visualization and interaction.

cs.DB↗

arXiv2017

L-Graphs and Monotone L-Graphs

In an $\mathsf{L}$-embedding of a graph, each vertex is represented by an $\mathsf{L}$-segment, and two segments intersect each other if and only if the corresponding vertices are adjacent in the graph. If the corner of each $\mathsf{L}$-segment in an $\mathsf{L}$-embedding lies on a straight line, we call it a monotone $\mathsf{L}$-embedding. In this paper we give a full characterization of monotone $\mathsf{L}$-embeddings by introducing a new class of graphs which we call "non-jumping" graphs. We show that a graph admits a monotone $\mathsf{L}$-embedding if and only if the graph is a non-jumping graph. Further, we show that outerplanar graphs, convex bipartite graphs, interval graphs, 3-leaf power graphs, and complete graphs are subclasses of non-jumping graphs. Finally, we show that distance-hereditary graphs and $k$-leaf power graphs ($k\le 4$) admit $\mathsf{L}$-embeddings.

cs.CG↗