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Recently neural scene representations have provided very impressive results for representing 3D scenes visually, however, their study and progress have mainly been limited to visualization of virtual models in computer graphics or scene…
The cell complex structure is one of the most fundamental structures in topology and combinatorics, the Morse decomposition of a dynamical system analyzes the global gradient behavior, and the Reeb graph of a function is an elementary tool…
The core challenge faced by multi-document summarization is the complexity of relationships among documents and the presence of information redundancy. Graph clustering is an effective paradigm for addressing this issue, as it models the…
We introduce a persistence-type invariant for finite weighted graphs based on combinatorial multivector dynamics. For each threshold parameter, a relation matrix determines a graph multivector field, whose induced directed dynamics admits a…
For safe operation, a robot must be able to avoid collisions in uncertain environments. Existing approaches for motion planning under uncertainties often assume parametric obstacle representations and Gaussian uncertainty, which can be…
The overview-driven visual analysis of large-scale dynamic graphs poses a major challenge. We propose Multiscale Snapshots, a visual analytics approach to analyze temporal summaries of dynamic graphs at multiple temporal scales. First, we…
Generating interpretable visualizations from complex data is a common problem in many applications. Two key ingredients for tackling this issue are clustering and representation learning. However, current methods do not yet successfully…
Unsupervised classification called clustering is a process of organizing objects into groups whose members are similar in some way. Clustering of uncertain data objects is a challenge in spatial data bases. In this paper we use Probability…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…
Molecular clouds show complex structures reflecting their non-linear dynamics. Many studies investigating the bridge between their morphology and physical properties have shown the value of non-Gaussian higher-order statistics in capturing…
Graphical models have demonstrated their exceptional capabilities across numerous applications. However, their performance, confidence, and trustworthiness are often limited by the inherent randomness in data generation and the lack of…
Topological abstractions offer a method to summarize the behavior of vector fields but computing them robustly can be challenging due to numerical precision issues. One alternative is to represent the vector field using a discrete approach,…
The success of scene graphs for visual scene understanding has brought attention to the benefits of abstracting a visual input (e.g., image) into a structured representation, where entities (people and objects) are nodes connected by edges…
Discrete Morse theory has recently been applied in metric graph reconstruction from a given density function concentrated around an (unknown) underlying embedded graph. We propose a new noise model for the density function to reconstruct a…
In this paper, we propose a probabilistic method to generate abstract scene graphs for table-top scenes from 6D object pose estimates. We explicitly make use of task-specfic context knowledge by encoding this knowledge as descriptive rules…
How to extract useful insights from data is always a challenge, especially if the data is multidimensional. Often, the data can be organized according to certain hierarchical structure that are stemmed either from data collection process or…
A strategy is presented to incorporate prior information from conceptual geological models in probabilistic inversion of geophysical data. The conceptual geological models are represented by multiple-point statistics training images (TIs)…
Achieving level-5 driving automation in autonomous vehicles necessitates a robust semantic visual perception system capable of parsing data from different sensors across diverse conditions. However, existing semantic perception datasets…
Statistical shape modeling (SSM) directly from 3D medical images is an underutilized tool for detecting pathology, diagnosing disease, and conducting population-level morphology analysis. Deep learning frameworks have increased the…
We introduce time-varying extremum graph (TVEG), a topological structure to support visualization and analysis of a time-varying scalar field. The extremum graph is a substructure of the Morse-Smale complex. It captures the adjacency…