Related papers: A Mathematical Foundation for the Spatial Uncertai…
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…
We study computing geometric problems on uncertain points. An uncertain point is a point that does not have a fixed location, but rather is described by a probability distribution. When these probability distributions are restricted to a…
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…
An important task in visualization is the extraction and highlighting of dominant features in data to support users in their analysis process. Topological methods are a well-known means of identifying such features in deterministic fields.…
Both the current trends in technology such as smartphones, general mobile devices, stationary sensors, and satellites as well as a new user mentality of using this technology to voluntarily share enriched location information produces a…
Uncertainty quantification is a primary challenge for reliable modeling and simulation of complex stochastic dynamics. Such problems are typically plagued with incomplete information that may enter as uncertainty in the model parameters, or…
In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map…
Advances in architectural design, data availability, and compute have driven remarkable progress in semantic segmentation. Yet, these models often rely on relaxed Bayesian assumptions, omitting critical uncertainty information needed for…
Spatial statistics is concerned with the analysis of data that have spatial locations associated with them, and those locations are used to model statistical dependence between the data. The spatial data are treated as a single realisation…
Whenever eye movements are measured, a central part of the analysis has to do with where subjects fixate, and why they fixated where they fixated. To a first approximation, a set of fixations can be viewed as a set of points in space: this…
Computing mountain passes is a standard way of finding critical points. We describe a numerical method for finding critical points that is convergent in the nonsmooth case and locally superlinearly convergent in the smooth finite…
Spatial confounding is a persistent challenge in spatial statistics, influencing the validity of statistical inference in models that analyze spatially-structured data. The concept has been interpreted in various ways but is broadly defined…
Nearly all spatial reasoning problems involve uncertainty of one sort or another. Uncertainty arises due to the inaccuracies of sensors used in measuring distances and angles. We refer to this as directional uncertainty. Uncertainty also…
This paper investigates methods for estimating uncertainty in semantic segmentation predictions derived from satellite imagery. Estimating uncertainty for segmentation presents unique challenges compared to standard image classification,…
Spatial dynamic microsimulations probabilistically project geographically referenced units with individual characteristics over time. Like any projection method, their outcomes are inherently uncertain and sensitive to multiple factors.…
Location data is inherently uncertain for many reasons including 1) imprecise location measurements, 2) obsolete observations that are often interpolated, and 3) deliberate obfuscation to preserve location privacy. What makes handling…
Critical points of an invariant function may or may not be symmetric. We prove, however, that if a symmetric critical point exists, those adjacent to it are generically symmetry breaking. This mathematical mechanism is shown to carry…
Prompted by modern technologies in data acquisition, the statistical analysis of spatially distributed function-valued quantities has attracted a lot of attention in recent years. In particular, combinations of functional variables and…
Measuring uncertainties in the output of a deep learning method is useful in several ways, such as in assisting with interpretation of the outputs, helping build confidence with end users, and for improving the training and performance of…
In statistical and nonlinear systems, two qualitatively distinct parameter regions are typically identified: the regular region, characterized by smooth behavior of key quantities, and the critical region, where these quantities exhibit…