Related papers: Probabilistic Gradient-Based Extrema Tracking
Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…
Topological data analysis (TDA) provides a growing body of tools for computing geometric and topological information about spaces from a finite sample of points. We present a new adaptive algorithm for finding provably dense samples of…
Persistent Homology is a powerful tool in Topological Data Analysis (TDA) to capture topological properties of data succinctly at different spatial resolutions. For graphical data, shape, and structure of the neighborhood of individual data…
Topological Data Analysis (TDA), an emerging field in investment sciences, harnesses mathematical methods to extract data features based on shape, offering a promising alternative to classical portfolio selection methodologies. We utilize…
Detecting small targets at range is difficult because there is not enough spatial information present in an image sub-region containing the target to use correlation-based methods to differentiate it from dynamic confusers present in the…
In topological data analysis and visualization, topological descriptors such as persistence diagrams, merge trees, contour trees, Reeb graphs, and Morse-Smale complexes play an essential role in capturing the shape of scalar field data. We…
A wide range of data that appear in scientific experiments and simulations are multivariate or multifield in nature, consisting of multiple scalar fields. Topological feature search of such data aims to reveal important properties useful to…
Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…
This paper presents a new event-based method for detecting and tracking features from the output of an event-based camera. Unlike many tracking algorithms from the computer vision community, this process does not aim for particular…
Topological data analysis (TDA) is an active field of mathematics for quantifying shape in complex data. Standard methods in TDA such as persistent homology (PH) are typically focused on the analysis of data consisting of a single entity…
Machine learning models for repeated measurements are limited. Using topological data analysis (TDA), we present a classifier for repeated measurements which samples from the data space and builds a network graph based on the data topology.…
Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent…
This paper describes a localized algorithm for the topological simplification of scalar data, an essential pre-processing step of topological data analysis (TDA). Given a scalar field f and a selection of extrema to preserve, the proposed…
A basic issue in optimization, inverse theory,neural networks, computational chemistry and many other problems is the geometrical characterization of high dimensional functions. In inverse calculations one aims to characterize the set of…
Recently, weighted patch representation has been widely studied for alleviating the impact of background information included in bounding box to improve visual tracking results. However, existing weighted patch representation models…
We present a novel formulation of the multiple object tracking problem which integrates low and mid-level features. In particular, we formulate the tracking problem as a quadratic program coupling detections and dense point trajectories.…
Spatial relationships in multi-species data can indicate and affect system outcomes and behaviors, ranging from disease progression in cancer to coral reef resilience in ecology; therefore, quantifying these relationships is an important…
More powerful feature representations derived from deep neural networks benefit visual tracking algorithms widely. However, the lack of exploitation on temporal information prevents tracking algorithms from adapting to appearances changing…
We propose a novel method for continuous-time feature tracking in event cameras. To this end, we track features by aligning events along an estimated trajectory in space-time such that the projection on the image plane results in maximally…
This work explores a novel approach for adaptive, differentiable parametrization of large-scale non-stationary random fields. Coupled with any gradient-based algorithm, the method can be applied to variety of optimization problems,…