Related papers: Topology-Preserving Line Densification for Creatin…

Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these…

We propose a new approach, named PolyMapper, to circumvent the conventional pixel-wise segmentation of (aerial) images and predict objects in a vector representation directly. PolyMapper directly extracts the topological map of a city from…

Inspired by cartographic generalization principles, we present a generalization technique for rendering line charts at different sizes, preserving the important semantics of the data at that display size. The algorithm automatically…

Supervised machine learning pipelines trained on features derived from persistent homology have been experimentally observed to ignore much of the information contained in a persistence diagram. Computing persistence diagrams is often the…

High-dimensional data, characterized by many features, can be difficult to visualize effectively. Dimensionality reduction techniques, such as PCA, UMAP, and t-SNE, address this challenge by projecting the data into a lower-dimensional…

Several aspects of managing a sensor network (e.g., motion planning for data mules, serial data fusion and inference) benefit once the network is linearized to a path. The linearization is often achieved by constructing a space filling…

It is challenging to directly estimate the human geometry from a single image due to the high diversity and complexity of body shapes with the various clothing styles. Most of model-based approaches are limited to predict the shape and pose…

We study crossing numbers of dense graph drawings whose vertices are uniformly distributed either on the unit sphere or in a compact convex planar domain. We prove a sharp inequality for weighted geodesic drawings on $\mathbb S^2$ in a…

High-density object counting in surveillance scenes is challenging mainly due to the drastic variation of object scales. The prevalence of deep learning has largely boosted the object counting accuracy on several benchmark datasets.…

Multi-scale tile maps are essential for geographic information services, serving as fundamental outcomes of surveying and cartographic workflows. While existing image generation networks can produce map-like outputs from remote sensing…

Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence diagrams and similar topological descriptors has yet to come.…

Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…

Transport-based density estimation methods are receiving growing interest because of their ability to efficiently generate samples from the approximated density. We further invertigate the sequential transport maps framework proposed from…

We consider the problem of establishing dense correspondences within a set of related shapes of strongly varying geometry. For such input, traditional shape matching approaches often produce unsatisfactory results. We propose an ensemble…

Spatial transcriptomics studies are becoming increasingly large and commonplace, necessitating simultaneous analysis of a large number of spatially resolved variables. Correspondingly, a diverse range of methodologies have been proposed to…

In this paper, we present an approach to enhance and improve the current normal map rendering technique. Our algorithm is based on semi-discrete Optimal Mass Transportation (OMT) theory and has a solid theoretical base. The key difference…

Creating high definition maps that contain precise information of static elements of the scene is of utmost importance for enabling self driving cars to drive safely. In this paper, we tackle the problem of drivable road boundary extraction…

Cartograms are map-based data visualizations in which the area of each map region is proportional to an associated numeric data value (e.g., population or gross domestic product). A cartogram is called contiguous if it conforms to this area…

Dimensionality reduction is an integral part of data visualization. It is a process that obtains a structure preserving low-dimensional representation of the high-dimensional data. Two common criteria can be used to achieve a dimensionality…

Persistent Homology (PH) has been successfully used to train networks to detect curvilinear structures and to improve the topological quality of their results. However, existing methods are very global and ignore the location of topological…