Related papers: Topology-Preserving Line Densification for Creatin…
Existing auto-regressive mesh generation approaches suffer from ineffective topology preservation, which is crucial for practical applications. This limitation stems from previous mesh tokenization methods treating meshes as simple…
Multidimensional Projection is a fundamental tool for high-dimensional data analytics and visualization. With very few exceptions, projection techniques are designed to map data from a high-dimensional space to a visual space so as to…
This article presents a novel approach to identifying and classifying intersections for semantic and topological mapping. More specifically, the proposed novel approach has the merit of generating a semantically meaningful map containing…
We present a novel methodology that combines graph and dense segmentation techniques by jointly learning both point and pixel contour representations, thereby leveraging the benefits of each approach. This addresses deficiencies in typical…
Mapping is one of the crucial tasks enabling autonomous navigation of a mobile robot. Conventional mapping methods output a dense geometric map representation, e.g. an occupancy grid, which is not trivial to keep consistent for prolonged…
Cartograms combine statistical and geographical information in thematic maps, where areas of geographical regions (e.g., countries, states) are scaled in proportion to some statistic (e.g., population, income). Cartograms make it possible…
We present an algorithm for creating contiguous cartograms using meshes. We use numerical optimization to minimize cartographic error and distortion by transforming the mesh vertices. The vertices can either be optimized in the plane or…
We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The…
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…
We introduce a linear dimensionality reduction technique preserving topological features via persistent homology. The method is designed to find linear projection $L$ which preserves the persistent diagram of a point cloud $\mathbb{X}$ via…
Persistent homology is an effective method for extracting topological information, represented as persistent diagrams, of spatial structure data. Hence it is well-suited for the study of protein structures. Attempts to incorporate…
Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly…
Let $G$ be a simple topological graph and let $\Gamma$ be a polyline drawing of $G$. We say that $\Gamma$ \emph{partially preserves the topology} of $G$ if it has the same external boundary, the same rotation system, and the same set of…
Density-equalizing maps are a class of mapping methods in which the shape deformation is driven by prescribed density information. In recent years, they have been widely used for data visualization on planar domains and planar…
Line-based density plots are used to reduce visual clutter in line charts with a multitude of individual lines. However, these traditional density plots are often perceived ambiguously, which obstructs the user's identification of…
We present a method for computing the topological entropy of one-dimensional maps. As an approximation scheme, the algorithm converges rapidly and provides both upper and lower bounds.
Street intersection counts and densities are ubiquitous measures in transport geography and planning. However, typical street network data and typical street network analysis tools can substantially overcount them. This article explains the…
Regionalization is the task of dividing up a landscape into homogeneous patches with similar properties. Although this task has a wide range of applications, it has two notable challenges. First, it is assumed that the resulting regions are…
The density-equalizing map, a technique developed for cartogram creation, has been widely applied to data visualization but only for 2D applications. In this work, we propose a novel method called the volumetric density-equalizing reference…
We present in this paper a framework which leverages the underlying topology of a data set, in order to produce appropriate coordinate representations. In particular, we show how to construct maps to real and complex projective spaces,…