Related papers: Multivariate Topology Simplification
Reeb graphs are widely used in a range of fields for the purposes of analyzing and comparing complex spaces via a simpler combinatorial object. Further, they are closely related to extended persistence diagrams, which largely but not…
We unify and extend previous bijections on plane quadrangulations to bipartite and quasibipartite plane maps. Starting from a bipartite plane map with a distinguished edge and two distinguished corners (in the same face or in two different…
We present a robust method to find region-level correspondences between shapes, which are invariant to changes in geometry and applicable across multiple shape representations. We generate simplified shape graphs by jointly decomposing the…
We present a novel model for text complexity analysis which can be fitted to ordered categorical data measured on multiple scales, e.g. a corpus with binary responses mixed with a corpus with more than two ordered outcomes. The multiple…
The humble loop shrinking property played a central role in the inception of modern topology but it has been eclipsed by more abstract algebraic formalism. This is particularly true in the context of detecting relevant non-contractible…
We present an analytic approximation model for non-rigid point set registration, grounded in the multivariate Taylor expansion of vector-valued functions. By exploiting the algebraic structure of Taylor expansions, we construct a structured…
Contour trees offer an abstract representation of the level set topology in scalar fields and are widely used in topological data analysis and visualization. However, applying contour trees to large-scale scientific datasets remains…
Graph layout is the process of creating a visual representation of a graph through a node-link diagram. Node-attribute graphs have additional data stored on the nodes which describe certain properties of the nodes called attributes. Typical…
Multiplexed imaging allows multiple cell types to be simultaneously visualised in a single tissue sample, generating unprecedented amounts of spatially-resolved, biological data. In topological data analysis, persistent homology provides…
We introduce a new "subpixel-smoothed projection" (SSP) formulation for differentiable binarization in topology optimization (TopOpt) as a drop-in replacement for previous projection schemes, which suffer from near-non-differentiability and…
A visualized graph is a powerful tool for data analysis and synthesis tasks. In this case, the task of visualization constitutes not only in displaying vertices and edges according to the graph representation, but also in ensuring that the…
The Reeb space of a generic map is the space of all connected components of preimages of the map. Reeb spaces are fundamental and useful tools in the theory of Morse functions and higher dimensional variants and their applications to…
This paper reports on a simple visual technique that boils extracting a subgraph down to two operations---pivots and filters---that is agnostic to both the data abstraction, and its visual complexity scales independent of the size of the…
We introduce the Stellar decomposition, a model for efficient topological data structures over a broad range of simplicial and cell complexes. A Stellar decomposition of a complex is a collection of regions indexing the complex's vertices…
Symplectic invariants introduced in math-ph/0702045 can be computed for an arbitrary spectral curve. For some examples of spectral curves, those invariants can solve loop equations of matrix integrals, and many problems of enumerative…
One approach to understanding complex data is to study its shape through the lens of algebraic topology. While the early development of topological data analysis focused primarily on static data, in recent years, theoretical and applied…
Reeb spaces of continuous real-valued functions on topological spaces are fundamental and strong tools in investigating the spaces. The Reeb space is the natural quotient space of the space of the domain represented by connected components…
A simply laced Dynkin diagram gives rise to a family of curves over $\mathbb{Q}$ and a coregular representation, using deformations of simple singularities and Vinberg theory respectively. Thorne has conjectured and partially proven a…
We present an innovative algorithm that simplifies the topology of a cross-field. Our algorithm works through macro-operations that allow us editing the graph of separatrices, which is extracted from a cross-field, while maintaining it…
We introduce Reeb complexes in order to capture how generators of homology flow along sections of a real valued continuous function. This intuition suggests a close relation of Reeb complexes to established methods in topological data…