Related papers: Interactive Visualization of 2-D Persistence Modul…
Persistent homology is a widely-used tool in topological data analysis (TDA) for understanding the underlying shape of complex data. By constructing a filtration of simplicial complexes from data points, it captures topological features…
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…
In this work, we propose an efficient algorithm for the calculation of the Betti matching, which can be used as a loss function to train topology aware segmentation networks. Betti matching loss builds on techniques from topological data…
The diffusion of minimally invasive, endovascular interventions motivates the development of visualization methods for complex vascular networks. We propose a planar representation of blood vessel trees which preserves the properties that…
A persistence module $M$, with coefficients in a field $\mathbb{F}$, is a finite-dimensional linear representation of an equioriented quiver of type $A_n$ or, equivalently, a graded module over the ring of polynomials $\mathbb{F}[x]$. It is…
Large-scale numerical simulations of planetary interiors require dedicated visualization algorithms that are able to efficiently extract a large amount of information in an interactive and user-friendly way. Here we present a software…
In this paper, we present Hi-D maps, a novel method for the visualization of multi-dimensional categorical data. Our work addresses the scarcity of techniques for visualizing a large number of data-dimensions in an effective and…
We present a row reduction algorithm to compute the barcode decomposition of persistence modules. This algorithm dualises the standard persistence one and clarifies the symmetry between clear and compress optimisations.
In Topological Data Analysis, a common way of quantifying the shape of data is to use a persistence diagram (PD). PDs are multisets of points in $\mathbb{R}^2$ computed using tools of algebraic topology. However, this multi-set structure…
Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and…
The complexity of modern Just-In-Time (JIT) compiler optimization poses significant challenges for developers seeking to understand and debug intermediate representation (IR) behavior. This work introduces JITScope, an interactive…
A robust evaluation toolset has been designed for Naval Research Laboratory's Real-Time Ocean Forecasting System RELO with the purpose of facilitating an adaptive sampling strategy and providing more educated guidance for routing underwater…
Material node graphs are programs that generate the 2D channels of procedural materials, including geometry such as roughness and displacement maps, and reflectance such as albedo and conductivity maps. They are essential in computer…
The past few years have witnessed vibrant efforts in discovering new two-dimensional (2D) semiconductor materials from both academia and the industry, due to their promising potential in resolving the severe performance deterioration of…
We present vivid, an R package for visualizing variable importance and variable interactions in machine learning models. The package provides a range of displays including heatmap and graph-based displays for viewing variable importance and…
Vision Transformers (ViTs) have established new performance benchmarks in vision tasks such as image recognition and object detection. However, these advancements come with significant demands for memory and computational resources,…
In persistent homology analysis, interval modules play a central role in describing the birth and death of topological features across a filtration. In this work, we extend this setting, and propose the use of bipath persistent homology,…
Advanced manufacturing creates increasingly complex objects with material compositions that are often difficult to characterize by a single modality. Our collaborating domain scientists are going beyond traditional methods by employing both…
Several visualization schemes have been developed for imaging materials at the atomic level through atom probe tomography. The main shortcoming of these tools is their inability to parallel process data using multi-core computing units to…
Pursuing a continuous visual representation that offers flexible frequency modulation and fast rendering speed has recently garnered increasing attention in the fields of 3D vision and graphics. However, existing representations often rely…